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Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and...
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Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 August 2023) | Viewed by 62103

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Dr. Shujin Laima

E-Mail Website
Guest Editor
School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, China
Interests: numerical simulation in fluid dynamics; wind engineering; bridge engineering; fluid mechanics; fluid-structrure interaction; machine learning
Special Issues, Collections and Topics in MDPI journals
Dr. Yong Cao

E-Mail Website
Guest Editor
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Interests: computational fluid dynamics; turbulence simulation; bluff-body aerodynamics; separated flow; wind engineering
Special Issues, Collections and Topics in MDPI journals
Dr. Xiaowei Jin

E-Mail Website
Guest Editor
School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China
Interests: bluff body aerodynamics; data-driven modeling for fluid mechanics; physics-informed machine learning for scientific computing
Special Issues, Collections and Topics in MDPI journals
Dr. Hehe Ren

E-Mail Website
Guest Editor
Department of Civil and Airport Engineering, School of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Interests: multi-scale wind field simulation methods; high-resolution typhoon numerical simulation and physical mechanism analysis; airport engineering and offshore wind turbine disaster prevention and mitigation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical modeling and numerical solutions are the mainstream way to represent and predict the complex scientific and engineering problems nowadays, leading to the analysis and design of engineering products and systems. It is significantly supported by the fast development of advanced numerical methods and high-performance computers. The computer methods include mathematical models and numerical algorithms related to finite element, finite difference, finite volume, and meshless discretization method. In addition to the traditional methods, artificial intelligence technology is rapidly popularized in the wide fields of science and engineering, and has enormous potential for solution of the complex physical problems.

This Special Issue intends to collect advances in development and use of mathematical models and numerical methods for the solution of problems in engineering and the sciences. The range of appropriate contributions is very wide, and includes papers on the mathematical modeling and numerical simulations in all aspects of mechanics, including solid (structures), fluids, and multiphysics. The novel mathematical models and computational methods based on finite volume, finite element, finite difference, meshless discretization methods, artificial intelligence, parallel computing, as well as probabilistic and stochastic approaches are also useful for this Special Issue.

Prof. Dr. Shujin Laima
Prof. Dr. Yong Cao
Dr. Xiaowei Jin
Dr. Hehe Ren
Guest Editors

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Keywords

  • mathematical modeling
  • numerical simulation
  • mechanics
  • engineering
  • finite element method
  • computer fluid dynamics
  • machine learning
  • reduced order modelling
  • inverse problems

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Published Papers (28 papers)

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Research

16 pages, 2443 KiB  
Article
Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space
by Dachang Zhu, Yonglong He, Xuezhe Yu and Fangyi Li
Mathematics 2023, 11(21), 4509; https://doi.org/10.3390/math11214509 - 1 Nov 2023
Cited by 3 | Viewed by 2245
Abstract
Delta parallel robots have been widely used in precision processing, handling, sorting, and the assembly of parts, and their high efficiency and motion stability are important indexes of their performance.Corners created by small line segments in trajectory planning cause abrupt changes in a [...] Read more.
Delta parallel robots have been widely used in precision processing, handling, sorting, and the assembly of parts, and their high efficiency and motion stability are important indexes of their performance.Corners created by small line segments in trajectory planning cause abrupt changes in a tangential discontinuous trajectory, and the vibration and shock caused by such changes seriously affect the robot’s high-speed and high-precision performance. In this study, a trajectory-planning method combining Cartesian space and joint space is proposed. Firstly, the vector method and microelement integration method were used to establish the complete kinematic and dynamic equations of a delta parallel robot, and an inverse kinematic/dynamic model-solving program was written based on the MATLAB software R2020a. Secondly, the end-effector trajectory of the delta parallel robot was planned in Cartesian space, and the data points and inverse control points of the end effector’s trajectory were obtained using the normalization method. Finally, the data points and control points were mapped to the joint space through the inverse kinematic equation, and the fifth-order B-spline curve was adopted for quadratic trajectory planning, which allowed the high-order continuous smoothing of the trajectory planning to be realized. The simulated and experimental results showed that the trajectory-smoothing performance in continuous high-order curvature changes could be improved with the proposed method. The peak trajectory tracking error was reduced by 10.53%, 41.18%, and 44.44%, respectively, and the peak torque change of the three joints was reduced by 3.5%, 11.6%, and 1.6%, respectively. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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18 pages, 1240 KiB  
Article
A Hybrid Large Eddy Simulation Algorithm Based on the Implicit Domain Decomposition
by Amir E. Fard and Sergey Utyuzhnikov
Mathematics 2023, 11(20), 4340; https://doi.org/10.3390/math11204340 - 19 Oct 2023
Viewed by 1216
Abstract
The resolution of small near-wall eddies encountered in high-Reynolds number flows using large eddy simulation (LES) requires very fine meshes that may be computationally prohibitive. As a result, the use of wall-modeled LES as an alternative is becoming more popular. In this paper, [...] Read more.
The resolution of small near-wall eddies encountered in high-Reynolds number flows using large eddy simulation (LES) requires very fine meshes that may be computationally prohibitive. As a result, the use of wall-modeled LES as an alternative is becoming more popular. In this paper, the near-wall domain decomposition (NDD) approach that was originally developed for Reynolds-averaged Navier–Stokes simulations (RANSs) is extended to the hybrid RANS/LES zonal decomposition. The algorithm is implemented in two stages. First, the solution is computed everywhere with LES on a coarse grid using a new non-local slip boundary condition for the instantaneous velocity at the wall. The solution is then recomputed in the near-wall region with RANS. The slip boundary conditions used in the first stage guarantee that the composite solution is smooth at the inner/outer region interface. Another advantage of the model is that the turbulent viscosity in the inner region is computed based on the corresponding RANS velocity. This shows improvement over those hybrid models that have only one velocity field in the whole domain obtained from LES. The model is realized in the open source code OpenFOAM with different approximations of turbulent viscosity and is applied to the planar channel flow at frictional Reynolds numbers of Reτ=950, 2000, and 4200. Mean streamwise velocity and Reynolds stress intensities are predicted reasonably well in comparison to the solutions obtained with unresolved LES and available DNS benchmarks. No additional forcing at the interface is required, while the log–layer mismatch is essentially reduced in all cases. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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20 pages, 6990 KiB  
Article
An Improved Incremental Procedure for the Ground Reaction Based on Hoek-Brown Failure Criterion in the Tunnel Convergence-Confinement Method
by Yu-Lin Lee, Chi-Huang Ma and Chi-Min Lee
Mathematics 2023, 11(15), 3389; https://doi.org/10.3390/math11153389 - 3 Aug 2023
Cited by 2 | Viewed by 1470
Abstract
The purpose of this study is to introduce the Hoek–Brown nonlinear failure criterion into the convergence–confinement method (CCM), which is based on the linear failure criterion, and implant it into the ground reaction curve (GRC) in this theory. Based on consistent and rigorous [...] Read more.
The purpose of this study is to introduce the Hoek–Brown nonlinear failure criterion into the convergence–confinement method (CCM), which is based on the linear failure criterion, and implant it into the ground reaction curve (GRC) in this theory. Based on consistent and rigorous theoretical analysis and according to the mechanical relationships, the principle of equilibrium, the material constitutive law, and the strain/displacement compatibility equation are used to deduce the closed-form analytical solution of the stress/displacement of the rock mass in the plastic region and to complete the simulation and interpretation of the nonlinear behavior of surrounding rock due to the advancing excavation of a circular tunnel. In this paper, confinement loss is regarded as the concept of increment in numerical analysis, and the calculation process and analysis steps of the explicit analysis method (EAM) are proposed. This method can not only realize the calculation of analytical solutions but can also be performed using simple spreadsheets. In addition, to verify the feasibility of this calculation method, this study uses published data to verify the validity of the analytical solution implemented by the incremental procedure and to study the influence of nonlinear failure criteria on the GRC, especially the mechanical behavior at the intrados of the tunnel and the distributions of tress/displacement on the cross-section of the tunnel. A comparison between the published results and the proposed solution in this study reveals consistent and favorable trends. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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23 pages, 10334 KiB  
Article
Numerical Simulation of Long-Span Bridge Response under Downburst: Parameter Optimization Using a Surrogate Model
by Yu Feng, Lingfeng Xin, Jianming Hao, Nan Ding and Feng Wang
Mathematics 2023, 11(14), 3150; https://doi.org/10.3390/math11143150 - 17 Jul 2023
Cited by 1 | Viewed by 1373
Abstract
Long-span bridges located in thunderstorm-prone areas can potentially be struck by downburst transient winds. In this study, the downburst time-varying mean wind was simulated by an impinging jet model based on computational fluid dynamics (CFD). To make the simulation results fit well with [...] Read more.
Long-span bridges located in thunderstorm-prone areas can potentially be struck by downburst transient winds. In this study, the downburst time-varying mean wind was simulated by an impinging jet model based on computational fluid dynamics (CFD). To make the simulation results fit well with the measurements, a parameter optimization method was developed. The objective function was established based on the errors between the simulated characteristic points and the target values from the measurement data. To increase the effectiveness, a Kriging surrogate model that was trained using data from numerical simulations was used. The parameter optimization method and the Kriging model were verified using five groups of test samples. The optimization efficiency was significantly increased by replacing the numerical model with a surrogate model during the optimization iteration. The simulation accuracy was clearly improved by the numerical modeling of a downburst based on optimized parameters. Subsequently, the nonstationary turbulent downburst wind was obtained by the combination of the Hilbert-based nonstationary fluctuations and the CFD-based time-varying trend. Finally, the dynamic response of a long-span bridge subjected to the moving downburst was presented. The results based on the simulation validate the optimized downburst wind field and highlight the significant influence on the bridge’s aerodynamics and buffeting response. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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21 pages, 4527 KiB  
Article
A Continuum Damage-Based Anisotropic Hyperelastic Fatigue Model for Short Glass Fiber Reinforced Polyamide 66
by Elouni Chebbi, Lotfi Ben Said, Badreddine Ayadi and Fakhreddine Dammak
Mathematics 2023, 11(6), 1508; https://doi.org/10.3390/math11061508 - 20 Mar 2023
Viewed by 1652
Abstract
A phenomenological 3D anisotropic nonlinear fatigue damage model has been developed for a short glass fiber-reinforced polyamide. The model is formulated within the framework of continuum damage mechanics and is based on a proposed anisotropic hyperelastic strain energy function. The proposed model accounts [...] Read more.
A phenomenological 3D anisotropic nonlinear fatigue damage model has been developed for a short glass fiber-reinforced polyamide. The model is formulated within the framework of continuum damage mechanics and is based on a proposed anisotropic hyperelastic strain energy function. The proposed model accounts for the effects of fiber content and nonlinear material behavior. The mechanical behavior of polyamide reinforced with 20% and 30% wt short glass fiber has been experimentally investigated under quasi-static and fatigue loading. Fatigue tests under bending loading are carried out on rectangular specimens cut in the parallel and perpendicular direction to the mold flow direction. The proposed fatigue damage model allows predicting the fatigue damage of composite materials reinforced with short fiberglass, considering fiber orientation and fiber content. The model is used to predict the damage evolution and the number of cycles to failure, and good agreement between predicted values and experimental data is observed. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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16 pages, 1795 KiB  
Article
The Use of Trigonometric Series for the Study of Isotropic Beam Deflection
by Adrian Ioan Botean
Mathematics 2023, 11(6), 1426; https://doi.org/10.3390/math11061426 - 15 Mar 2023
Cited by 1 | Viewed by 1444
Abstract
The average deformed fiber is a continuous and smooth function of the fourth order. The deflection and rotation of beams can be determined by various methods available in the literature. Thus, in this paper, the expression of the average deformed fiber is defined [...] Read more.
The average deformed fiber is a continuous and smooth function of the fourth order. The deflection and rotation of beams can be determined by various methods available in the literature. Thus, in this paper, the expression of the average deformed fiber is defined in advance, then it is considered an infinite sum of sinusoidal functions that are successively evaluated using sinusoidal trigonometric series if it is considered a periodic function, or using Fourier series if it is considered a non-periodic function. The method is examined by solving several beam problems. The results indicate that the method can be used with confidence for solving any bending beam problem. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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14 pages, 698 KiB  
Article
Faults Modeling in Networked Environment and Its Tolerant Control with Multiple Simultaneous Faults
by Atif Mahmood, Abdul Qayyum Khan, Nasim Ullah, Adil Sarwar Khan, Muhammad Asim Abbasi, Alsharef Mohammad and Abdulfattah Noorwali
Mathematics 2023, 11(4), 996; https://doi.org/10.3390/math11040996 - 15 Feb 2023
Viewed by 1476
Abstract
This paper presents two new fault models for networked systems. These fault models are more realistic and generalized for networked systems in the sense that they can represent the effects of fault at the node and network levels. At the network layer, the [...] Read more.
This paper presents two new fault models for networked systems. These fault models are more realistic and generalized for networked systems in the sense that they can represent the effects of fault at the node and network levels. At the network layer, the uncertain effects of the network lines are modeled using a Markov chain with complex transition probabilities simultaneously with the stochastic behavior of the network using a Bernoulli process. A new output feedback-based controller, which is two-mode dependent and considers network uncertainties and output measurements for gain calculation, is presented. Using the tools of robust control and stochastic stability, linear matrix inequality-based sufficient conditions are derived. The proposed controller successfully maintains the system’s performance by tolerating the effects of simultaneous sensor and actuator faults, ensuring the stability of networked loops. Simulation results verify the applicability of the presented fault-tolerant control against multiple simultaneous faults. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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16 pages, 3275 KiB  
Article
Analytical and Numerical Model of Sloshing in a Rectangular Tank Subjected to a Braking
by Oana-Maria Balaş, Cristian Vasile Doicin and Elena Corina Cipu
Mathematics 2023, 11(4), 949; https://doi.org/10.3390/math11040949 - 13 Feb 2023
Cited by 1 | Viewed by 1683
Abstract
This paper examines the movement of waves that occur in a fuel tank—both with and without a wave breaker—when a car is travelling at a constant speed and then suddenly brakes. This phenomenon is known as slosh noise, and the paper presents an [...] Read more.
This paper examines the movement of waves that occur in a fuel tank—both with and without a wave breaker—when a car is travelling at a constant speed and then suddenly brakes. This phenomenon is known as slosh noise, and the paper presents an analysis of the movement of free surfaces in relation to the level of noise generated. The paper focuses on mathematical models of the fluid flow for both tanks—one without any technical solutions for breaking waves, and the other with a solution for breaking waves. The model is constructed based on a set of initial hypotheses about the fluid flow within the tank, by developing the speed potential in a series of fundamental solutions and considering the main variables that affect the phenomenon of sloshing, such as the depth of the liquid, the tank’s geometry, and the frequency and amplitude of the initial external force acting on the tank. The analysis of free surface movement is used to find the correlation with the sound generated in the tank. Nonlinearities that arise from the sudden braking are also modelled and numerically studied using MATLAB software. Following the mathematical model, a technical wave-breaking solution was implemented and tested, and it was shown that the amplitude of the movement of the free surface is reduced by half. Further research on the correspondence between the free surface movement based on the behaviour of potential energies in the two cases may be developed. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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13 pages, 2541 KiB  
Article
Design Optimisation of Bi-Cruciate Retaining Total Knee Arthroplasty (TKA) Prosthesis via Taguchi Methods
by Natrisya Qistina Mohd Mukhtar, Solehuddin Shuib, Muhamad Azhan Anuar, Mohd Fairudz Mohd Miswan and Mohd Afzan Mohd Anuar
Mathematics 2023, 11(2), 312; https://doi.org/10.3390/math11020312 - 7 Jan 2023
Cited by 2 | Viewed by 2965
Abstract
Total knee replacement has become a viable option for treating severe knee arthritis. The demand for more kinematically functional implants that better replicate natural knee kinematics led to the development of total knee arthroplasty (TKA), including bi-cruciate-retaining (BCR) TKA. However, optimised design parameters [...] Read more.
Total knee replacement has become a viable option for treating severe knee arthritis. The demand for more kinematically functional implants that better replicate natural knee kinematics led to the development of total knee arthroplasty (TKA), including bi-cruciate-retaining (BCR) TKA. However, optimised design parameters of BCR TKA knee implants that can help achieve a long-term prosthetic survival rate remain unknown. Therefore, this study aimed to investigate the effect of the design parameters of BCR TKA knee implants on the mechanics of knee joints and optimise and individualise the knee implant design parameters using the Taguchi method incorporating finite element analysis. Herein, experimental factors and levels were selected and nine finite element models of BCR TKA knee implants were developed to optimise the design of the following parameters: the curvature ratio on the sagittal plane, curvature ratio on the coronal plane, and tibial slope. In addition, finite element analysis was used to determine the effect of the design parameters on the peak contact stress on ultra-high-molecular-weight polyethylene (UHMWPE) and its deformation. Consequently, among the three parameters that affect the peak contact stress and its deformation, the curvature ratio on the sagittal plane had the greatest effect (range = 10.96), followed by the curvature ratio on the coronal plane (range = 3.54), and the tibial slope (range = 2.56). The optimal design parameters for the BCR TKA knee implant were a curvature ratio of 1.5 on both the sagittal and coronal planes and a tibial slope of 5°. Under these conditions, the peak contact stress and deformation were 25.80 MPa and 0.0835 mm, respectively. The optimisation method based on finite element analysis and the Taguchi method can produce one of the highest-performing BCR TKA knee implant designs, thereby reducing the peak contact stress and deformation. This method sheds fresh light on the development of the BCR TKA knee implant as well as biomechanical decision-making to implant the TKA prosthesis correctly. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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16 pages, 7119 KiB  
Article
Numerical Formulation of Anisotropic Elastoplastic Behavior Coupled with Damage Model in Forming Processes
by Lotfi Ben Said, Marwa Allouch, Mondher Wali and Fakhreddine Dammak
Mathematics 2023, 11(1), 204; https://doi.org/10.3390/math11010204 - 30 Dec 2022
Cited by 7 | Viewed by 1685
Abstract
The present paper proposes a mathematical development of the plasticity and damage approaches to simulate sheet metal forming processes. It focuses on the numerical prediction of the deformation of the sheet metal during the deep drawing process when a crack appears. Anisotropic plasticity [...] Read more.
The present paper proposes a mathematical development of the plasticity and damage approaches to simulate sheet metal forming processes. It focuses on the numerical prediction of the deformation of the sheet metal during the deep drawing process when a crack appears. Anisotropic plasticity constitutive equations are proposed. A fully implicit integration of the coupling constitutive equations is used and leads to two nonlinear local scalar equations that are solved by Newton’s method. The developed model allows predicting the onset of cracks in sheet metals during cold forming operations. The numerical model is implemented in ABAQUS software using user-defined subroutines, which are VUMAT and UMAT. The accuracy of the anisotropic elastoplastic model fully coupled with ductile damage is evaluated using numerical examples. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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26 pages, 676 KiB  
Article
Numerical Analysis of Fourier Finite Volume Element Method for Dirichlet Boundary Optimal Control Problems Governed by Elliptic PDEs on Complex Connected Domains
by Mengya Su, Liuqing Xie and Zhiyue Zhang
Mathematics 2022, 10(24), 4779; https://doi.org/10.3390/math10244779 - 15 Dec 2022
Cited by 1 | Viewed by 1670
Abstract
In this research, we investigate an optimal control problem governed by elliptic PDEs with Dirichlet boundary conditions on complex connected domains, which can be utilized to model the cooling process of concrete dam pouring. A new convergence result for two-dimensional Dirichlet boundary control [...] Read more.
In this research, we investigate an optimal control problem governed by elliptic PDEs with Dirichlet boundary conditions on complex connected domains, which can be utilized to model the cooling process of concrete dam pouring. A new convergence result for two-dimensional Dirichlet boundary control is proven with the Fourier finite volume element method. The Lagrange multiplier approach is employed to find the optimality systems of the Dirichlet boundary optimal control problem. The discrete optimal control problem is then obtained by applying the Fourier finite volume element method based on Galerkin variational formulation for optimality systems, that is, using Fourier expansion in the azimuthal direction and the finite volume element method in the radial direction, respectively. In this way, the original two-dimensional problem is reduced to a sequence of one-dimensional problems, with the Dirichlet boundary acting as an interval endpoint at which a quadratic interpolation scheme can be implemented. The convergence order of state, adjoint state, and Dirichlet boundary control are therefore proved. The effectiveness of the method is demonstrated numerically, and numerical data is provided to support the theoretical analysis. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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22 pages, 8998 KiB  
Article
The Effect of Diameter and Position of Transverse Cylindrical Vortex Generators on Heat Transfer Improvement in a Wavy Channel
by Stanislav Kotšmíd and Zuzana Brodnianská
Mathematics 2022, 10(23), 4546; https://doi.org/10.3390/math10234546 - 1 Dec 2022
Cited by 1 | Viewed by 1360
Abstract
The present study investigates the effect of outer diameter (10 mm and 15 mm) and 5 positions of cylindrical vortex generators (CVGs) installed to the wavy channel in order to improve heat transfer parameters in conjunction with low-pressure drops. The wavy channels with [...] Read more.
The present study investigates the effect of outer diameter (10 mm and 15 mm) and 5 positions of cylindrical vortex generators (CVGs) installed to the wavy channel in order to improve heat transfer parameters in conjunction with low-pressure drops. The wavy channels with and without CVGs are compared in terms of the local heat transfer coefficient, mean Nusselt number, Colburn factor, friction, and thermal performance for Re in the range of 857 to 8001. Furthermore, the effect of the cooling air flow direction (forward and backward) is assessed. Inserting the CVGs to the channel causes the enhancement of Nusselt numbers and Colburn factors for all CVGs positions and Re in comparison with the channels without CVGs. The maximum thermal performance factor TPFB = 0.8229 was achieved for the channel with CVGs position ‘5’ and 15 mm diameter, backward air flow, and Re = 1677. The backward air flow is more efficient compared with forward air flow since the cooling air gets into the valleys to a greater extent, and thus, better mixing of the fluid occurs. The numerical investigation, conducted with Ansys Fluent software, is compared with the experimental one acquired by holographic interferometry at good agreement of the local heat transfer coefficients. Finally, new correlating equations for the mean Nusselt number were created. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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19 pages, 6434 KiB  
Article
Interaction of Variable Fluid Properties with Electrokinetically Modulated Peristaltic Flow of Reactive Nanofluid: A Thermodynamical Analysis
by Yasir Akbar, Shiping Huang and Hammad Alotaibi
Mathematics 2022, 10(23), 4452; https://doi.org/10.3390/math10234452 - 25 Nov 2022
Cited by 2 | Viewed by 1492
Abstract
In the present study, the interaction of variable fluid properties with electrokinetically regulated peristaltic transportation of a reactive nanofluid embedded in a porous space is studied. The nanofluid saturates the porous space/medium with inhomogeneous porosity, which changes with distance from the channel boundary. [...] Read more.
In the present study, the interaction of variable fluid properties with electrokinetically regulated peristaltic transportation of a reactive nanofluid embedded in a porous space is studied. The nanofluid saturates the porous space/medium with inhomogeneous porosity, which changes with distance from the channel boundary. It is assumed that nanofluids are accompanied by variable thermal conductivity and viscosity. The impacts of magnetic field, Brownian motion, electric field, viscous dissipation, chemical reaction, mixed convection, and thermophoresis are incorporated. Moreover, the contribution of zero mass flux boundary condition is executed. The complexity of the equations describing the flow of a nanofluid is reduced by applying the lubrication theory. The fully non-linear equations are solved by utilizing a numerical technique. Particular attention is paid to the analysis of entropy optimization, since its minimization is the best measure to enhance the efficiency of thermal systems. These results demonstrate that a positively oriented external electric field contributes to an increase in nanofluid velocity. Temperature of nanofluid increases more rapidly due to an augmentation in Joule heating parameter. It is noticed that the temperature of water is comparatively lower than that of kerosene. The system’s energy loss can be reduced when the thermal conductivity parameter enhance. The magnitude of Bejan number is enhanced by increasing electroosmotic parameter. Further, a substantial decrement in concentration profile is perceived when the Schmidt number is augmented. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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23 pages, 6813 KiB  
Article
A Fully Coupled Thermomechanical Phase Field Method for Modeling Cracks with Frictional Contact
by Wan Wan and Pinlei Chen
Mathematics 2022, 10(23), 4416; https://doi.org/10.3390/math10234416 - 23 Nov 2022
Viewed by 2227
Abstract
In this paper, a thermomechanical coupled phase field method is developed to model cracks with frictional contact. Compared to discrete methods, the phase field method can represent arbitrary crack geometry without an explicit representation of the crack surface. The two distinguishable features of [...] Read more.
In this paper, a thermomechanical coupled phase field method is developed to model cracks with frictional contact. Compared to discrete methods, the phase field method can represent arbitrary crack geometry without an explicit representation of the crack surface. The two distinguishable features of the proposed phase field method are: (1) for the mechanical phase, no specific algorithm is needed for imposing contact constraints on the fracture surfaces; (2) for the thermal phase, formulations are proposed for incorporating the phase field damage parameter so that different thermal conductance conditions are accommodated. While the stress is updated explicitly in the regularized interface regions under different contact conditions, the thermal conductivity is determined under different conductance conditions. In particular, we consider a pressure-dependent thermal conductance model (PDM) that is fully coupled with the mechanical phase, along with the other three thermal conductance models, i.e., the fully conductive model (FCM), the adiabatic model (ACM), and the uncoupled model (UCM). The potential of this formulation is showcased by several benchmark problems. We gain insights into the role of the temperature field affecting the mechanical field. Several 2D boundary value problems are addressed, demonstrating the model’s ability to capture cracking phenomena with the effect of the thermal field. We compare our results with the discrete methods as well as other phase field methods, and a very good agreement is achieved. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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14 pages, 2044 KiB  
Article
Modern Physical-Mathematical Models and Methods for Design Surface Acoustic Wave Devices: COM Based P-Matrices and FEM in COMSOL
by Aleksey S. Koigerov
Mathematics 2022, 10(22), 4353; https://doi.org/10.3390/math10224353 - 19 Nov 2022
Cited by 8 | Viewed by 2453
Abstract
Comparative results of calculation and measurement of the frequency responses of the surface acoustic waves filter on a piezoelectric substrate of 64°YX-cut lithium niobate and delay line on a piezoelectric substrate of 128°YX-cut lithium niobate is presented. The calculation was performed on the [...] Read more.
Comparative results of calculation and measurement of the frequency responses of the surface acoustic waves filter on a piezoelectric substrate of 64°YX-cut lithium niobate and delay line on a piezoelectric substrate of 128°YX-cut lithium niobate is presented. The calculation was performed on the basis of two approaches—the finite element method in the COMSOL Multiphysics software and using the model of coupling of modes based on P-matrices. A brief overview and features of each approach are presented. The calculation results based on the two approaches are in good agreement with each other and with the experimental results of measurements of the characteristics of the bandpass filter. The delay line operating with the use of the third harmonic frequency is calculated by FEM. The results showed a good match between numerical simulation and experiment. The considered approaches for designing SAW devices allow us to relatively quickly and accurately predict the frequency responses at the simulation stage, thereby reducing the number of experimental iterations and increasing the efficiency of development. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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15 pages, 3234 KiB  
Article
Gain-Switched Short Pulse Generation from 1.55 µm InAs/InP/(113)B Quantum Dot Laser Modeled Using Multi-Population Rate Equations
by Hilal S. Duranoglu Tunc, Nuran Dogru and Erkan Cengiz
Mathematics 2022, 10(22), 4316; https://doi.org/10.3390/math10224316 - 17 Nov 2022
Cited by 2 | Viewed by 1409
Abstract
The gain-switching properties of an InAs-InP (113)B quantum dot laser based on multi-population rate equations are examined theoretically in detail to generate shorter pulses with the application of a Gaussian pulse beam to the laser excited state. The numerical results demonstrated that as [...] Read more.
The gain-switching properties of an InAs-InP (113)B quantum dot laser based on multi-population rate equations are examined theoretically in detail to generate shorter pulses with the application of a Gaussian pulse beam to the laser excited state. The numerical results demonstrated that as the homogeneous and the inhomogeneous broadening increase, the differential gain, the gain compression factor, and the threshold current of the excited state decrease while the threshold current of the ground state increases. It was also observed that the contribution of the excited state to gain-switched output pulses depend on not only the value of the inhomogeneous broadening but also the magnitude of the applied current. Additionally, it was found that without an optical beam, the output pulse has a long pulse width due to ground state emissions and the change in the parameters strongly affecting the output. However, under the optical beam, narrow pulses around 26 ps have high peak power owing to the excited state emission generated even at low currents and also the change in the laser parameters having a negligible effect. Finally, the gain-switching characteristics with and without a Gaussian pulse beam are shown to be similar for liner-gain and nonlinear-gain cases except that higher peak power and narrower output pulses are obtained for the linear-gain case. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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16 pages, 3817 KiB  
Article
Power Scheduling Optimization Method of Wind-Hydrogen Integrated Energy System Based on the Improved AUKF Algorithm
by Yong Wang, Xuan Wen, Bing Gu and Fengkai Gao
Mathematics 2022, 10(22), 4207; https://doi.org/10.3390/math10224207 - 10 Nov 2022
Cited by 38 | Viewed by 2407
Abstract
With the proposal of China’s green energy strategy, the research and development technologies of green energy such as wind energy and hydrogen energy are becoming more and more mature. However, the phenomenon of wind abandonment and anti-peak shaving characteristics of wind turbines have [...] Read more.
With the proposal of China’s green energy strategy, the research and development technologies of green energy such as wind energy and hydrogen energy are becoming more and more mature. However, the phenomenon of wind abandonment and anti-peak shaving characteristics of wind turbines have a great impact on the utilization of wind energy. Therefore, this study firstly builds a distributed wind-hydrogen hybrid energy system model, then proposes the power dispatching optimization technology of a wind-hydrogen integrated energy system. On this basis, a power allocation method based on the AUKF (adaptive unscented Kalman filter) algorithm is proposed. The experiment shows that the power allocation strategy based on the AUKF algorithm can effectively reduce the incidence of battery overcharge and overdischarge. Moreover, it can effectively deal with rapid changes in wind speed. The wind hydrogen integrated energy system proposed in this study is one of the important topics of renewable clean energy technology innovation. Its grid-connected power is stable, with good controllability, and the DC bus is more secure and stable. Compared with previous studies, the system developed in this study has effectively reduced the ratio of abandoned air and its performance is significantly better than the system with separate grid connected fans and single hydrogen energy storage. It is hoped that this research can provide some solutions for the research work on power dispatching optimization of energy systems. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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18 pages, 6425 KiB  
Article
A Novel Cam-Based Variable Stiffness Actuator: Pitch Curve Synthetic Approach for Reconfiguration Design
by Fanghua Mei, Shusheng Bi and Bianhong Li
Mathematics 2022, 10(21), 4088; https://doi.org/10.3390/math10214088 - 2 Nov 2022
Viewed by 1645
Abstract
Variable stiffness actuators (VSA) have attracted much attention because of their potential for human-like interaction behaviors. This paper devotes to improving the VSA’s versatility. VSA with different characteristics can be obtained by shape reconfiguration of its internal driving cams. The proposed VSA mainly [...] Read more.
Variable stiffness actuators (VSA) have attracted much attention because of their potential for human-like interaction behaviors. This paper devotes to improving the VSA’s versatility. VSA with different characteristics can be obtained by shape reconfiguration of its internal driving cams. The proposed VSA mainly includes a variable stiffness module and a cam-based driven module. A common node connects the two modules. It is placed in the common grooves of the dual cams. Kinematically, the radial position of the node can be changed for stiffness adjustment by cam differential motion. Mechanically, the driven force on this node can be resolved into two orthogonal directions by cam groove, one for stiffness adjustment and another for position balance., The paper establishes the analytical relationship between the pressure angle of the cam pitch curve, stiffness adjustment speed and accuracy, and load distribution. Furtherly, the pitch curve synthetic approach for VSA reconfiguration is provided. A special cam shape with a favorable load distribution is proposed to verify the method. The correctness of the design was effectively proved by experiments in the virtual model and physical prototype. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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16 pages, 4875 KiB  
Article
Numerical Method for System Level Simulation of Long-Distance Pneumatic Conveying Pipelines
by Xiaoming Zhou, Fang Fang and Yadong Li
Mathematics 2022, 10(21), 4073; https://doi.org/10.3390/math10214073 - 1 Nov 2022
Cited by 3 | Viewed by 1943
Abstract
Pneumatic conveying pipelines (PCPs) provide an effective manner for long-distance transport of capsules because of their advantages in high speed, superior safety, and full automation. For better development of PCPs, a system-level simulation tool is desired, but not yet available. In this work, [...] Read more.
Pneumatic conveying pipelines (PCPs) provide an effective manner for long-distance transport of capsules because of their advantages in high speed, superior safety, and full automation. For better development of PCPs, a system-level simulation tool is desired, but not yet available. In this work, a new 1D model describing systemic dynamics of airflow and capsule movement in PCPs is presented, and 3D simulation is proposed to obtain the characteristic coefficients in the 1D model. The complete model accounts for those phenomena that most profoundly affect the performance of PCPs, such as the 3D layout of the pipeline, the geometry of capsules, as well as the compressibility of air in a long pipeline. A finite volume method is also presented to numerically calculate the model equations, and thereby realize the successful system-level simulation of practical PCPs for the first time. Experimental data were used for validation. For a 550 m-long and small-diameter (27.86 mm) PCP, the errors of predicted conveying times were within 4.43%. For another 30 m-long and large-diameter (125.6 mm) PCP, the errors of predicted conveying time and maximum capsule velocity were within 1%. By enabling readily and accurate prediction of the conveying process, the method provides a feasible tool for the design and application of PCP systems. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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19 pages, 2164 KiB  
Article
Mathematical Modeling of the Reliability of Polymer Composite Materials
by Madina E. Isametova, Rollan Nussipali, Nikita V. Martyushev, Boris V. Malozyomov, Egor A. Efremenkov and Aysen Isametov
Mathematics 2022, 10(21), 3978; https://doi.org/10.3390/math10213978 - 26 Oct 2022
Cited by 39 | Viewed by 3086
Abstract
An urgent task in creating and using composite materials is the assessment and prediction of their performance properties and reliability. Currently, when studying the reliability of the materials, there is little experimental data, mathematical descriptions, and models for both probabilistic and deterministic methods [...] Read more.
An urgent task in creating and using composite materials is the assessment and prediction of their performance properties and reliability. Currently, when studying the reliability of the materials, there is little experimental data, mathematical descriptions, and models for both probabilistic and deterministic methods to assess reliability. Based on the obtained experimental data, this article discusses the development of a methodology for predicting reliability. The article also proposes a statistical model for assessing reliability by the criterion of the structural strength of products made of polymer composite materials. The characteristics of the reliability changes in the materials when in operation are presented. The calculation allowed obtaining graphs showing the dispersion and statistical variability of the characteristics of polypropylene-based polymeric materials at the design, production, and operation stages of the product life cycle. The computational experimental results for determining the influence of the shape of inclusions and mass on the mechanical properties of a polymer composite material aimed at improving the strength characteristics of the products are presented. Based on a computational experiment in the MSC Digimat MF nonlinear solver, equations are provided to demonstrate the regression dependence of the strength of a part made of a polymer composite material on technological factors. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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21 pages, 96542 KiB  
Article
Characterization of Blast Wave Parameters in the Detonation Locus and Near Field for Shaped Charges
by Nestor Mejía, Rodrigo Mejía and Theofilos Toulkeridis
Mathematics 2022, 10(18), 3261; https://doi.org/10.3390/math10183261 - 8 Sep 2022
Cited by 3 | Viewed by 4731
Abstract
Understanding physical phenomena such as blast shock waves produced by controlled explosions are relevant for issues appearing in the fields of military and civilian activities. The current study analyzes detonations of cylindrical and 3D cone-shaped charges through experimental trials and numerical simulations. In [...] Read more.
Understanding physical phenomena such as blast shock waves produced by controlled explosions are relevant for issues appearing in the fields of military and civilian activities. The current study analyzes detonations of cylindrical and 3D cone-shaped charges through experimental trials and numerical simulations. In order to accomplish such goals, the work is divided into three sections, which include (a) numerical studies on spherical charges to define an accurate model; (b) numerical and experimental studies to assess the influence of cylindrical and 3D cone-shaped charges on incident peak pressure and the shape of shock wave propagation; and (c) numerical studies to define the magnitude of incident peak pressure as a function of orientation, L/D aspect ratio and scaled distance. Validation studies proved that the applied model was reasonably accurate. Furthermore, relevant findings included the observation that when the L/D aspect ratio decreases, more release energy is concentrated in the axial direction for a 3D cone-shaped charge, while as the aspect ratio increases, more release energy is concentrated in the radial direction for a cylindrical-shaped charge. Additionally, the blast shock wave produced a great quantity of energy for the explosive charge with the largest surface. Finally, the orientation has less influence than the L/D aspect ratio on the incident pressure contours. Therefore, cylindrical charges have the potential of inflicting great damage when used as confined charges, and 3D charges are able to cut solid materials in case of a direct contact. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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26 pages, 5648 KiB  
Article
Machine Learning-Based Models for Shear Strength Prediction of UHPFRC Beams
by Xiangyong Ni and Kangkang Duan
Mathematics 2022, 10(16), 2918; https://doi.org/10.3390/math10162918 - 13 Aug 2022
Cited by 10 | Viewed by 2224
Abstract
Estimating shear strength is a crucial aspect of beam design. The goal of this research is to develop a shear strength calculation technique for ultra-high performance fiber reinforced concrete (UHPFRC) beams. To begin, a shear test database of 200 UHPFRC beam specimens is [...] Read more.
Estimating shear strength is a crucial aspect of beam design. The goal of this research is to develop a shear strength calculation technique for ultra-high performance fiber reinforced concrete (UHPFRC) beams. To begin, a shear test database of 200 UHPFRC beam specimens is established. Then, random forest (RF) is used to evaluate the importance of influence factors for the shear strength of UHPFRC beams. Subsequently, three machine learning (ML)-based models, including artificial neural network (ANN), support vector regression (SVR), and eXtreme-gradient boosting (XGBoost), are proposed to compute shear strength. Results demonstrate that the area of longitudinal reinforcement has the greatest influence on the shear capacity of UHPFRC beams, and ten parameters with high importance (e.g., the area of longitudinal reinforcement, the stirrup strength, the cross-section area, the shear span ratio, fiber volume fraction, etc.) are selected as input parameters. The models of ANN, SVR, and XGBoost have close accuracy, and their R2 are 0.8825, 0.9016, and 0.8839, respectively, which are much larger than those of existing theoretical models. In addition, the average ratios of prediction values of ANN, SVR, and XGBoost models to experimental results are 1.08, 1.02, and 1.10, respectively; the coefficients of variation are 0.28, 0.21, and 0.28, respectively. The SVR model has the best accuracy and reliability. The accuracy and reliability of ML-based models are much better than those of existing models for calculating the shear strength of UHPFRC beams. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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19 pages, 860 KiB  
Article
An Improved Blind Kriging Surrogate Model for Design Optimization Problems
by Hau T. Mai, Jaewook Lee, Joowon Kang, H. Nguyen-Xuan and Jaehong Lee
Mathematics 2022, 10(16), 2906; https://doi.org/10.3390/math10162906 - 12 Aug 2022
Cited by 5 | Viewed by 2811
Abstract
Surrogate modeling techniques are widely employed in solving constrained expensive black-box optimization problems. Therein, Kriging is among the most popular surrogates in which the trend function is considered as a constant mean. However, it also encounters several challenges related to capturing the overall [...] Read more.
Surrogate modeling techniques are widely employed in solving constrained expensive black-box optimization problems. Therein, Kriging is among the most popular surrogates in which the trend function is considered as a constant mean. However, it also encounters several challenges related to capturing the overall trend with a relatively limited number of function evaluations as well as searching feasible points with complex or discontinuous feasible regions. To address this above issue, this paper presents an improved surrogate blind Kriging (IBK) and a combined infill strategy to find the optimal solution. According to enhancing the prediction accuracy of metamodels of objective and constraints, the high-order effects of regression function in the blind Kriging are identified by promising a variable selection technique. In addition, an infill strategy is developed based on the probability of feasibility, penalization, and constrained expected improvement for updating blind Kriging metamodels of the objective and constraints. At each iteration, two infill sample points are allocated at the positions to achieve improvement in optimality and feasibility. The IBK metamodels are updated by the newly-added infill sample points, which leads the proposed framework search to rapidly converge to the optimal solution. The performance and applicability of the proposed model are tested on several numerical benchmark problems via comparing with other metamodel-based constrained optimization methods. The obtained results indicate that IBK generally has a greater efficiency performance and outperforms the competitors in terms of a limited number of function evaluations. Finally, IBK is successfully applied to structural design optimization. The optimization results show that IBK is able to find the best feasible design with fewer evaluation functions compared with other studies, and this demonstrates the effectiveness and practicality of the proposed model for solving the constrained expensive black-box engineering design optimization problems. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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16 pages, 698 KiB  
Article
A Hybrid Approach Based on Principal Component Analysis for Power Quality Event Classification Using Support Vector Machines
by Akash Saxena, Ahmad M. Alshamrani, Adel Fahad Alrasheedi, Khalid Abdulaziz Alnowibet and Ali Wagdy Mohamed
Mathematics 2022, 10(15), 2780; https://doi.org/10.3390/math10152780 - 5 Aug 2022
Cited by 13 | Viewed by 2166
Abstract
Power quality has emerged as a sincere denominator in the planning and operation of a power system. Various events affect the quality of power at the distribution end of the system. Detection of these events has been a major thrust area in the [...] Read more.
Power quality has emerged as a sincere denominator in the planning and operation of a power system. Various events affect the quality of power at the distribution end of the system. Detection of these events has been a major thrust area in the last decade. This paper presents the application of Support Vector Machine (SVM) in classifying the power quality events. Well-known signal processing techniques, namely Hilbert transform and Wavelet transform, are employed to extract the potential features from the observation sets of voltages. Supervised architecture consisting of SVM has been constructed by tuning the parameters of SVM by various algorithms. It has been observed that Augmented Crow Search Algorithm (ACSA) yields the best accuracy compared to other contemporary optimizers. Further, Principal Component Analysis (PCA) is employed to choose the most significant features from the available features. On the basis of PCA, three different models of tuned SVMs are constructed. Comparative analysis of these three models, along with recently published approaches, is exhibited. Results are validated by the statistical one-way analysis of variance (ANOVA) method. It is observed that SVM, which contains attributes from both signal-processing techniques, gives satisfactory results. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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40 pages, 11938 KiB  
Article
Output Power Control and Load Mitigation of a Horizontal Axis Wind Turbine with a Fully Coupled Aeroelastic Model: Novel Sliding Mode Perspective
by Hongfu Zhang, Jiahao Wen, Farshad Golnary and Lei Zhou
Mathematics 2022, 10(15), 2735; https://doi.org/10.3390/math10152735 - 2 Aug 2022
Viewed by 1909
Abstract
The power control of horizontal axis wind turbines can affect significantly the vibration loads and fatigue life of the tower and the blades. In this paper, we both consider the power control and vibration load mitigation of the tower fore-aft vibration. For this [...] Read more.
The power control of horizontal axis wind turbines can affect significantly the vibration loads and fatigue life of the tower and the blades. In this paper, we both consider the power control and vibration load mitigation of the tower fore-aft vibration. For this purpose, at first, we developed a fully coupled model of the NREL 5MW turbine. This model considers the full aeroelastic behaviour of the blades and tower and is validated by experiment results, comparing the time history data with the FAST (Fatigue, Aerodynamics, Structures, and Turbulence) code which is developed by NREL (National Renewable Energy Lab in the United States). In the next, novel sensorless control algorithms are developed based on the supper twisting sliding mode control theory and sliding mode observer for disturbance rejection. In region II (the wind speed is between the cut-in and rated wind velocity), the novel sensorless control algorithm increased the power coefficient in comparison to the conventional indirect speed control (ISC) method (the conventional method in the industry). In region III (the wind speed is between the rated and cut-out speed), an adaptive neural fuzzy inference system (ANFIS) is developed to estimate pitch sensitivity. The rotor speed, pitch angle, and effective wind velocity are inputs, and pitch sensitivity is the output. The designed novel pitch control performance is compared with the gain scheduled PI (GPI) method (the conventional approach in this region). The simulation results demonstrate that the flapwise blade displacement is reduced significantly. Finally, to reduce the fore-aft vibration of the tower, a tuned mass damper (TMD) was designed by using the genetic algorithm and the fully coupled model. In comparison to the literature body, we demonstrate that the fully coupled model provides much better accuracy in comparison to the uncoupled model to estimate the vibration loads. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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13 pages, 1047 KiB  
Article
Micropolar Dusty Fluid: Coriolis Force Effects on Dynamics of MHD Rotating Fluid When Lorentz Force Is Significant
by Quanfu Lou, Bagh Ali, Saif Ur Rehman, Danial Habib, Sohaib Abdal, Nehad Ali Shah and Jae Dong Chung
Mathematics 2022, 10(15), 2630; https://doi.org/10.3390/math10152630 - 27 Jul 2022
Cited by 76 | Viewed by 2754
Abstract
The main objective of this investigation to examine the momentum and thermal transportation of rotating dusty micropolar fluid flux with suspension of conducting dust particles across the stretched sheet. The novelty of the flow model is the exploration of the significance of boosting [...] Read more.
The main objective of this investigation to examine the momentum and thermal transportation of rotating dusty micropolar fluid flux with suspension of conducting dust particles across the stretched sheet. The novelty of the flow model is the exploration of the significance of boosting the volume concentration of dust particles in fluid dynamics. The governing PDEs of the problem for both phase models are transmuted into nonlinear coupled non-dimensional ODEs by utilizing suitable similarity modifications. The bvp4c technique was utilized in MATLAB script to acquire a graphical representation of the experimental results. This study illustrates the analysis of repercussions of pertinent parameters on non-Newtonian fluid and the dusty phase of fluid. By improving the volume concentration of dust particles and rotating parameters, the axial velocity for both phases depreciates, whereas temperature and transverse velocity for both phases have the opposite behavior. The micro-rotation distribution rises with higher contributions of rotating and material parameters, whereas it decreases against larger inputs of volume concentration of dust particles. The growing strength of the dust volume fraction (ϕd) caused the coefficient of skin friction to decrease along the x direction, and the skin friction coefficient is raised along the y direction. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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18 pages, 2193 KiB  
Article
Theoretical Study of the Static and Dynamic Characteristics of a Slotted Adaptive Hydrostatic Thrust Bearing with a Regulator of the Lubricant Output Flow
by Vladimir Kodnyanko, Andrey Kurzakov, Alexey Surovtsev, Lilia Strok, Olga Grigorieva, Maxim Brungardt, Svetlana Belyakova and Ludmila Gogol
Mathematics 2022, 10(3), 355; https://doi.org/10.3390/math10030355 - 24 Jan 2022
Viewed by 2192
Abstract
This manuscript considers the design of a slotted adaptive hydrostatic thrust bearing with a regulator of the lubricant output flow. A theoretical study of its static and dynamic characteristics was carried out. The aim of the study was to test the reliability of [...] Read more.
This manuscript considers the design of a slotted adaptive hydrostatic thrust bearing with a regulator of the lubricant output flow. A theoretical study of its static and dynamic characteristics was carried out. The aim of the study was to test the reliability of the hypothesis concerning the possibility of obtaining a stable-to-oscillation adaptive thrust bearing of negative compliance, avoiding the need for a complex system of external combined throttling by replacing it with a simple slotted throttle. Mathematical modeling of the thrust bearing movement was carried out. The possibility of reducing the compliance to negative values is shown, providing the bearing with an adaptive function, consisting of using the structure as a bearing and as an active deformation compensator of the elastic system of a metal-cutting machine in order to improve the quality of the metalwork. Analysis of load static characteristics showed that negative compliance is provided over a wide range of loads, which can be up to 75% or more of the range of permissible bearing loads. Based on the study of dynamic characteristics, it was concluded that with a targeted selection of parameters that have a major effect on the dynamics of the structure, the considered adaptive hydrostatic thrust bearing can attain a very high quality of dynamics. It is shown that the viscous damping of the lubricating film enclosed in the gaps and the damping of the material of the elastic ring of the regulator are important resources for ensuring the optimal dynamics of the thrust bearing. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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15 pages, 1144 KiB  
Article
A Parallel Approach of the Enhanced Craig–Bampton Method
by Petr Pařík, Jin-Gyun Kim, Martin Isoz and Chang-uk Ahn
Mathematics 2021, 9(24), 3278; https://doi.org/10.3390/math9243278 - 16 Dec 2021
Cited by 5 | Viewed by 2428
Abstract
The enhanced Craig–Bampton (ECB) method is a novel extension of the original Craig–Bampton (CB) method, which has been widely used for component mode synthesis (CMS). The ECB method, using residual modal compensation that is neglected in the CB method, provides dramatic accuracy improvement [...] Read more.
The enhanced Craig–Bampton (ECB) method is a novel extension of the original Craig–Bampton (CB) method, which has been widely used for component mode synthesis (CMS). The ECB method, using residual modal compensation that is neglected in the CB method, provides dramatic accuracy improvement of reduced matrices without an increasing number of eigenbasis. However, it also needs additional computational requirements to treat the residual flexibility. In this paper, an efficient parallelization of the ECB method is presented to handle this issue and accelerate the applicability for large-scale structural vibration problems. A new ECB formulation within a substructuring strategy is derived to achieve better scalability. The parallel implementation is based on OpenMP parallel architecture. METIS graph partitioning and Linear Algebra Package (LAPACK) are used to automated algebraic partitioning and computational linear algebra, respectively. Numerical examples are presented to evaluate the accuracy, scalability, and capability of the proposed parallel ECB method. Consequently, based on this work, one can expect effective computation of the ECB method as well as accuracy improvement. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering)
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