Mathematics

Editorial

Jump to: Research, Review

3 pages, 161 KiB

Open AccessEditorial

Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition

by Maria Luminita Scutaru and Catalin-Iulian Pruncu

Mathematics 2024, 12(2), 341; https://doi.org/10.3390/math12020341 - 19 Jan 2024

Viewed by 1487

Abstract

Although it has been considered difficult to make further contributions in the field of mechanics, the spectacular evolution of technology and numerical calculation techniques has made these opinions shift, and increasingly sophisticated models have been developed, which should predict, as accurately as possible, [...] Read more.

Although it has been considered difficult to make further contributions in the field of mechanics, the spectacular evolution of technology and numerical calculation techniques has made these opinions shift, and increasingly sophisticated models have been developed, which should predict, as accurately as possible, the phenomena that take place in dynamic systems [...] Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

Research

Jump to: Editorial, Review

13 pages, 806 KiB

Open AccessArticle

Mathematical Model for Fault Handling of Singular Nonlinear Time-Varying Delay Systems Based on T-S Fuzzy Model

by Jianing Cao and Hua Chen

Mathematics 2023, 11(11), 2547; https://doi.org/10.3390/math11112547 - 1 Jun 2023

Viewed by 1237

Abstract

In this paper, a mathematical model based on the T-S fuzzy model is proposed to solve the fault estimation (FE) and fault-tolerant control (FTC) problem for singular nonlinear time-varying delay (TVD) systems with sensor fault. TVD is is extremely difficult to solve and [...] Read more.

In this paper, a mathematical model based on the T-S fuzzy model is proposed to solve the fault estimation (FE) and fault-tolerant control (FTC) problem for singular nonlinear time-varying delay (TVD) systems with sensor fault. TVD is is extremely difficult to solve and the Laplace transform is devised to build an equal system free of TVD. Additionally, the sensor fault is changed to actuator fault by the developed coordinate transformation. A fuzzy learning fault estimator is first built to estimate the detailed sensor fault information. Then, a PI FTC scheme is suggested aiming at minimizing the damage caused by the fault. Simulation results from multiple faults reveal that the FE and FTC algorithms are able to estimate the fault and guarantee the system performance properly. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

20 pages, 9213 KiB

Open AccessArticle

A Posteriori Error Estimators for the Quasi-Newtonian Stokes Problem with a General Boundary Condition

by Omar El Moutea, Lahcen El Ouadefli, Abdeslam El Akkad, Nadia Nakbi, Ahmed Elkhalfi, Maria Luminita Scutaru and Sorin Vlase

Mathematics 2023, 11(8), 1943; https://doi.org/10.3390/math11081943 - 20 Apr 2023

Cited by 2 | Viewed by 1144

Abstract

In this paper, we approach two nonlinear differential equations applied in fluid mechanics by finite element methods (FEM). Our objective is to approach the solution to these problems; the first one is the “p-Laplacian” problem and the second one is the [...] Read more.

In this paper, we approach two nonlinear differential equations applied in fluid mechanics by finite element methods (FEM). Our objective is to approach the solution to these problems; the first one is the “p-Laplacian” problem and the second one is the “Quasi-Newtonian Stokes” problem with a general boundary condition. To study and analyze our solutions, we introduce the a posteriori error indicator; this technique allows us to control the error, and each is shown the equivalent between the true and the a posterior errors estimators. The performance of the finite element method by this type of general boundary condition is presented via different numerical simulations. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

33 pages, 19838 KiB

Open AccessArticle

Modern Dimensional Analysis-Based Heat Transfer Analysis: Normalized Heat Transfer Curves

by Ioan Száva, Sorin Vlase, Ildikó-Renáta Száva, Gábor Turzó, Violeta Mihaela Munteanu, Teofil Gălățanu, Zsolt Asztalos and Botond-Pál Gálfi

Mathematics 2023, 11(3), 741; https://doi.org/10.3390/math11030741 - 1 Feb 2023

Cited by 1 | Viewed by 1464

Abstract

In this contribution, the authors continued their initial study on the efficiency of the analysis of experimentally obtained temperature curves, in order to determine some basic parameters that are as simple and reliable as possible, such as “m”, the heat transfer [...] Read more.

In this contribution, the authors continued their initial study on the efficiency of the analysis of experimentally obtained temperature curves, in order to determine some basic parameters that are as simple and reliable as possible, such as “m”, the heat transfer coefficient. After the brief review of the previous results, on which the present article is based, the authors offered a brief argumentation of the importance of dimensional methods, especially the one called modern dimensional analysis, in these theoretical-experimental investigations regarding the propagation of the thermal field of structural elements with solid sections, and especially with tubular-rectangular sections. It could be concluded that modern experimental investigations mostly follow the behavior of models attached to the initial structures, i.e., prototypes, because there are clear advantages in this process of forecasting the behavior of the prototype based on the measurement results obtained on the attached model. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

17 pages, 439 KiB

Open AccessArticle

Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra

by Jesús Alfonso Medrano-Hermosillo, Ricardo Lozoya-Ponce, Abraham Efraím Rodriguez-Mata and Rogelio Baray-Arana

Mathematics 2023, 11(3), 572; https://doi.org/10.3390/math11030572 - 21 Jan 2023

Cited by 2 | Viewed by 2078

Abstract

The following paper talks about the dynamic modeling and control of robot manipulators using Hamilton’s equations in the screw theory framework. The difference between the proposed work with diverse methods in the literature is the ease of obtaining the laws of control directly [...] Read more.

The following paper talks about the dynamic modeling and control of robot manipulators using Hamilton’s equations in the screw theory framework. The difference between the proposed work with diverse methods in the literature is the ease of obtaining the laws of control directly with screws and co-screws, which is considered modern robotics by diverse authors. In addition, geometric algebra (GA) is introduced as a simple and iterative tool to obtain screws and co-screws. On the other hand, such as the controllers, the Hamiltonian equations of motion (in the phase space) are developed using co-screws and screws, which is a novel approach to compute the dynamic equations for robots. Regarding the controllers, two laws of control are designed to ensure the error’s convergence to zero. The controllers are computed using the traditional feedback linearization and the sliding mode control theory. The first one is easy to program and the second theory provides robustness for matched disturbances. On the other hand, to prove the stability of the closed loop system, different Lyapunov functions are computed with co-screws and screws to guarantee its convergence to zero. Finally, diverse simulations are illustrated to show a comparison of the designed controllers with the most famous approaches. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

15 pages, 3721 KiB

Open AccessArticle

Steady-State Solutions for MHD Motions of Burgers’ Fluids through Porous Media with Differential Expressions of Shear on Boundary and Applications

by Constantin Fetecau, Abdul Rauf, Tahir Mushtaq Qureshi and Dumitru Vieru

Mathematics 2022, 10(22), 4228; https://doi.org/10.3390/math10224228 - 12 Nov 2022

Cited by 6 | Viewed by 1269

Abstract

Steady-state solutions for two mixed initial-boundary value problems are provided. They describe isothermal MHD steady-state motions of incompressible Burgers’ fluids over an infinite flat plate embedded in a porous medium when differential expressions of shear stress are given on a part of the [...] Read more.

Steady-state solutions for two mixed initial-boundary value problems are provided. They describe isothermal MHD steady-state motions of incompressible Burgers’ fluids over an infinite flat plate embedded in a porous medium when differential expressions of shear stress are given on a part of the boundary. The fluid is electrically conductive under the influence of a uniform transverse magnetic field. For the validation of the results, the expressions of the obtained solutions are presented in different forms and their equivalence is graphically proved. All of the obtained results could easily be particularized to give exact solutions for the incompressible Oldroyd-B, Maxwell, second-grade, and Newtonian fluids that were performing similar motions. For illustration, the solutions corresponding to Newtonian fluids are provided. In addition, as an application, the velocity fields were used to determine the time required to reach the steady or permanent state for distinct values of magnetic and porous parameters. We found that this time declined with increasing values of the magnetic or porous parameters. Consequently, the steady state for such motions of Burgers’ fluids was earlier reached in the presence of a magnetic field or porous medium. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

15 pages, 4188 KiB

Open AccessArticle

Dynamic Absorption of Vibration in a Multi Degree of Freedom Elastic System

by Maria Luminita Scutaru, Marin Marin and Sorin Vlase

Mathematics 2022, 10(21), 4045; https://doi.org/10.3390/math10214045 - 31 Oct 2022

Cited by 4 | Viewed by 1667

Abstract

The paper aims to identify the situations in which a complex elastic system, which is subject to mechanical vibrations, can act as a dynamic absorber of vibrations for certain frequencies. The conditions that the system must fulfill in order to achieve this goal [...] Read more.

The paper aims to identify the situations in which a complex elastic system, which is subject to mechanical vibrations, can act as a dynamic absorber of vibrations for certain frequencies. The conditions that the system must fulfill in order to achieve this goal are determined and then a calculation example is presented. The method is interesting because it allows to avoid attaching an absorber specially built for this, a situation that complicates the project and increases manufacturing costs. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

12 pages, 3997 KiB

Open AccessArticle

CFD Model Studies of Dust Dispersion in Driven Dog Headings

by Magdalena Tutak, Jarosław Brodny, Antoni John, Janos Száva, Sorin Vlase and Maria Luminita Scutaru

Mathematics 2022, 10(20), 3798; https://doi.org/10.3390/math10203798 - 14 Oct 2022

Cited by 1 | Viewed by 1400

Abstract

Dust is one of the most burdensome hazards found in the environment. It is composed of crushed solids that pose a threat to the health and life of people, machines and machine components. At high concentration levels, it can reduce visibility. All of [...] Read more.

Dust is one of the most burdensome hazards found in the environment. It is composed of crushed solids that pose a threat to the health and life of people, machines and machine components. At high concentration levels, it can reduce visibility. All of these negative phenomena occur during the process of underground mining, where dust hazards are common. The negative impact of dust on the efficacy of the mining process prompts research in this area. The following study presents a method developed for model studies of dust dispersion in driven dog headings. This issue is immensely important due to the fact that these dog headings belong to a group of unidirectional excavations (including tunnelling). This paper presents the results of model studies on dust dispersion in driven dog headings. The main focus is on the analysis of the distribution of dust concentration along a dog heading during the mining process. In order to achieve this goal, a model test method based on the finite volume method, which is included in the group of CFD methods, was developed. Analyses were carried out for two different values of dust emission from the face of the excavation for the transient state. The results made it possible to determine areas with the highest potential for dust concentration. The size and location of these areas are mainly dependent on the amount of dust emissions during the mining process. The results can support the process of managing dust prevention and protection of workers during the mining excavation process. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

10 pages, 2820 KiB

Open AccessArticle

Study on Vibration Friction Reducing Mechanism of Materials

by Yunnan Teng, Quan Wen, Liyang Xie and Bangchun Wen

Mathematics 2022, 10(19), 3529; https://doi.org/10.3390/math10193529 - 28 Sep 2022

Viewed by 1783

Abstract

Friction has a vital role in studying materials’ and systems’ behavior. The friction between two objects and the inner friction of materials under the condition of vibration usually can present different characteristics. These characteristics are different from the conventional conditions. It is shown [...] Read more.

Friction has a vital role in studying materials’ and systems’ behavior. The friction between two objects and the inner friction of materials under the condition of vibration usually can present different characteristics. These characteristics are different from the conventional conditions. It is shown in practice that vibration can reduce the friction coefficient and friction force between two objects. Vibration can lighten abrasion of objects and reduce energy consumption. All of these can give great efficiency, but, until now, the vibration friction-reducing mechanism has not been fully revealed. In this manuscript, the friction-reducing mechanism of materials under arbitrary vibration forces is investigated. The results show that the effective friction coefficient of materials under arbitrary vibration forces is always the minimum. The relationship between the effective friction coefficient and the negative gradient is investigated in this research. When the vibration force direction projects are in the first and the third quadrants, the negative gradient of the effective friction coefficient gets larger slowly, and then it becomes stable. When the vibration force direction projects are in the second and the fourth quadrants, the negative gradient of the effective friction coefficient decays to zero at the initial stage and then increases rapidly. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

12 pages, 3928 KiB

Open AccessArticle

Numerical Simulation for Brinkman System with Varied Permeability Tensor

by Lahcen El Ouadefli, Abdeslam El Akkad, Omar El Moutea, Hassan Moustabchir, Ahmed Elkhalfi, Maria Luminița Scutaru and Radu Muntean

Mathematics 2022, 10(18), 3242; https://doi.org/10.3390/math10183242 - 6 Sep 2022

Cited by 4 | Viewed by 1469

Abstract

The aim of this paper is to study a stationary Brinkman problem in an anisotropic porous medium by using a mini-element method with a general boundary condition. One of the important aspects of the [...] Read more.

The aim of this paper is to study a stationary Brinkman problem in an anisotropic porous medium by using a mini-element method with a general boundary condition. One of the important aspects of the

P 1 - B u b b l e / P 1

method is satisfying the inf-sup condition, which allows us the existence and the uniqueness of the weak solution to our problem. To go further in this theoretical study, an a priori error estimate is established. To see the importance of this method in reality, we applied this method to a real problem. The numerical simulation studies support our results and demonstrate the effectiveness of this method. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

15 pages, 466 KiB

Open AccessArticle

Lie Symmetry Classification and Qualitative Analysis for the Fourth-Order Schrödinger Equation

by Andronikos Paliathanasis, Genly Leon and Peter G. L. Leach

Mathematics 2022, 10(17), 3204; https://doi.org/10.3390/math10173204 - 5 Sep 2022

Cited by 1 | Viewed by 1442

Abstract

The Lie symmetry analysis for the study of a

1 + n

fourth-order Schrödinger equation inspired by the modification of the deformation algebra in the presence of a minimum length is applied. Specifically, we perform a detailed classification for the scalar field potential [...] Read more.

The Lie symmetry analysis for the study of a

1 + n

fourth-order Schrödinger equation inspired by the modification of the deformation algebra in the presence of a minimum length is applied. Specifically, we perform a detailed classification for the scalar field potential function where non-trivial Lie symmetries exist and simplify the Schrödinger equation. Then, a qualitative analysis allows for the reduced ordinary differential equation to be analysed to understand the asymptotic dynamics. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

22 pages, 5153 KiB

Open AccessArticle

Entropy Analysis of Sutterby Nanofluid Flow over a Riga Sheet with Gyrotactic Microorganisms and Cattaneo–Christov Double Diffusion

by Muhammad Faizan, Farhan Ali, Karuppusamy Loganathan, Aurang Zaib, Ch Achi Reddy and Sara I. Abdelsalam

Mathematics 2022, 10(17), 3157; https://doi.org/10.3390/math10173157 - 2 Sep 2022

Cited by 82 | Viewed by 2648

Abstract

In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This exhibition produces electromagnetic hydrodynamic phenomena over a fluid flow. A new study model is formed with the Sutterby nanofluid flow through [...] Read more.

In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This exhibition produces electromagnetic hydrodynamic phenomena over a fluid flow. A new study model is formed with the Sutterby nanofluid flow through the Riga plate, which is crucial to the structure of several industrial and entering advancements, including thermal nuclear reactors, flow metres and nuclear reactor design. This article addresses the entropy analysis of Sutterby nanofluid flow over the Riga plate. The Cattaneo–Christov heat and mass flux were used to examine the behaviour of heat and mass relaxation time. The bioconvective motile microorganisms and nanoparticles are taken into consideration. The system of equations for the current flow problems is converted from a highly non-linear partial system to an ordinary system through an appropriate transformation. The effect of the obtained variables on velocity, temperature, concentration and motile microorganism distributions are elaborated through the plots in detail. Further, the velocity distribution is enhanced for a greater Deborah number value and it is reduced for a higher Reynolds number for the two cases of pseudoplastic and dilatant flows. Microorganism distribution decreases with the increased magnitude of Peclet number, Bioconvection Lewis number and microorganism concentration difference number. Two types of graphical outputs are presented for the Sutterby fluid parameter (β = −2.5, β = 2.5). Finally, the validation of the present model is achieved with the previously available literature. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

13 pages, 4291 KiB

Open AccessArticle

Modelling and Fault Detection for Specific Cavitation Damage Based on the Discharge Pressure of Axial Piston Pumps

by Shiqi Xia, Yimin Xia and Jiawei Xiang

Mathematics 2022, 10(14), 2461; https://doi.org/10.3390/math10142461 - 14 Jul 2022

Cited by 7 | Viewed by 2068

Abstract

Cavitation will increase the leakage and discharge pressure fluctuation of axial piston pumps. In particular, specific cavitation damage may aggravate the pressure impact and performance degradation. The influence of the specific cavitation damage on the discharge pressure is unclear, and the need for [...] Read more.

Cavitation will increase the leakage and discharge pressure fluctuation of axial piston pumps. In particular, specific cavitation damage may aggravate the pressure impact and performance degradation. The influence of the specific cavitation damage on the discharge pressure is unclear, and the need for fault detection of this damage is urgent. In this paper, we propose a discharge pressure-based model and fault detection methodology for the specific cavitation damage of axial piston pumps. The discharge pressure model with specific damage is constructed using a slender hole. The simulation model is solved through numerical integration. Experimental investigation of cavitation damage detection is carried out. Discharge pressure features in the time domain and frequency domain are compared. The results show that waveform distortions, spectrum energy relocation, generation of new frequencies and sidebands can be used as features for fault detection regarding the specific cavitation damage of axial piston pumps. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

► Show Figures

Figure 1

Review

Jump to: Editorial, Research

15 pages, 302 KiB

Open AccessReview

Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

by Sorin Vlase, Marin Marin and Negrean Iuliu

Mathematics 2022, 10(2), 257; https://doi.org/10.3390/math10020257 - 15 Jan 2022

Cited by 3 | Viewed by 2201

Abstract

This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write [...] Read more.

This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)

Journal Menu

Journal Browser

Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Related Special Issues

Published Papers (14 papers)

Editorial

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI