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Symmetry
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Symmetry in Applied Continuous Mechanics
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Symmetry in Applied Continuous Mechanics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (15 September 2019) | Viewed by 50995

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

Special Issue Editors

Prof. Dr. Marin Marin

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, Romania
Interests: differential equations; partial differential equations; equations of evolution; integral equations; mixed initial-boundary value problems for PDE; termoelasticity; media with microstretch; environments goals; nonlinear problems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Dumitru Baleanu

grade E-Mail Website
Guest Editor
1. Institute of Space Sciences, P.O. Box MG-23, RO-077125 Magurele-Bucharest, Romania
2. Department of Mathematics, Cankaya University, Ankara 06530, Turkey
Interests: fractional dynamics; fractional differential equations; discrete mathematics; fractals; image processing; bio-informatics; mathematical biology; soliton theory; Lie symmetry; dynamic systems on time scales; computational complexity; the wavelet method
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Sorin Vlase

E-Mail Website
Guest Editor
Department of Mechanics, “Transilvania” University of Brasov, Brasov, Romania
Interests: mechanics; vibrations; elasticity; composite materials; analytical mechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Engineering practice requires the use of structures containing identical components or parts, useful from several points of view: less information is needed to describe the system, design is made quicker and easier, components are made faster than a complex assembly, and finally the time to achieve the structure and the cost of manufacturing decreases. Also, the subsequent maintenance of the system becomes easier and cheaper.

This Special Issue is dedicated to this kind of mechanical structure, describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are considered.

Theoretical models, mathematical methods, numerical analysis of the systems, such as the finite element method and experimental methods are expected to be used in the researches. Machine building, automotive, aerospace and civil engineering are the main areas in which such applications appear, but they are found in most engineering fields.

Prof. Dr. Marin Marin
Prof. Dumitru Baleanu
Prof. Dr. Sorin Vlase
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Symmetry
  • Skew symmetry
  • identical parts
  • automotive engineering
  • structure
  • numerical analysis
  • modal analysis
  • finite element method (FEM)
  • aerospace engineering
  • theoretical models
  • elastic systems
  • eigenvalue
  • eigenmode
  • experimental methods
  • civil engineering

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Published Papers (15 papers)

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Editorial

Jump to: Research

5 pages, 217 KiB  
Editorial
Symmetry in Applied Continuous Mechanics
by Marin Marin, Dumitru Băleanu and Sorin Vlase
Symmetry 2019, 11(10), 1286; https://doi.org/10.3390/sym11101286 - 14 Oct 2019
Viewed by 1701
Abstract
Engineering practice requires the use of structures containing identical components or parts, which are useful from several points of view: less information is needed to describe the system, design is made quicker and easier, components are made faster than a complex assembly, and [...] Read more.
Engineering practice requires the use of structures containing identical components or parts, which are useful from several points of view: less information is needed to describe the system, design is made quicker and easier, components are made faster than a complex assembly, and finally the time to achieve the structure and the cost of manufacturing decreases. Additionally, the subsequent maintenance of the system becomes easier and cheaper. This Special Issue is dedicated to this kind of mechanical structure, describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are considered. Theoretical models, mathematical methods, and numerical analysis of the systems, such as the finite element method and experimental methods, are expected to be used in the research. Such applications can be used in most engineering fields including machine building, automotive, aerospace, and civil engineering. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)

Research

Jump to: Editorial

12 pages, 4552 KiB  
Article
Impact-Damage Equivalency for Twisted Composite Blades with Symmetrical Configurations
by Yadong Zhou, Youchao Sun and Tianlin Huang
Symmetry 2019, 11(10), 1292; https://doi.org/10.3390/sym11101292 - 15 Oct 2019
Cited by 10 | Viewed by 2855
Abstract
In spite of potential advantages for aircraft structures, composite laminates can be subjected to bird-strike hazard in civil aviation. For purpose of future surrogate experiments, in this study, impact-damage equivalency for twisted composite blades is numerically investigated by Smoothed Particle Hydrodynamics (SPH) and [...] Read more.
In spite of potential advantages for aircraft structures, composite laminates can be subjected to bird-strike hazard in civil aviation. For purpose of future surrogate experiments, in this study, impact-damage equivalency for twisted composite blades is numerically investigated by Smoothed Particle Hydrodynamics (SPH) and finite element method (FEM). Cantilever slender flat plates are usually used for basic impact tests, the impact-damage equivalency is being considered by comparing damage modes and energies of three impact configurations: (1) twisted blade; (2) flat blade (axisymmetric); and (3) inclined flat blade (centrosymmetric). The damage maps and energy variations were comparatively investigated. Results indicate that both symmetrical flat and inclined flat blades can be, to a certain extent, regarded as alternatives for real twisted blades under bird impact; however, both types of blade have their own merits and drawbacks, and hence should be used carefully. These results aim to serve as tentative design guideline for future prototype or model experimental study of laminated blades in real aeronautical structures. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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17 pages, 958 KiB  
Article
Analysis of a Poro-Thermo-Viscoelastic Model of Type III
by Noelia Bazarra, José A. López-Campos, Marcos López, Abraham Segade and José R. Fernández
Symmetry 2019, 11(10), 1214; https://doi.org/10.3390/sym11101214 - 29 Sep 2019
Cited by 2 | Viewed by 2591
Abstract
In this work, we numerically study a thermo-mechanical problem arising in poro-viscoelasticity with the type III thermal law. The thermomechanical model leads to a linear system of three coupled hyperbolic partial differential equations, and its weak formulation as three coupled parabolic linear variational [...] Read more.
In this work, we numerically study a thermo-mechanical problem arising in poro-viscoelasticity with the type III thermal law. The thermomechanical model leads to a linear system of three coupled hyperbolic partial differential equations, and its weak formulation as three coupled parabolic linear variational equations. Then, using the finite element method and the implicit Euler scheme, for the spatial approximation and the discretization of the time derivatives, respectively, a fully discrete algorithm is introduced. A priori error estimates are proved, and the linear convergence is obtained under some suitable regularity conditions. Finally, some numerical results, involving one- and two-dimensional examples, are described, showing the accuracy of the algorithm and the dependence of the solution with respect to some constitutive parameters. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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20 pages, 4987 KiB  
Article
Synthesis on the Acceleration Energies in the Advanced Mechanics of the Multibody Systems
by Iuliu Negrean and Adina-Veronica Crișan
Symmetry 2019, 11(9), 1077; https://doi.org/10.3390/sym11091077 - 27 Aug 2019
Cited by 12 | Viewed by 3583
Abstract
The present paper’s objective is to highlight some new developments of the main author in the field of advanced dynamics of systems and higher order dynamic equations. These equations have been developed on the basis of the matrix exponentials which prove to have [...] Read more.
The present paper’s objective is to highlight some new developments of the main author in the field of advanced dynamics of systems and higher order dynamic equations. These equations have been developed on the basis of the matrix exponentials which prove to have undeniable advantages in the matrix study of any complex mechanical system. The present paper proposes some new approaches, based on differential principles from analytical mechanics, by using some important dynamics notions, regarding the acceleration energies of the first, second and third order. This study extended the equations of the higher order, which provide the possibility of applying the initial motion conditions in the positions, velocities and accelerations of the first and second order. In order to determine the time variation laws for the generalized variables, the driving forces and acceleration energies of the higher order are applied by the time polynomial functions of the fifth order. According to inverse kinematics also named control kinematics of the robots, the applications of polynomial functions lead to the kinematic control functions of mechanical motions, especially the transitory motions. They influence the dynamic behavior of multibody systems, in which robot structures are included. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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18 pages, 11875 KiB  
Article
Hysteretically Symmetrical Evolution of Elastomers-Based Vibration Isolators within α-Fractional Nonlinear Computational Dynamics
by Silviu Nastac, Carmen Debeleac and Sorin Vlase
Symmetry 2019, 11(7), 924; https://doi.org/10.3390/sym11070924 - 15 Jul 2019
Cited by 8 | Viewed by 2806
Abstract
This study deals with computational analysis of vibration isolators’ behavior, using the fractional-order differential equations (FDE). Numerical investigations regarding the influences of α-fractional derivatives have been mainly focused on the dissipative component within the differential constitutive equation of rheological model. Two classical models [...] Read more.
This study deals with computational analysis of vibration isolators’ behavior, using the fractional-order differential equations (FDE). Numerical investigations regarding the influences of α-fractional derivatives have been mainly focused on the dissipative component within the differential constitutive equation of rheological model. Two classical models were considered, Voigt-Kelvin and Van der Pol, in order to develop analyses both on linear and nonlinear formulations. The aim of this research is to evaluate the operational capability, provided by the α-fractional derivatives within the viscous component of certain rheological model, to enable an accurate response regarding the realistic behavior of elastomeric-based vibration isolators. The hysteretic response followed, which has to be able to assure the symmetry of dynamic evolution under external loads, and at the same time, properly providing dissipative and conservative characteristics in respect of the results of experimental investigations. Computational analysis was performed for different values of α-fractional order, also taking into account the integer value, in order to facilitate the comparison between the responses. The results have shown the serviceable capability of the α-fractional damping component to emulate, both a real dissipative behavior, and a virtual conservative characteristic, into a unitary way, only by tuning the α-order. At the same time, the fractional derivative models are able to preserve the symmetry of hysteretic behavior, comparatively, e.g., with rational-power nonlinear models. Thereby, the proposed models are accurately able to simulate specific behavioral aspects of rubber-like elastomers-based vibration isolators, to the experiments. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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16 pages, 326 KiB  
Article
On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure
by M. Marin, S. Vlase, R. Ellahi and M.M. Bhatti
Symmetry 2019, 11(7), 863; https://doi.org/10.3390/sym11070863 - 2 Jul 2019
Cited by 120 | Viewed by 3911
Abstract
We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based [...] Read more.
We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
8 pages, 233 KiB  
Article
Two-Dimensional Finite Element in General Plane Motion Used in the Analysis of Multi-Body Systems
by Eliza Chircan, Maria-Luminiţa Scutaru and Cătălin Iulian Pruncu
Symmetry 2019, 11(7), 848; https://doi.org/10.3390/sym11070848 - 1 Jul 2019
Cited by 4 | Viewed by 2421
Abstract
A description of the motion equation of a single two-dimensional finite element used to model a multi-body system with elastic elements is made in the article. To establish them, the Lagrange’s equations are used. Obtaining the dynamic response of a system with deformable [...] Read more.
A description of the motion equation of a single two-dimensional finite element used to model a multi-body system with elastic elements is made in the article. To establish them, the Lagrange’s equations are used. Obtaining the dynamic response of a system with deformable components has become important for technical applications in recent decades. These engineering applications are characterized by high applied loads and high acceleration and velocities. A study of such mechanical systems leads to the identification of different mechanical phenomena (due to high deformations, resonance phenomena, and stability). Coriolis effects and relative motions significantly modify the motion equations and, implicitly, the dynamic response. These effects are highlighted in this paper for plane motion. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
11 pages, 1007 KiB  
Article
Inference about the Ratio of the Coefficients of Variation of Two Independent Symmetric or Asymmetric Populations
by Zhang Yue and Dumitru Baleanu
Symmetry 2019, 11(6), 824; https://doi.org/10.3390/sym11060824 - 21 Jun 2019
Cited by 6 | Viewed by 3555
Abstract
Coefficient of variation (CV) is a simple but useful statistical tool to make comparisons about the independent populations in many research areas. In this study, firstly, we proposed the asymptotic distribution for the ratio of the CVs of two separate symmetric or asymmetric [...] Read more.
Coefficient of variation (CV) is a simple but useful statistical tool to make comparisons about the independent populations in many research areas. In this study, firstly, we proposed the asymptotic distribution for the ratio of the CVs of two separate symmetric or asymmetric populations. Then, we derived the asymptotic confidence interval and test statistic for hypothesis testing about the ratio of the CVs of these populations. Finally, the performance of the introduced approach was studied through simulation study. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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10 pages, 859 KiB  
Article
On Comparing and Classifying Several Independent Linear and Non-Linear Regression Models with Symmetric Errors
by Ji-Jun Pan, Mohammad Reza Mahmoudi, Dumitru Baleanu and Mohsen Maleki
Symmetry 2019, 11(6), 820; https://doi.org/10.3390/sym11060820 - 20 Jun 2019
Cited by 45 | Viewed by 3730
Abstract
In many real world problems, science fields such as biology, computer science, data mining, electrical and mechanical engineering, and signal processing, researchers aim to compare and classify several regression models. In this paper, a computational approach, based on the non-parametric methods, is used [...] Read more.
In many real world problems, science fields such as biology, computer science, data mining, electrical and mechanical engineering, and signal processing, researchers aim to compare and classify several regression models. In this paper, a computational approach, based on the non-parametric methods, is used to investigate the similarities, and to classify several linear and non-linear regression models with symmetric errors. The ability of each given approach is then evaluated using simulated and real world practical datasets. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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16 pages, 10847 KiB  
Article
Vibration Analysis of a Guitar considered as a Symmetrical Mechanical System
by Mariana D. Stanciu, Sorin Vlase and Marin Marin
Symmetry 2019, 11(6), 727; https://doi.org/10.3390/sym11060727 - 28 May 2019
Cited by 14 | Viewed by 5230
Abstract
This paper aimed to use the symmetry that exists to the body of a guitar to ease the analysis behavior to vibrations. Symmetries can produce interesting properties when studying the dynamic and steady-state response of such systems. These properties can, in some cases, [...] Read more.
This paper aimed to use the symmetry that exists to the body of a guitar to ease the analysis behavior to vibrations. Symmetries can produce interesting properties when studying the dynamic and steady-state response of such systems. These properties can, in some cases, considerably decrease the effort made for dynamic analysis at the design stage. For a real guitar, these properties are used to determine the eigenvalues and eigenvectors. Finite element method (FEM) is used for a numerical modeling and to prove the theoretically determined properties in this case. In this paper, different types of guitar plates related to symmetrical reinforcement patterns were studied in terms of modal analysis performed using finite element analysis (FEA). The dynamic response differs in terms of amplitude, eigenvalues, modal shapes in accordance with number and pattern of stiffening bars. In this study, the symmetrical and asymmetric modes of modal analysis were highlighted in the case of constructive symmetrical structures. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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17 pages, 2194 KiB  
Article
A Hybrid Model Based on a Two-Layer Decomposition Approach and an Optimized Neural Network for Chaotic Time Series Prediction
by Xinghan Xu and Weijie Ren
Symmetry 2019, 11(5), 610; https://doi.org/10.3390/sym11050610 - 1 May 2019
Cited by 21 | Viewed by 3292
Abstract
The prediction of chaotic time series has been a popular research field in recent years. Due to the strong non-stationary and high complexity of the chaotic time series, it is difficult to directly analyze and predict depending on a single model, so the [...] Read more.
The prediction of chaotic time series has been a popular research field in recent years. Due to the strong non-stationary and high complexity of the chaotic time series, it is difficult to directly analyze and predict depending on a single model, so the hybrid prediction model has become a promising and favorable alternative. In this paper, we put forward a novel hybrid model based on a two-layer decomposition approach and an optimized back propagation neural network (BPNN). The two-layer decomposition approach is proposed to obtain comprehensive information of the chaotic time series, which is composed of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD). The VMD algorithm is used for further decomposition of the high frequency subsequences obtained by CEEMDAN, after which the prediction performance is significantly improved. We then use the BPNN optimized by a firefly algorithm (FA) for prediction. The experimental results indicate that the two-layer decomposition approach is superior to other competing approaches in terms of four evaluation indexes in one-step and multi-step ahead predictions. The proposed hybrid model has a good prospect in the prediction of chaotic time series. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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12 pages, 253 KiB  
Article
Thermoelasticity of Initially Stressed Bodies with Voids: A Domain of Influence
by Marin Marin, Mohamed I. A. Othman, Sorin Vlase and Lavinia Codarcea-Munteanu
Symmetry 2019, 11(4), 573; https://doi.org/10.3390/sym11040573 - 19 Apr 2019
Cited by 13 | Viewed by 2299
Abstract
In our study, we will extend the domain of influence in order to cover the thermoelasticity of initially stressed bodies with voids. In what follows, we prove that, for a finite time t > 0 , the displacement field u i , the [...] Read more.
In our study, we will extend the domain of influence in order to cover the thermoelasticity of initially stressed bodies with voids. In what follows, we prove that, for a finite time t > 0 , the displacement field u i , the dipolar displacement field φ j k , the temperature θ and the change in volume fraction ϕ generate no disturbance outside a bounded domain B. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
24 pages, 6767 KiB  
Article
Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates
by Krzysztof Kamil Żur and Piotr Jankowski
Symmetry 2019, 11(3), 429; https://doi.org/10.3390/sym11030429 - 22 Mar 2019
Cited by 25 | Viewed by 3584
Abstract
Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse [...] Read more.
Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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18 pages, 6923 KiB  
Article
On the Effect of Thomson and Initial Stress in a Thermo-Porous Elastic Solid under G-N Electromagnetic Theory
by Elsayed M. Abd-Elaziz, Marin Marin and Mohamed I. A. Othman
Symmetry 2019, 11(3), 413; https://doi.org/10.3390/sym11030413 - 20 Mar 2019
Cited by 124 | Viewed by 4275
Abstract
The present work investigated the effect of Thomson and initial stress in a thermo-porous elastic solid under G-N electromagnetic theory. The Thomson coefficient affects the heat condition equation. A constant Thomson coefficient, instead of traditionally a constant Seebeck coefficient, is assumed. The charge [...] Read more.
The present work investigated the effect of Thomson and initial stress in a thermo-porous elastic solid under G-N electromagnetic theory. The Thomson coefficient affects the heat condition equation. A constant Thomson coefficient, instead of traditionally a constant Seebeck coefficient, is assumed. The charge density of the induced electric current is taken as a function of time. A normal mode method is proposed to analyze the problem and to obtain numerical solutions. The results that were obtained for all physical sizes are graphically illustrated and we offer a comparison between the type II G-N theory and the G-N theory of type III, both in the present case and in the absence of specific parameters, as initial stress, pores and the Thomson effect. Some particular cases are also discussed in the context of the problem. The results indicate that the effect of initial stress, Thomson coefficient effect, and magnetic field are very pronounced. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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12 pages, 574 KiB  
Article
New Exact Solutions of the Generalized Benjamin–Bona–Mahony Equation
by Behzad Ghanbari, Dumitru Baleanu and Maysaa Al Qurashi
Symmetry 2019, 11(1), 20; https://doi.org/10.3390/sym11010020 - 27 Dec 2018
Cited by 75 | Viewed by 4004
Abstract
The recently introduced technique, namely the generalized exponential rational function method, is applied to acquire some new exact optical solitons for the generalized Benjamin–Bona–Mahony (GBBM) equation. Appropriately, we obtain many families of solutions for the considered equation. To better understand of the physical [...] Read more.
The recently introduced technique, namely the generalized exponential rational function method, is applied to acquire some new exact optical solitons for the generalized Benjamin–Bona–Mahony (GBBM) equation. Appropriately, we obtain many families of solutions for the considered equation. To better understand of the physical features of solutions, some physical interpretations of solutions are also included. We examined the symmetries of obtained solitary waves solutions through figures. It is concluded that our approach is very efficient and powerful for integrating different nonlinear pdes. All symbolic computations are performed in Maple package. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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