Editorial

5 pages, 217 KiB

Open AccessEditorial

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 1445

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

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12 pages, 4552 KiB

Open AccessArticle

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 9 | Viewed by 2433

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

Open AccessArticle

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 2202

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

Open AccessArticle

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 3027

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

Open AccessArticle

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 7 | Viewed by 2414

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

Open AccessEditor’s ChoiceArticle

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 - 02 Jul 2019

Cited by 115 | Viewed by 3514

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

Open AccessArticle

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 - 01 Jul 2019

Cited by 4 | Viewed by 2071

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

Open AccessArticle

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 3077

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

Open AccessArticle

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 44 | Viewed by 3252

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

Open AccessArticle

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 4502

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

Open AccessArticle

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 - 01 May 2019

Cited by 18 | Viewed by 2834

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

Open AccessArticle

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 12 | Viewed by 2005

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

Open AccessArticle

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 22 | Viewed by 3211

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

Open AccessArticle

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 121 | Viewed by 3803

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

Open AccessArticle

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 70 | Viewed by 3400

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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