scholarly journals The Propagation of Thermoelastic Waves in Anisotropic Media of Orthorhombic, Hexagonal, and Tetragonal Syngonies

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Nurlybek A. Ispulov ◽  
Abdul Qadir ◽  
Marat Zhukenov ◽  
Erkin Arinov
Keyword(s):  
Wave Propagation ◽  
Fundamental Solutions ◽  
Thermoelastic Medium ◽  
Thermoelastic Wave ◽  
Economic Implications ◽  
First Order ◽  
The Given ◽  
Thermoelastic Waves ◽  
Hexagonal Syngony ◽  
Equations Of Motions

The investigation of wave propagation in elastic medium with thermomechanical effects is bound to have important economic implications in the field of composite materials, seismology, geophysics, and so on. In this article, thermoelastic wave propagation in anisotropic mediums of orthorhombic and hexagonal syngony having heterogeneity along z-axis is studied. Such medium has second-order axis symmetry. By using analytical matriciant method, a set of equations of motions in thermoelastic medium are reduced to an equivalent set of the first-order differential equations. In the general case, for the given set of equations, structures of fundamental solutions are made and dispersion relations are obtained.

scholarly journals The Analytical Form of the Dispersion Equation of Elastic Waves in Periodically Inhomogeneous Medium of Different Classes of Crystals

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Nurlybek A. Ispulov ◽  
Abdul Qadir ◽  
Marat K. Zhukenov ◽  
Talgat S. Dossanov ◽  
Tanat G. Kissikov
Keyword(s):  
Elastic Waves ◽  
Material Science ◽  
Analytical Form ◽  
Fundamental Solutions ◽  
Difficulty Level ◽  
Elastic Media ◽  
Thermoelastic Wave ◽  
First Order ◽  
First Order Differential Equations ◽  
Equations Of Motions

The investigation of thermoelastic wave propagation in elastic media is bound to have much influence in the fields of material science, geophysics, seismology, and so on. The heat conduction equations and bound equations of motions differ by the difficulty level and presence of many physical and mechanical parameters in them. Therefore thermoelasticity is being extensively studied and developed. In this paper by using analytical matrizant method set of equation of motions in elastic media are reduced to equivalent set of first-order differential equations. Moreover, for given set of equations, the structure of fundamental solutions for the general case has been derived and also dispersion relations are obtained.

Numerical Simulation of Elastic and Thermoelastic Wave Propagation in Two-Dimensional Classical and Generalized Coupled Thermoelasticity

2010 ◽  
Author(s):  
S. K. Hosseini zad ◽  
A. Komeili ◽  
A. H. Akbarzadeh ◽  
M. R. Eslami
Keyword(s):  
Wave Propagation ◽  
Two Dimensional ◽  
Governing Equations ◽  
Fe Method ◽  
Finite Element Scheme ◽  
Thermoelastic Wave ◽  
Virtual Displacement ◽  
Coupled Thermoelasticity ◽  
Time Domains ◽  
Thermoelastic Waves

This study concentrates on the simulation of elastic and thermoelastic wave propagation in two-dimensional thermoelastic regions based on the classical and generalized coupled thermoelasticity. A finite element scheme is employed to obtain the field variables directly in the space and time domains. The FE method is based on the virtual displacement and the Galerkin technique, which is directly applied to the governing equations. The Newmark algorithm is used to solve the FE problem in time domain. Solving 2D coupled thermoelasticity equations leads to obtain the distribution of temperature, displacement and stresses through the domain. The problem is solved for two different type of boundary conditions (BCs), and the behavior of temperature, displacement and stress waves according to these BCs and based on the classical and generalized coupled thermoelasticity theories are shown and compared with each other. Several characteristics of the thermoelastic waves in two-dimensional domains are discussed according to this analysis.

Heat Transfer Due to Thermoelastic Wave Propagation in a Porous Rod

2021 ◽  
Vol 143 (4) ◽  
Author(s):  
Baljeet Singh
Keyword(s):  
Heat Transfer ◽  
Wave Propagation ◽  
Thermal Relaxation ◽  
Porous Solid ◽  
Governing Equations ◽  
Thermoelastic Wave ◽  
One Dimensional ◽  
Circular Frequency ◽  
Thermoelastic Waves ◽  
Homogeneous Linear

Abstract This paper investigates the propagation of thermoelastic waves in a homogeneous, linear, and isotropic porous solid. For physical and mathematical simplicity, one-dimensional wave propagation in a porous solid rod is considered to explain the concept of heat transfer caused by motion. The solutions of governing equations show that the transfer of heat in a porous rod is not only due to the conduction but also produced by the local particle displacement phenomenon. It is observed that the time-averaged transfer of heat depends on the circular frequency, porosity, thermal conductivity, thermal relaxation, specific heat, and other material coefficients.

Boundary Integral Equation Formulation in Generalized Linear Thermo-Viscoelasticity With Rheological Volume

2003 ◽  
Vol 70 (5) ◽  
pp. 661-667 ◽  
Author(s):  
A. S. El-Karamany
Keyword(s):  
Integral Equation ◽  
Rheological Properties ◽  
Boundary Integral Equation ◽  
Relaxation Times ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Phase Lag ◽  
Integral Equation Formulation ◽  
Special Cases ◽  
The Given

A general model of generalized linear thermo-viscoelasticity for isotropic material is established taking into consideration the rheological properties of the volume. The given model is applicable to three generalized theories of thermoelasticity: the generalized theory with one (Lord-Shulman theory) or with two relaxation times (Green-Lindsay theory) and with dual phase-lag (Chandrasekharaiah-Tzou theory) as well as to the dynamic coupled theory. The cases of thermo-viscoelasticity of Kelvin-Voigt model or thermoviscoelasticity ignoring the rheological properties of the volume can be obtained from the given model. The equations of the corresponding thermoelasticity theories result from the given model as special cases. A formulation of the boundary integral equation (BIE) method, fundamental solutions of the corresponding differential equations are obtained and an example illustrating the BIE formulation is given.

Plane wave propagation in microstretch thermoelastic medium with microtemperatures

2014 ◽  
Vol 21 (16) ◽  
pp. 3403-3416
Author(s):  
Rajneesh Kumar ◽  
Mandeep Kaur ◽  
SC Rajvanshi
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Thermoelastic Medium ◽  
Plane Wave Propagation

On two pursuit differential game problems with state and geometric constraints in a Hilbert space

2021 ◽  
Vol 65 (3) ◽  
pp. 5-16
Author(s):  
Abbas Ja’afaru Badakaya ◽  
Keyword(s):  
Differential Game ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Nonempty Closed Convex Subset ◽  
Geometric Constraints ◽  
First Order ◽  
Control Functions ◽  
Closed Convex Set ◽  
The Given ◽  
First Order Differential Equations

This paper concerns with the study of two pursuit differential game problems of many pursuers and many evaders on a nonempty closed convex subset of R^n. Throughout the period of the games, players must stay within the given closed convex set. Players’ laws of motion are defined by certain first order differential equations. Control functions of the pursuers and evaders are subject to geometric constraints. Pursuit is said to be completed if the geometric position of each of the evader coincides with that of a pursuer. We proved two theorems each of which is solution to a problem. Sufficient conditions for the completion of pursuit are provided in each of the theorems. Moreover, we constructed strategies of the pursuers that ensure completion of pursuit.

Integration of one-dimensional equations of motions

2020 ◽  
pp. 79-90
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Potential Energy ◽  
Field Change ◽  
One Dimensional ◽  
System A ◽  
Small Correction ◽  
The Law ◽  
The One ◽  
The Given ◽  
Equations Of Motions

If the potential energy is independent of time, the energy of the system remains constant during the motion of a closed system. A system with one degree of freedom allows for the determination of the law of motion in quadrature. In this chapter, the authors consider motion of the particles in the one-dimensional fields. They discuss also how the law and the period of a particle moving in the potential field change due to adding to the given field a small correction.

Sign in / Sign up

Export Citation Format

Share Document