Effect of magneto-thermo-viscoelasticity in an unbounded body with a spherical cavity subjected to a harmonically varying temperature without energy dissipation

The present work is devoted to study effects of the thermally induced vibration, magnetic field and viscoelasticity in an isotropic homogeneous unbounded body with a spherical cavity. The GN model of thermoelasticity without energy dissipation is applied. The closed form solutions for distributions of displacement, temperature and radial and hoop stresses are illustrated. The boundary conditions for the temperature and mechanical and Maxwell’s stresses are employed. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. The results obtained are calculated for a copper material and presented graphically. It’s deduced that the magnetic field, viscosity and thermally induced vibration are very pronounced on displacement, temperature and stresses.     

Analytical Solution for a Free Vibration of a Thermoelastic Hollow Sphere

For a free vibration problem of a thermoelastic hollow sphere into the context of the generalized thermoelasticity theory with one relaxation time, exact analytic solutions are obtained with the use of eigenvalue approach. Both the inner and outer curved surfaces of the sphere are considered stress-free and isothermal surfaces. The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollow sphere are derived. The numerical results have been presented graphically in respect of natural frequencies, thermoelastic damping, and frequency shift.     

Analysis of dispersion relations of a coupled thermoelasticity problem with regard to heat flux relaxation

Dispersion relations for a coupled thermoelasticity problem including a hyperbolic heat conduction equation are derived, and their asymptotic analysis is performed. Dependences of the wave number and characteristics of the vibration damping rate on frequency are obtained and compared with similar diagrams in the classical model.     

Three-dimensional vibration analysis of a thermoelastic cylindrical panel with voids

In this paper, based on three-dimensional linear generalized thermoelasticity, an exact analysis of free vibration of a simply supported homogeneous isotropic, thermally conducting, cylindrical panel with voids initially at uniform temperature and undeformed state has been presented. Three displacement potential functions are introduced for solving the equations of motion, heat conduction and volume fraction field. The purely transverse wave gets decoupled from rest of motion and is not affected by thermal and volume fraction (voids) fields. After expanding the displacement potentials, volume fraction and temperature functions with orthogonal series, the equations of the considered vibration problem are reduced to five-second order coupled ordinary differential equations whose formal solution can be expressed by using Bessel functions with complex arguments. The corresponding results for thermoelastic panel without voids, elastic panel with and without voids have been deduced as special cases from the present analysis. In order to illustrate the analytical results, the numerical solutions of various relations and equations have been obtained to compute the lowest frequency as function of different cylindrical panel parameters. The computer simulated results have been presented graphically.     

Generalized thermoelastic infinite transversely isotropic body with a cylindrical cavity due to moving heat source and harmonically varying heat

In this paper, the induced temperature, displacement, and stress fields in an infinite transversely isotropic unbounded medium with cylindrical cavity due to a moving heat source and harmonically varying heat are investigated. This problem is solved in the context of the linear theory of generalized thermoelasticity with dual phase lag model. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique the inversion of Laplace transform is done numerically. The numerical estimates of the displacement, temperature and stress are obtained and presented graphically. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and thermoelasticity without energy dissipation can extracted as special cases. Some comparisons have been shown in figures to present the effect of the heat source, dual phase lags parameters and the angular frequency of thermal vibration on all the studied fields.     

受移动简谐力作用的多孔弹性半平面问题

研究了匀速移动的振动荷载作用下半无限多孔饱和固体中产生的应力和孔隙水压力．应用Fourier变换求解该问题的控制偏微分方程,考虑了荷载的移动速度及振动频率对多孔饱和固体中应力与孔隙水压力的影响,并与相应的弹性介质的解答进行了比较．结果显示多孔饱和半平面中应力和孔隙水压力随荷载的移动速度与振动频率的增加而增大,多孔饱和固体在移动荷载下的动力响应与相应的单相弹性固体的动力响应有较大的差别。     

A boundary element method for anisotropic coupled thermoelasticity

Summary A boundary element formulation is presented for the solution of the equations of fully coupled thermoelasticity for materials of arbitrary degree of anisotropy. By employing the fundamental solutions of anisotropic elastostatics and stationary heat conduction, a system of equations with time-independent matrices is obtained. Since the fundamental solutions are uncoupled and time-independent, a domain integral remains in the representation formula which contains the time-dependence as well as the thermoelastic coupling. This domain integral is transformed to the boundary by means of the dual reciprocity method. By taking this approach, the use of dynamic fundamental solutions is avoided, which enables an efficient calculation of system matrices. In addition, the solution of transient processes as well as, free and forced vibration analysis becomes straightforward and can be carried out with standard time-stepping schemes and eigensystem solvers. Another important advantage of the present formulation is its versatility, since it includes a number of simplified thermoelastic theories, viz. the theory of thermal stresses, coupled and uncoupled quasi-static thermoelasticity, and stationary thermoelasticity. The accuracy of the new thermoelastic boundary element method is demonstrated by a number of example problems. Support by the Deutsche Forschungsgemeinschaft (DFG) of the Graduate Collegium Modelling and discretization methods for continua and fluids (GKKS) at the University of Stuttgart is gratefully acknowledged.     

Spatial Stability for the Quasi-static Problem of Thermoelasticity

This paper is concerned with the quasi-static problem of thermoelasticity. The classical system of equations of thermoelasticity is a coupling of an elliptic equation with a parabolic equation. It poses some new mathematical difficulties. Here we study the exponential spatial decay of solutions. An upper bound for the amplitude in terms of the boundary and initial conditions is obtained. The extension of the spatial stability results to thermoelasticity of type III is also treated. Dedicated to C.O. Horgan on the occasion of his 60th birthdayMathematics Subject Classifications (2000) 74F05, 74G50.     

WAVE PROPAGATION IN A TRANSVERSELY ISOTROPIC THERMOELASTIC SOLID CYLINDER OF ARBITRARY CROSS-SECTION

The wave propagation in an infinite, homogeneous, transversely isotropic solid cylinder of arbitrary cross-section is studied using Fourier expansion collocation method, within the frame work of linearized, three-dimensional theory of thermoelasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat conduction. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for elliptic and parabolic cross-sectional zinc cylinders. The computed non-dimensional wave numbers are presented in the form of dispersion curves.     

On the final boundary value problems in linear thermoelasticity

In the present study we derive some uniqueness criteria for solutions of the Cauchy problem for the standard equations of dynamical linear thermoelasticity backward in time. We use Lagrange-Brun identities combined with some differential inequalities in order to show that the final boundary value problem associated with the linear thermoelasticity backward in time has at most one solution in appropriate classes of displacement-temperature fields. The uniqueness results are obtained under the assumptions that the density mass and the specific heat are strictly positive and the conductivity tensor is positive definite.     

Influence of boundary conditions on the solution of a hyperbolic thermoelasticity problem

We consider a series of problems with a short laser impact on a thin metal layer accounting various boundary conditions of the first and second kind. The behavior of the material is modeled by the hyperbolic thermoelasticity of Lord–Shulman type. We obtain analytical solutions of the problems in the semi-coupled formulation and numerical solutions in the coupled formulation. Numerical solutions are compared with the analytical ones. The analytical solutions of the semi-coupled problems and numerical solutions of the coupled problems show qualitative match. The solutions of hyperbolic thermoelasticity problems are compared with those obtained in the frame of the classical thermoelasticity. It was determined that the most prominent difference between the classical and hyperbolic solutions arises in the problem with fixed boundaries and constant temperature on them. The smallest differences were observed in the problem with unconstrained, thermally insulated edges. It was shown that a cooling zone is observed if the boundary conditions of the first kind are given for the temperature. Analytical expressions for the velocities of the quasiacoustic and quasithermal fronts as well as the critical value for the attenuation coefficient of the excitation impulse are verified numerically.     

双稳态电磁式振动能量捕获器超谐波响应研究

超谐波响应是非线性振动系统在较大激励下表现的特性,在某种条件下双稳态振动能量捕获系统的超谐波响应可使系统产生优越的输出功率。本文将质量-非线性弹簧-阻尼系统与双稳态振动能量捕获器相结合,提出了附加非线性振子的双稳态电磁式振动能量捕获器,建立系统的力学模型及控制方程。采用两项式谐波平衡法,获得了双稳态系统在简谐激励下产生大幅运动的基谐波和超谐波响应的解析解,借助数值仿真分析了质量比和调频比对双稳态振动能量捕获器产生大幅运动的影响规律,获得了双稳态系统的结构参数的最佳配置范围,且当外部激励频率处于低频段时,系统发电主要表现为超谐波发电,随着激励频率的增大,振动发电系统主要呈现基谐波发电。上述研究,为双稳态能量捕获装置的理论研究提供了参考。     

Propagation of harmonic perturbations in a thermoelastic medium with heat relaxation

The propagation of plane harmonic waves in a thermoelastic medium with heat-flux relaxation is studied; in particular, the dependences of the temperature and displacement on the coordinate are analyzed in a coupled formulation. The dependences of the group and phase velocities on frequency are investigated. The influence of the frequency and parameters of the material on the amplitude of thermoelastic waves is examined. The results are compared with the available results obtained using classical thermoelasticity theory.     

Thermoelastically coupled axisymmetric nonlinear vibration of shallow spherical and conical shells

The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of yon Ktirrntin and the theory of thermoelusticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin ‘ s technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors us well us boundary conditions on thermoelustically coupled nonlinear vibration behaviors are discussed.     

物性与温度相关材料广义热弹性模型及渐近分析

计及材料物性与温度的相关性,基于Clausius不等式和L-S广义热弹性理论,通过对自由能公式的高阶展开,构建了具有变物性特征的广义耦合热弹性动力学模型。推导了各向同性材料表面受热冲击问题的线性化控制方程组,利用热冲击的瞬时特征,借助于Laplace正、逆变换技术及其极限性质,给出了变物性条件下一维热冲击问题的温度场、位移场和应力场的渐近表达式。通过算例,得到了热冲击作用下各物理场的分布规律以及材料物性与温度相关性对于热弹性响应的影响规律。结果表明：材料物性与温度相关性对于各物理场的阶跃位置、阶跃间隔以及阶跃峰值均产生影响,但值得注意的是,相比于位移场和应力场的显著影响,其对温度场的影响效果并不明显。     

An approximate method of response analysis of vibrations for cracked beams

I.IntroductionTheinvestigationsonthed}'nan1icresponsesofcrackedbeamshavebeendonebymanyresearchers.Howeter,upti11now.totheauthors-knot"ledge,intheirwork,thereha\-ebeenmanypapersaboutnumericaln1ethodstobeusedasamainmeanstostudy,whileveryfewpapersab0utanalyt…     

On the Plane Orthotropic Stress Problem of Quasi-Static Thermoelasticity

The plane stress boundary value problem of quasi-static linear orthotropic thermoelasticity is discussed. The thermoelastic system on a bounded simply-connected domain is decoupled. The decoupled temperature equation is investigated by using accurate estimation and the contraction mapping principle. Representations of solutions of the field equation are obtained, and some solvability results are proved. The results are of both theoretical and numerical interest.     

复合干摩擦的准零刚度隔振系统的亚谐共振

利用增量平均法研究了复合干摩擦阻尼器的准零刚度非线性隔振系统在外部简谐激励作用下的1/3次亚谐共振. 首先利用平均法得到了复合干摩擦的准零刚度隔振系统的主共振近似解析解, 然后在系统主共振近似解析解的基础上将系统的亚谐共振响应看作增量, 并利用平均法得到了准零刚度隔振系统的亚谐共振近似解析解. 利用李雅普诺夫方法得到了准零刚度隔振系统主共振和亚谐共振稳态解的稳定性条件, 并推导了系统1/3次亚谐共振的存在条件. 根据近似解析解分别得到了复合干摩擦的准零刚度隔振系统的主共振和亚谐共振力传递率. 利用数值解验证了准零刚度隔振系统主共振和亚谐共振近似解析解的准确性. 利用系统的近似解析解详细分析了准零刚度参数和干摩擦力对系统主共振和亚谐共振的幅频响应以及力传递特性的影响. 分析结果表明, 通过选取合适的干摩擦力参数, 可以消除准零刚度隔振系统在主共振区域的亚谐共振. 通过复合干摩擦阻尼器不但可以提高准零刚度隔振系统在低频区域的振幅抑制效果, 而且可以降低准零刚度隔振系统的起始隔振频率, 但是会增大系统在有效隔振频带内的力传递率.      

多自由度线性阻尼系统的频域及时域响应分析

本文从分析频率方程解的形式出发，通过设定响应的频域形式，得出自由振动时域响应的显式解，并导出任意强迫振动的Ｄｕｈａｍｅｌ积分．文中的分析方法适用于系统质量、阻尼、刚度阵均为非对称的情形，且属于精确求解．     

Relaxation Effects of a Saturated Porous Media Using the Two-Dimensional Generalized Thermoelastic Theory

A model of the equations of a generalized thermoelasticity (GT) with relaxation times for a saturated porous medium is given in this article. The formulation can be applied to the GT theories: Lord–Shulman theory, Green–Lindsay theory, and Coupled theory for the porous medium. A two-dimensional thermoelastic problem that is subjected to a time-dependent thermal/mechanical source is investigated with the model of the generalized porous thermoelasticity. By using the Laplace transform and the Fourier transform technique, solutions for the displacement, temperature, pore pressure, and stresses are obtained with a semi-analytical approach in the transform domain. Numerical results are also performed for portraying the nature of variations of the field variables. In addition, comparisons are presented with the corresponding four theories.