Axisymmetric free vibrations of infinite micropolar thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Rayleigh lamb waves in micropolar isotropic elastic plate

The propagation of waves in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. At short wave limit, the secular equations for symmetric and skew symmetric waves in a stress free circular plate reduces to Rayleigh surface wave frequency equation. Thin plate results are also obtained. The amplitudes of displacements and microrotation components are obtained and depicted graphically. Some special cases are also deduced from the present investigations. The secular equations for symmetric and skew symmetric modes are also presented graphically.     

Free vibration of microstretch thermoelastic plate with one relaxation time

The propagation of waves in microstretch thermoelastic homogeneous isotropic plate subjected to stress free thermally insulated and isothermal conditions is investigated in the context of conventional coupled thermoelasticity (CT) and Lord and Shulman (L–S) theories of thermoelasticity. The secular equations for both symmetric and skew-symmetric wave mode propagation have been obtained. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation. The amplitudes of dilatation, microrotation, microstretch and temperature distribution for the symmetric and skew symmetric wave modes are computed analytically and presented graphically for different theories of thermoelasticity. The theoretical and numerical computations are found to be in close agreement.     

Analysis of plane waves in anisotropic thermoelastic diffusive medium

This paper concentrates on the study of the propagation of harmonic plane waves in a homogeneous anisotropic thermoelastic diffusive medium in the context of different theories of thermoelastic diffusion. It is found that five types of waves propagate in an anisotropic thermoelastic diffusive medium, namely a quasi-elastodiffusive (QED-mode), two quasi-transverse (QSH-mode and QSV-mode), a quasi-mass diffusive (QMD-mode) and a quasi-thermo diffusive (QTD-mode) wave. The governing equations for homogeneous transversely isotropic diffusive medium in different theories of thermoelastic diffusion are taken as a special case. It is noticed that when plane waves propagate in one of the planes of transversely isotropic thermoelastic diffusive solid, purely quasitransverse wave mode(QSH) decouples from rest of the motion and is not affected by the thermal and diffusion vibrations. On the other hand, when plane waves propagate along the axis of solid, two quasi-transverse wave modes (QSH and QSV) decouple from the rest of the motion and are not affected by the thermal and diffusion vibrations. From the obtained results, the different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically for a single crystal of magnesium. The effects of diffusion and relaxation times on phase velocity, attenuation coefficient, specific loss and penetration depth has been studied. Some particular cases are also discussed.     

Propagation of waves in the transversely isotropic thermoelastic Green-Naghdi type II and type III medium

The article is presented to enhance our knowledge about the propagation of the Rayleigh-Lamb waves in the layer of a transversely isotropic medium in the context of thermoelastic model of GN type II and type III. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. Amplitudes of displacements and temperature distributions are also obtained. Finally, a numerical solution is found for cobalt as a medium material, and dispersion curves, amplitudes of displacements, and temperature distributions for symmetric and skew-symmetric wave modes are presented. Some particular cases are also deduced.     

Lamb waves in micropolar thermoelastic solid plates immersed in liquid with varying temperature

In the present paper the theory of micropolar generalized thermoelastic continua has been employed to study the propagation of plane waves in micropolar thermoelastic plates bordered with inviscid liquid layers (or half-spaces) with varying temperature on both sides. The secular equations in closed form and isolated mathematical conditions are derived and discussed. Thin plate and short wave length results have also been deduced under different cases and situations and discussed as special cases of this work. The results in case of conventional coupled and uncoupled theories of thermoelasticity can be obtained both in case of micropolar elastic and elastokinetics from the present analysis by appropriate choice of relevant parameters. The various secular equations and relevant relations have been solved numerically by using functional iteration method in order to illustrate the analytical developments. Effect of characteristic length and coupling factors have also been studied on phase velocity. The computer simulated results in case of phase velocity, attenuation coefficient and specific loss of symmetric and skew symmetric are presented graphically.     

Propagation of Rayleigh waves on free surface of transversely isotropic generalized thermoelastic diffusion

The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized thermoelastic diffusion theory. The Green-Lindsay（GL） theory is used in the study. In this theory, thermodiffusion and thermodiffusion mechanical relaxations are governed by four different time constants. Secular equations for surface wave propagation in the considered media are derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient are graphically presented in order to present the analytical results and make comparison. Some special cases of frequency equations are derived from the present investigation.     

Degenerate weakly non-linear elastic plane waves

Weakly non-linear plane waves are considered in hyperelastic crystals. Evolution equations are derived at a quadratically non-linear level for the amplitudes of quasi-longitudinal and quasi-transverse waves propagating in arbitrary anisotropic media. The form of the equations obtained depends upon the direction of propagation relative to the crystal axes. A single equation is found for all propagation directions for quasi-longitudinal waves, but a pair of coupled equations occurs for quasi-transverse waves propagating along directions of degeneracy, or acoustic axes. The coupled equations involve four material parameters but they simplify if the wave propagates along an axis of material symmetry. Thus, only two parameters arise for propagation along an axis of twofold symmetry, and one for a threefold axis. The transverse wave equations decouple if the axis is fourfold or higher. In the absence of a symmetry axis it is possible that the evolution equations of the quasi-transverse waves decouple if the third-order elastic moduli satisfy a certain identity. The theoretical results are illustrated with explicit examples.     

Effect of Rotation on Rayleigh—Lamb Waves in an Isotropic Generalized Thermoelastic Diffusive Plate

The present investigation is aimed at studying the effect of rotation on propagation of Rayleigh—Lamb waves in a homogeneous isotropic thermoelastic diffusive plate of finite width in the framework of different theories of thermoelasticity, including the Coriolis and centrifugal forces. The medium is subjected to stress-free, thermally insulated, isothermal, and chemical potential boundary conditions and is rotating about an axis perpendicular to its plane. Secular equations corresponding to the symmetric and skew-symmetric modes of the plate are derived. Phase velocities and attenuation coefficients of various possible modes of wave propagation are computed from the secular equations. Amplitudes of displacements, temperature, and concentration for symmetric and skew-symmetric modes of plate vibrations are computed numerically. The computed results are presented graphically.     

Effect of relaxation times on circular crested waves in thermoelastic diffusive plate

The propagation of circularly crested thermoelastic diffusive waves in an infinite homogeneous transversely isotropic plate subjected to stress free, isothermal/insulated and chemical potential conditions is investigated in the framework of different thermo- elastic diffusion theories. The dispersion equations of thermoelastic diffusive Lamb type waves are derived. Some special cases of the dispersion equations are also deduced.     

GUIDED THERMOELASTIC WAVE PROPAGATION IN LAYERED PLATES WITHOUT ENERGY DISSIPATION

In this paper, the propagation of guided thermoelastic waves in laminated orthotropic plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The validity of the method is confirmed through a comparison. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement and temperature distributions are shown to discuss the differences between the elastic modes and thermal modes.     

Effect of rotation on generalized thermo-viscoelastic Rayleigh–Lamb waves

The present paper is aimed at studying the effects of rotation on the thermoelastic interaction in an infinite Kelvin–Voigt-type viscoelastic, thermally conducting plate rotating about the normal to its faces with uniform angular velocity. This facilitates the decoupling of anti-plane/in-plane motion which is not possible, in general. The upper and lower surfaces of the plate are subjected to stress-free, thermally insulated or isothermal conditions. The formulation is applied according to three theories of the generalized thermoelasticity: Lord-Shulman with one relaxation time, Green–Lindsay with two relaxation times, as well as the coupled theory. Secular equations are derived for the plate in closed form isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms. In the absence of mechanical relaxations (Rotation and viscous effects), the results for generalized and couple theories of thermoelasticity were obtained as particular cases from the derived secular equations. In the absence of thermomechanical coupling, the analysis for a viscoelastic plate can be deduced from the present one. Finally the numerical solution is carried out for copper material. The function iteration numerical scheme is used to solve the complex secular equations, in order to obtain phase velocity and attenuation coefficients of propagating wave mode. The dispersion curves and attenuation coefficients profiles so obtained for symmetric and skew-symmetric wave modes are presented graphically to illustrate and compare the theoretical results in the presence and absence of rotation. The study may be useful in the construction and design of gyroscopes and rotation sensors as well as in the application in diverse fields.     

Effect of a biasing electric field on the propagation of symmetric Lamb waves in piezoelectric plates

This paper is concerned with the effect of a biasing electric field on the propagation of Lamb waves in a piezoelectric plate. On the basis of three dimensional linear elastic equations and piezoelectric constitutive relations, the differential equations of motion under a biasing electric field are obtained and solved. Due to the symmetry of the plate, there are symmetric and antisymmetric modes with respect to the median plane of the piezoelectric plate. According to the characteristics of symmetric modes (odd potential state) and antisymmetric modes (even potential state), the phase velocity equations of symmetric and antisymmetric modes of Lamb wave propagation are obtained for both electrically open and shorted cases. The effect of a biasing electric field on the phase velocity, electromechanical coupling coefficient, stress field and mechanical displacement of symmetric and antisymmetric Lamb wave modes are discussed in this paper and an accompanying paper respectively. It is shown that the biasing electric field has significant effect on the phase velocity and electromechanical coupling coefficient, the time delay owning to the velocity change is useful for high voltage measurement and temperature compensation, the increase in the electromechanical coupling coefficient can be used to improve the efficiency of transduction.     

横观各向同性液体饱和多孔介质中平面波的传播

基于孔隙介质的Ｂｉｏｔ理论１，研究了横观各向同性液体饱和多孔介质中平面波的传播特性。首先导出了波传播的特征方程并给出了其解析解，结果显示：有４种不同波速的平面体波传播；第一准纵波，第二准纵波，准横波和反平面横波。文中给出了波速和衰减的解析表达式，数值计算了频散曲线和衰减曲线，并讨论了各类准体波位移之间的耦合关系。     

非局部广义热弹性理论下半导体微结构中波的反射研究

论文基于非局部热弹性理论,研究了纳米半导体介质中波的反射问题。首先建立了在耦合的非局部弹性理论,波型热传导理论和等离子扩散理论下问题的控制方程;然后运用谐波法,得到耗散方程的解以及反射系数率的解析表达式;最后通过数值计算给出了硅纳米结构中相速度、群速度随非局部参数的变化,讨论了非局部参数、热电耦合参数以及热弹性耦合参数对反射系数率的影响。     

轴对称热载作用厚板的热弹性运动效应分析

对板的上下表面存在一般温度边界条件的情况，解出了板表面受轴对称热辐射作用时，板内轴对称二维瞬态温度场的一般表达式；导出了厚板的热弯曲运动和热平面运动的位移型动力学方程，得出了板的挠度、转角和平面径向位移的无穷积分型公式；提出了一个求解弯曲波传播速度的方法；然后完成了一个代表性算例分析，给出了弯曲波传播规律的直观图象，得出了热加载和热卸载过程中，板内热弯曲波的时空变化特点；找出了剪切变形和旋转惯性对弯曲波传播速度的影响规律；最后，将理论结果与相应的实验结果进行了比较，两者吻合良好。     

偏压电场对压电板中Lamb波相速度的影响

本文研究了偏压电场作用下,Lamb波在压电板中的传播行为，首先给出了偏压电场作用时压电板中的应力场及电位移场，然后通过求解含初应力及初电位移的小幅波动问题的耦合方程，分别给出了Lamb波的对称模态和反对称模态的相速度方程，以典型的PZT－5H压电陶瓷板为例进行了数值计算,并讨论了偏压电场对Lamb波相速度及频散曲线的影响，结果表明，偏压电场可以显著地改变Lamb波的传播速度，借此可使声波器件获得延时效果。     

Inhomogeneous waves at the boundary of a generalized thermoelastic anisotropic medium

The Christoffel equation is derived for the propagation of plane harmonic waves in a generalized thermoelastic anisotropic (GTA) medium. Solving this equation for velocities implies the propagation of four attenuating waves in the medium. The same Christoffel equation is solved into a polynomial equation of degree eight. The roots of this equation define the vertical slownesses of the eight attenuating waves existing at a boundary of the medium. Incidence of inhomogeneous waves is considered at the boundary of the medium. A finite non-dimensional parameter defines the inhomogeneity of incident wave and is used to calculate its (complex) slowness vector. The reflected attenuating waves are identified with the values of vertical slowness. Procedure is explained to calculate the slowness vectors of the waves reflected from the boundary of the medium. The slowness vectors are used, further, to calculate the phase velocities, phase directions, directions and amounts of attenuations of the reflected waves. Numerical examples are considered to analyze the variations of these propagation characteristics with the inhomogeneity and propagation direction of incident wave. Incidence of each of the four types of waves is considered. Numerical example is also considered to study the propagation and attenuation of inhomogeneous waves in the unbounded medium.     

Wave propagation in thermally conducting linear fibre-reinforced composite materials

The propagation of plane waves in a fibre-reinforced, anisotropic, generalized thermoelastic media is discussed. The governing equations in x–y plane are solved to obtain a cubic equation in phase velocity. Three coupled waves, namely quasi-P, quasi-SV and quasi-thermal waves are shown to exist. The propagation of Rayleigh waves in stress free thermally insulated and transversely isotropic fibre-reinforced thermoelastic solid half-space is also investigated. The frequency equation is obtained for these waves. The velocities of the plane waves are shown graphically with the angle of propagation. The numerical results are also compared to those without thermal disturbances and anisotropy parameters.