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首页> 外文期刊>Journal of thermal stresses >PROPAGATION OF GENERALIZED VISCOTHERMO-ELASTIC RAYLEIGH-LAMB WAVES IN HOMOGENEOUS ISOTROPIC PLATES
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PROPAGATION OF GENERALIZED VISCOTHERMO-ELASTIC RAYLEIGH-LAMB WAVES IN HOMOGENEOUS ISOTROPIC PLATES

机译：均匀黏弹性Rayrayg-Lamb波在均质各向同性平板中的传播

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The present paper is aimed at studying the thermoelastic interaction in an infinite Kelvin-Voigt-type viscoelastic, thermally conducting plate. The upper and lower surfaces of the plate are subjected to stress-free, thermally insulated or isothermal conditions. The coupled dynamic thermoelasticity and generalized theories of thermo-elasticity, namely, Lord and Shulman's, Green and Lindsay's, and Green and Nagdhi's are employed to understand the thermomechanical coupling and thermal and mechanical relaxation effects. Secular equations for the plate in closed from and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms are derived. In the absence of mechanical relaxations (viscous effect), the results for generalized and coupled theories of thermoelasticity have been 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. The various forms and regions of Rayleigh-Lamb-type secular equation have been obtained and discussed in addition to Lame modes, decoupled shear horizontal (SH) modes, and thin-plate results. At short-wavelength limits, the secular equations for symmetric and skew-symmetric waves in a stress-free insulated and stress-free isothermal plate reduce to the Rayleigh surface wave frequency equation. The amplitudes of temperature and displacement components during symmetric and skew-symmetric motion of the plate have been computed and discussed. Finally, the numerical solution is carried out for copper material. The dispersion curves, and amplitudes of temperature change and displacements for symmetric and skew-symmetric wave modes are presented to illustrate and compare the theoretical results.
机译：本文旨在研究无限Kelvin-Voigt型粘弹性导热板中的热弹性相互作用。板的上下表面均处于无应力，隔热或等温的条件下。耦合的动态热弹性和广义的热弹性理论，即Lord和Shulman的，Green和Lindsay的以及Green和Nagdhi的，用于理解热机械耦合以及热和机械松弛效应。推导了在完全分离的条件下，对称和倾斜对称波模式传播在封闭和隔离数学条件下封闭的板的长期方程。在没有机械松弛（粘滞效应）的情况下，作为特殊情况，可以从导出的长期方程中获得广义和耦合热弹性理论的结果。在没有热机械耦合的情况下，可以从本发明推导出对粘弹性板的分析。除了Lame模式，解耦剪切水平（SH）模式和薄板结果外，还获得并讨论了Rayleigh-Lamb型长期方程的各种形式和区域。在短波极限下，无应力绝缘和无应力等温板中对称波和斜对称波的长期方程简化为瑞利面波频率方程。计算并讨论了板对称和斜对称运动过程中温度和位移分量的振幅。最后，对铜材料进行了数值求解。给出了对称和斜对称波模的色散曲线，温度变化幅度和位移，以说明和比较理论结果。

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