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首页> 外文期刊>Applied Mathematical Modelling >Extensional wave motion in homogenous isotropic thermoelastic plate by using asymptotic method
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Extensional wave motion in homogenous isotropic thermoelastic plate by using asymptotic method

机译：渐近法在均质各向同性热弹性板上的伸缩波运动

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摘要

The present investigation is concerned with the study of extensional wave motion in an infinite homogenous isotropic, thermoelastic plate by using asymptotic method. The governing equation for the extensional wave motions have been derived from the system of three-dimensional dynamical equations of linear coupled theory of thermoelasticity. All coefficients of the differential operator are expressed as explicit functions of the material parameters. The velocity dispersion equation for the extensional wave motion is deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity are also derived. The thermoelastic Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established to that of asymptotic method. The dispersion curves for phase velocity and attenuation coefficient are shown graphically for extensional wave motion of the plates.
机译：本研究涉及利用渐近法研究无限均质各向同性热弹性板中的伸展波运动。拉伸波运动的控制方程是从热弹性线性耦合理论的三维动力学方程组中得出的。微分算子的所有系数都表示为材料参数的显式函数。从热弹性板波的瑞利-兰姆频率方程的三维模拟中推导出了延伸波运动的速度色散方程。还推导出了长波和短波的近似值以及群速度的表达式。将所考虑板的热弹性瑞利-兰姆频率方程按幂级数展开，以获得与渐近方法等效的多项式频率和速度色散关系。图中显示了板的扩展波运动的相速度和衰减系数的色散曲线。

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