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Waves in thermoelastic solid half-space containing voids with liquid loadings
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-07-03 , DOI: 10.1002/zamm.202100093
Vijayata Pathania 1 , Pallvi Joshi 1
Affiliation  

The influence of the voids in the propagation of time-harmonic plane waves in a semi-infinite homogeneous isotropic thermoelastic medium in contact with inviscid liquid half-space has been explored under the Lord-Shulman theory of thermoelasticity. The incompressible and non-viscous liquid is taken in the upper half-space and the effect of gravity on the whole system is assumed to be negligible. The mathematical model is developed and the exact expressions for the considered variables are obtained by using the normal mode analysis method. The compact secular equation for the considered model is derived for thermally insulated and isothermal cases respectively. There exist four waves in the generalized thermoelastic porous solid half-space and one wave exists in the liquid half-space. In the solid half-space, one is a transverse wave and the remaining three is the set of coupled dilatational waves. The coupling among these waves is because of the presence of voids and thermal effects, also the amplitude of oscillation of these waves decreases with time. The transverse wave in the solid half-space is undamped in time and remains independent of the effects of voids and heat. The particle's motion is deduced for Rayleigh wave propagation and found to be elliptical in solid half-space and circular in liquid half-space. Also, the plane of particle motion is tilted due to the presence of void parameters in the medium. Magnesium crystal has been chosen for the numerical computation and the discussion of various graphs depicting the profiles are presented in the last section.

中文翻译:

包含带液体载荷的空隙的热弹性固体半空间中的波

在 Lord-Shulman 热弹性理论下,已经探索了空隙对时谐平面波在与无粘性液体半空间接触的半无限均匀各向同性热弹性介质中传播的影响。上半空间取不可压缩的非粘性液体,假设重力对整个系统的影响可以忽略不计。建立了数学模型,并通过使用正态模态分析方法获得了所考虑变量的精确表达式。所考虑模型的紧凑长期方程分别针对绝热和等温情况导出。广义热弹性多孔固体半空间存在四种波,液体半空间存在一种波。在固体半空间中,一个是横波,其余三个是耦合膨胀波的集合。这些波之间的耦合是因为存在空隙和热效应,而且这些波的振荡幅度随时间减小。固体半空间中的横波在时间上不受阻尼,并且不受空隙和热量的影响。推导出瑞利波传播的粒子运动,发现在固体半空间中为椭圆形,在液体半空间中为圆形。此外,由于介质中存在空隙参数,粒子运动平面会倾斜。已选择镁晶体进行数值计算,最后一节介绍了描绘轮廓的各种图表。这些波之间的耦合是因为存在空隙和热效应,而且这些波的振荡幅度随时间减小。固体半空间中的横波在时间上不受阻尼,并且不受空隙和热量的影响。推导出瑞利波传播的粒子运动,发现在固体半空间中为椭圆形,在液体半空间中为圆形。此外,由于介质中存在空隙参数,粒子运动平面会倾斜。已选择镁晶体进行数值计算,最后一节介绍了描绘轮廓的各种图表。这些波之间的耦合是因为存在空隙和热效应,而且这些波的振荡幅度随时间减小。固体半空间中的横波在时间上不受阻尼,并且不受空隙和热量的影响。推导出瑞利波传播的粒子运动,发现在固体半空间中为椭圆形,在液体半空间中为圆形。此外,由于介质中存在空隙参数,粒子运动平面会倾斜。已选择镁晶体进行数值计算,最后一节介绍了描绘轮廓的各种图表。固体半空间中的横波在时间上不受阻尼,并且不受空隙和热量的影响。推导出瑞利波传播的粒子运动,发现在固体半空间中为椭圆形,在液体半空间中为圆形。此外,由于介质中存在空隙参数,粒子运动平面会倾斜。已选择镁晶体进行数值计算,最后一节介绍了描绘轮廓的各种图表。固体半空间中的横波在时间上不受阻尼,并且不受空隙和热量的影响。推导出瑞利波传播的粒子运动,发现在固体半空间中为椭圆形,在液体半空间中为圆形。此外,由于介质中存在空隙参数,粒子运动平面会倾斜。已选择镁晶体进行数值计算,最后一节介绍了描绘轮廓的各种图表。
更新日期:2021-07-03
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