Li Yueqiu, Wei Peijun
Department of Mathematics, Qiqihar University, Qiqihar, 161006, China.
Department of Applied Mechanics, University of Science and Technology Beijing, Beijing, 100083, China.
J Acoust Soc Am. 2018 Jan;143(1):550. doi: 10.1121/1.5020780.
The reflection and transmission of thermal elastic waves at the interface between two different dipolar gradient elastic solids are studied based on the generalized thermo-elastic theory of Green and Naghdi [(1993). J. Elasticity 31, 189-208] (type II of no energy dissipation). First, some thermodynamic formulas are generalized to a dipolar gradient elastic solid and the function of free energy density is postulated. Second, equations of thermal motion and constitutive relations in a dipolar gradient elasticity are derived. Then the nontraditional interfacial conditions are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Some numerical results of the reflection and transmission coefficients in the form of an energy flux ratio are given for different microstructure parameters while thermal parameters are fixed. The numerical results are validated by the consideration of energy conservation. It is found that there are a total of five modes of dispersive waves, namely, coupled MT1 wave, coupled MT2 wave, coupled MT3 wave, SV wave, and one evanescent wave which reduces to the surface waves at an interface, namely, SS wave. The thermal parameters mainly affect the coupled MT2 wave while the microstructure parameters affect not only the coupled waves but also the SS surface waves.
基于格林和纳格迪（1993年，《弹性力学杂志》第31卷，第189 - 208页）的广义热弹性理论（无能量耗散的II型），研究了热弹性波在两种不同偶极梯度弹性固体界面处的反射和透射。首先，将一些热力学公式推广到偶极梯度弹性固体，并假设自由能密度函数。其次，推导了偶极梯度弹性中的热运动方程和本构关系。然后，利用非传统界面条件确定反射波和透射波相对于入射波的振幅比。在热参数固定的情况下，给出了不同微观结构参数下以能量通量比形式表示的反射系数和透射系数的一些数值结果。通过考虑能量守恒对数值结果进行了验证。结果发现，共有五种色散波模式，即耦合MT1波、耦合MT2波、耦合MT3波、SV波，以及一种在界面处简化为表面波的倏逝波，即SS波。热参数主要影响耦合MT2波，而微观结构参数不仅影响耦合波，还影响SS表面波。
