基于Lord-Shulman理论的热弹性波在偶应力三明治固体中的反射和透射

Reflection and Transmission of Thermoelastic Waves in Couple⁃Stress Sandwich Solids Based on Lord⁃Shulman Theory

在温度急剧变化、短时间极速加热等极端情况下,基于Fourier定律的热流矢量与温度梯度成正比关系的经典热传导理论不能准确描述其物理过程.经典热弹性理论的热传导方程是抛物型的,而广义热弹性理论包含双曲型方程,热将以具有有限传播速度的波动形式传播.本文基于Lord-Shulman广义热弹性理论和修正偶应力弹性理论,得到在偶应力热弹性固体中四种色散波,研究热弹性波的传播和在偶应力固体三明治结构中的反射透射问题,重点研究横波入射时偶应力参数和热弛豫时间对各种热弹性耦合波反射透射系数的影响.

In extreme conditions such as rapid heating for short periods of time and rapid temperature changes,the classical heat conduction theory based on Fourier law,in which the heat flow vector is proportional to the temperature gradient,cannot accurately describe the physical process.The heat transfer equation of classical thermoelastic theory is parabolic,while the generalized thermoelastic theory contains hyperbolic equation,in which heat will propagate in a wave form with limited propagation speed.Based on the Lord Shulman generalized thermoelastic theory and the modified couple-stress elastic theory,in this paper we obtain four kinds of dispersion waves in the couple-stress thermoelastic solid,and study the propagation of the thermoelastic wave and its reflection and transmission in the couple-stress solid sandwich structure.The influences of couple-stress parameters and thermal relaxation time on the reflection and transmission coefficients of thermoelastic coupled waves are studied.