Abstract Current investigation deals with the generalized thermoelastic response of a finite hollow disk made of a piezoelectric material. The constitutive equations of the piezoelectric media are reduced to a two dimensional plane-stress state. To capture the finite speed of temperature wave, the single relaxation time theory of Lord and Shulman is used. Three coupled differential equations in terms of radial displacement, electric potential, and temperature change are obtained. These equations are written in a dimensionless presentation. With the aid of the differential quadrature method (DQM) a time-dependent algebraic system of equations is extracted. The Newmark time marching scheme is applied to trace the temporal evolution of temperature change, electric potential, radial displacement, stresses, and electric displacement. Numerical results demonstrate that radial displacement and temperature waves propagate with finite speed while the electric potential propagates with infinite speed.

中文翻译：

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基于 Lord-Shulman 理论的压电盘的广义热电弹性

摘要 当前的研究涉及由压电材料制成的有限空心圆盘的广义热弹性响应。压电介质的本构方程被简化为二维平面应力状态。为了捕捉温度波的有限速度，使用了 Lord 和 Shulman 的单一弛豫时间理论。得到了径向位移、电势和温度变化三个耦合的微分方程。这些方程以无量纲表示形式编写。借助微分正交法 (DQM)，可以提取出与时间相关的代数方程组。纽马克时间推进方案用于追踪温度变化、电势、径向位移、应力和电位移的时间演变。