Abstract

In this study, the plane steady state thermoelastic frictional contact problem between a rigid cylindrical punch and a homogenous piezoelectric layer bonded to the rigid base is considered. The punch is assumed to be a perfect electric conductor and thermal insulator and slides over the piezoelectric layer with a small constant speed and heat flux is generated due to the friction. The general stress, displacement, and electrical expressions for the thermoelastic piezoelectric contact problem are derived using the theory of thermoelasticity and Fourier integral transform technique. Applying the boundary conditions, the present problem is reduced to Cauchy-type singular integral equations of the second kind in which the contact stress, the electrical displacement, and the contact width are unknown. The singular integral equations are solved numerically using Gauss–Jacobi and Gauss–Chebyshev integration formula with a developed effective method. The effect of moving velocity, friction coefficient, external load, electric charge, punch radius, and layer height on the contact stress, in-plane stress, electric displacement, and generated temperature are discussed in detail. This work is the first study that investigates a cylindrical punch on a thermoelastic contact of a piezoelectric layer.

摘要

在这项研究中，考虑了刚性圆柱冲头和粘合到刚性基座上的均匀压电层之间的平面稳态热弹性摩擦接触问题。冲头被假定为完美的电导体和热绝缘体，并以较小的恒定速度在压电层上滑动，并且由于摩擦而产生热通量。使用热弹性理论和傅里叶积分变换技术推导出热弹性压电接触问题的一般应力、位移和电气表达式。应用边界条件，将当前问题简化为第二类柯西型奇异积分方程，其中接触应力、电位移和接触宽度未知。奇异积分方程使用高斯-雅可比和高斯-切比雪夫积分公式以一种有效的方法进行数值求解。详细讨论了移动速度、摩擦系数、外载荷、电荷、冲头半径和层高对接触应力、面内应力、电位移和产生温度的影响。这项工作是第一项研究压电层热弹性接触上的圆柱形冲头。