压电空心圆柱中波的传播

WAVE PROPAGATION IN THE PIEZOELECTRIC HOLLOW CYLINDER

应用三维压电弹性体轴对称模型对压电空心圆柱中波的传播进行了研究,发现在圆柱中是否具有压电性质会对波的传播带来显著的差异,当波长趋向于零时,在压电圆柱中拟P波的波速渐进趋向于横观各向同性弹性体的准P波波速,而非压电圆柱中拟P波的波速渐进趋向于一维杆模型中的P波波速;在压电圆柱中拟SV波存在驻波现象,圆柱中的SH波同电场无关,所以在压电圆柱和非压电圆柱中SH波具有相同的频散曲线。应用积分变换方法将圆柱的控制方程同其侧边界条件相结合,得到了一组动力学方程,针对具体的侧边界条件,得到相对应的波导条件和频散方程,在此基础上通过数值计算模拟了圆柱受到端部应力脉冲激励后的瞬态响应,同时讨论了空心圆柱的半径比对轴向波传播的影响。

In this article, the wave propagation in the piezoelectric hollow cylinder is investigated by applying 3-D piezoelectric elastic axial symmetric model. While the cylinder has piezoelectric property, its guided wave very differs with the non-piezoelectric cylinder. When the wavelength tends to zero, the velocity of simulation-P wave (sim-P wave) in the piezoelectric cylinder asymptotically tends to the quasi-P wave velocity of transverse isotropic elastic body, but the velocity of sim-P wave in the non-piezoelectric cylinder asymptotically tends to the P wave velocity of 1-D bar model. The sim-SV wave in the piezoelectric cylinder has the standing wave phenomenon. The SH wave is independent of electric field, so the piezoelectric and non-piezoelectric cylinders have the same frequency dispersion curves about SH wave. In this paper, using Integral Transform Method to combine the boundary condition and the governing equations together, a group of dynamics equations, which are about the displacements and electric potential, is derived. To the assured boundary condition, the guided-wave condition and the frequency dispersion equations are obtained. Above such solution, the transient responses under a stress pulse at the end are simulated. At last the effect to the wave propagation about the radius' ratios of the hollow cylinders is discussed.