含压电谱单元及其在板结构中Lamb波传播模拟中的应用

结合压电材料本构方程及Lamb波数值模拟中的谱有限元方法，建立了含压电驱动器/传感器板的谱单元，并将其应用于Lamb波的激发、在板结构中的传播和接收的数值模拟中。将模拟结果与其他文献中的数值模拟结果及采用商用有限元软件ANSYS的数值模拟结果进行了对比，验证了所建立单元的正确性，且在计算精度相差不大的情况下，该方法较传统有限元方法更为高效。最后和以前不含压电的模拟过程进行比较，压电效应使得驱动器施加在节点上的力并不那么单一，并且传感器能够将多个自由度复杂的位移信号转换为单一的电信号，这使得考虑压电片与不考虑压电片的模拟结果之间有一定的差别。

Spectral Element with Piezoelectric Patches and Its Applications in Simulation of Lamb Wave Propagation in Plates

This paper combined constitutive equations of piezoelectric material and the SEM used in Lamb wave simulation frequently to develop a plate spectral element with piezoelectric actuator/sensor, and applied it in the numerical simulations of actuation, propagation and receiving of Lamb wave in plates. Comparisons with numerical simulation results reported in literatures and with the results obtained by using commercial software ANSYS verify the correctness of the proposed element. It is also shown that the SEM is more effective than traditional FEM in obtaining results with same accuracy. Finally, comparisons were made for the simulation results obtained without and with considering piezoelectric patches. It is clearly seen that due to the piezoelectric effect, a single force is applied at one node, and the output electric signal by the sensor is the combined effect of several displacements from nodes of element connected to the sensor. Therefore, slightly difference exists in the response signals obtained without and with considering piezoelectric patches.