A simple method to compute ultrasonic wave propagation in layered anisotropic media

Based on a simple second-order thin layer asymptotic expansion for the transfer matrix, an explicit asymptotic solution for the stiffness matrix for a generally anisotropic piezoelectric thin layer is obtained. The total transfer/stiffness matrix for thick layers or multilayers is calculated with arbitrary precision by subdividing these layers into thin sublayers and combining recursively the thin layer transfer/stifffiess matrices. It is shown that these methods converge to the exact solution and a hybrid transfer-stiffness matrix combination provides the smallest computational error. The new method is computationally stable, efficient and easy to implement. To solve by this method the wave propagation in a semi-space, the concept of a perfectly matched attenuating layer is introduced. The advantage of the method is that one does not need to compute the exact wave propagation solution for each anisotropic layer of the system and only the elastic constants of the layers are required. Examples are given for wave propagation in multidirectional composites and layered piezoelectric media.