A Generalized Method for Dispersion Analysis of Guided Waves in Multilayered Anisotropic Magneto-Electro-Elastic Structures

Abstract

Based on the symplectic structure of the Hamiltonian matrix, the precise integration method (PIM), and the Wittrick–Williams (W-W) algorithm, a generalized method for computing the dispersion curves of guided waves in multilayered anisotropic magneto-electro-elastic (MEE) structures for different types of mechanical, electrical, and magnetical boundaries is developed. A strictly theoretical analysis shows that the W-W algorithm cannot be applied directly to the MEE structure. This is because a block of the Hamiltonian matrix is not positive definite for MEE structures so that the eigenvalue count of the sublayer is not zero when the divided sublayer is sufficiently thin. To overcome this difficulty, based on the symplectic structure of the Hamiltonian matrix, a symplectic transformation is introduced to ensure that the W-W algorithm can be applied conveniently to solve wave propagation problems in multilayered anisotropic MEE structures. The application of the PIM based on the mixed energy matrix to solve the wave equation can ensure the stability and efficiency of the method, and all eigenfrequencies are found without the possibility of any being missed using the W-W algorithm. This research provides the necessary insight to apply the W-W algorithm in wave propagation and vibration problems of MEE structures.