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

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 ty...

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Bibliographic Details
Published in:Shock and vibration 2022, Vol.2022, p.1-16
Main Authors: Zhang, Yanhui, Gao, Qiang
Format: Article
Language:English
Subjects:
Algorithms
Anisotropy
Dispersion curve analysis
Eigenvalues
Elastic anisotropy
Magnetic fields
Mathematical analysis
Matrices (mathematics)
Methods
Numerical analysis
Propagation
Resonant frequencies
Wave equations
Wave propagation
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Summary: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.
ISSN:1070-9622
1875-9203
DOI:10.1155/2022/1346719