Analytical Solutions for Laminated Transversely Isotropic Magnetoelectroelastic Plates

Abstract:

The theory of Hamiltonian system is introduced for the problems of laminated transversely isotropic magnetoelectroelastic plates. The partial differential equations of the magnetoelectroelastic solids are derived corresponding to the Lagrange density function and Legendre’s transformation. These equations are a set of the first-order Hamiltonian equations and expressed with displacements, electric potential and magnetic potential, as well as their dual variables--lengthways stress, electric displacement and magnetic induction in the symplectic geometry space. To obtain the solutions of the equations, the schemes of separation of variables and expansion of eigenvector of Hamiltonian operator matrix in the polar direction are implemented. The homogenous solutions of the equations consist of zero eigen-solutions and nonzero eigen-solutions. All the eigen-solutions of zero eigenvalue are obtained in the symmetric deformation. These solutions give the classical Saint-Venant’s solutions because the Hamiltonian matrix is symplectic. The method is rational, analytical method and does not require any trial functions.

• Periodical: Advanced Materials Research (Volumes 634-638)
• Pages: 2425-2431
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.634-638.2425
• Online since: January 2013
• Authors: Xiao Chuan Li, Qing Li
• Keywords: Analytical Solution, Hamiltonian System, Magnetoelectroelastic Plate, Symmetric Deformation, Symplectic Dual Method

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