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A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates
Andrianarison, O. Benjeddou, Ayech
Andrianarison, O.
Benjeddou, Ayech
Date
2024-11
Advisor
Type
Article
Degree
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Chapter 9.pdf
Adobe PDF, 894.06 KB
Description
Abstract
A new Hamiltonian semi-analytical method is established to investigate the free vibration characteristics of piezoelectric multilayered plates. By performing a Legendre Transform, the classical Lagrangian functional is recast into a Hamiltonian one, so that the resulting variational formulation can be expressed in terms of the displacements and electric potential and their transverse stresses and electric displacement dual variables. Within the framework of this Hamiltonian formalism, the in-plane of the piezoelectric multilayered plate is discretized into two-dimensional p-type high-order spectral finite elements while the resulting first-order one dimensional differential system is solved analytically by enforcing the interface continuity constraints. The whole piezoelectric multilayered plate’s dynamic stiffness is then built, from which its circular frequencies are computed with the help of the Wittrick-Williams algorithm. A detailed discussion is provided on the implementation aspects, followed by some numerical examples to assess the robustness, accuracy and effectiveness of the proposed method. The obtained results are verified by comparison with published ones based on conventional approaches.