A wave propagation method in symplectic space for the vibration analysis of thin plates

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Journal of Vibration and Shock ›› 2014, Vol. 33 ›› Issue (12) : 1-6.

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A wave propagation method in symplectic space for the vibration analysis of thin plates

ZHANG Ya-hui, Ma Yong-bin

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Abstract

A new approach is presented for the steady state vibration analysis of thin plates which is based on the symplectic method of elasticity problem and the theory of wave propagation. The governing equations of thin plates are introduced into the symplectic duality system, the eigenvalue equations are formulated by applying the method of variable separation, and the eigenvalues (wave propagation parameters) and eigenvectors (wave modes) can be obtained. The equations of motion in physical domain are then transformed into “wave co-ordinates”, and the forced responses of thin plates are deduced by using the incident and reflection wave components. Taking a rectangular thin plate as an illustrative example, numerical results of the input mobility, kinetic energy and strain energy of the plate based on two combinations of simply supported (S) and clamped (C) boundary conditions, CCSS and SSSS, are computed. The accuracy and efficiency of the method are validated by comparing with the analytic solutions of the mode superposition method, the wave finite element method and ABAQUS software.

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symplectic duality system / waveguide / wave finite element / wave propagation

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ZHANG Ya-hui;Ma Yong-bin. A wave propagation method in symplectic space for the vibration analysis of thin plates[J]. Journal of Vibration and Shock, 2014, 33(12): 1-6