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

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