Numerical algorithm for dynamic problems of viscoelastic sandwich plates based on improved Fourier series
In this paper,a new numerical algorithm based on improved Fourier series is proposed to determine the free vibration characteristics of viscoelastic sandwich plates under arbitrary boundary conditions.The algorithm uses the first-order shear theory to establish the out-of-plane displacement field and the improved Fourier series to fit the displacement tolerance function,combines the Rayleigh-Ritz method to calculate the kinetic energy and potential energy,and uses the Hamilton variational principle to obtain the characteristic matrix equation.The results show that the errors of the natural frequencies and loss factors obtained by the algorithm are not more than 1％compared with the analytical solution,2D finite element solution,numerical calculation method and ABAQUS finite element software,whether it is a beam-plate structure or a sandwich plate structure under various boundary conditions.The calculation efficiency is increased by 10 times,and the limitation that the traditional method can only solve the vibration problem under specific boundary conditions is overcome.The method established in this paper has the characteristics of fast convergence,high calculation efficiency and strong adaptability.
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