Free vibration of soft-core sandwich panels with general boundary conditions by harmonic quadrature element method

In this paper, the harmonic quadrature element method is presented for free vibration analysis of soft-core sandwich panels with general boundary conditions. To remove limitations existing in various beam theories, the thin faces are modeled by Euler-Bernoulli beam theory but the soft-core is directly modeled by two-dimensional elasticity theory. A novel harmonic quadrature sandwich panel element with arbitrary number of nodes is developed and the equation of motion is established utilizing Hamilton principle. Explicit formulations are worked out to ease the implementation of the element. To show the applicability of the method, several examples, including two types of core material and five combinations of boundary conditions, are investigated. Results are compared to existing data as well as finite element data of ABAQUS. Comparisons show that the proposed method exhibits a high convergence rate and can yield accurate results in all cases.