A global Ritz formulation for the free vibration analysis of hybrid metal-composite thick trapezoidal plates

A general variational formulation for free vibration analysis of hybrid (metalcomposite) plates with a trapezoidal platform is presented in this paper. The plate is composed of two distinguished parts in the span direction, where the inboard section is assumed to be made of an isotropic metal, and the outboard section is from a laminated composite material. Kinematics, corresponding to the First-order Shear Deformation plate Theory (FSDT), is used to take into account the non-classic eects of transverse shear deformation and rotational inertia for both sections in the analysis. The developed approach is based on the global Ritz method, where the transverse de ection and two rotations of the plate are independently approximated by simple and Legendre polynomials. The algorithm allows one to obtain an approximate analytical solution for the hybrid plate with dierent geometric aspect ratios, numbers of layers, staking sequences and metal to composite ratios. The results of the present work for special cases, including pure metal and pure composite plates, are in good agreement with previous works.