A piecewise shear deformation theory for free vibration of composite and sandwich panels

The new piecewise low and high order shear deformation models, which contain the in-plane rigidity and the transverse shear rigidity of the core and skins, are proposed in this paper. The partial differential governing equations are obtained by applying Hamilton's principle, aiming to attain the natural frequencies for the sandwich panel constituted of orthotropic materials. The frequency equation is explicitly expressed for simply supported rectangular sandwich panel. The effects of the thickness and elastic modulus of the core on the fundamental frequency are also discussed in this paper. The results obtained from the proposed models are compared with those obtained from the classical analytical models, FEM, low and high order shear deformation theory, which verifies the theories have theoretical accuracy and broad application.