Free vibration analysis of laminated rectangular plates with varying thickness using Legendre-radial point interpolation method

The purpose of this paper is to investigate the free vibration characteristics of laminated rectangular plate with varying thickness (LRPVT) using the meshfree strong form method. The theoretical formulation for free vibration analysis is based on the first order shear deformation theory (FSDT), and the governing equations for the LRPVT are derived using Hamilton's principle. In order to approximate the displacement function in the governing equations, a novel Legendre-radial point interpolation method (LRPIM) shape function using combined basis of thin plate spline (TPS) radial functions and Legendre polynomials is presented. The boundary conditions are generalized by the introduction of an artificial spring technique, and the type of boundary conditions is selected according to the spring stiffness values. The accuracy and reliability of the LRPIM shape function are verified by comparing with the results of the literatures and finite element software ABAQUS. The free vibration characteristics including natural frequencies and mode shapes of the LRPVT with various geometry and boundary conditions are presented through numerical examples.