A meshfree method for free vibration analysis of ply drop-off laminated rectangular plates

Abstract

The purpose of this paper is to develop a more effective meshfree shape function for free vibration analysis of ply drop-off laminated rectangular plates. The proposed meshfree Tchebychev-radial point interpolation method (TRIPM) shape function uses the Tchebychev polynomials and multi-quadrics (MQ) radial functions as the basis. The first order shear deformation theory (FSDT) is applied to the formulation for free vibration analysis of ply drop-off laminated rectangular plate, and the field functions are approximated by TRIPM shape function. The governing equations and boundary conditions for the substructures of ply drop-off laminated plate are derived, and the equations of the whole system are obtained by combining them using a continuous condition. The boundary and continuous conditions are generalized by the introduction of an artificial spring technique, and the type of boundary conditions is selected according to the spring stiffness. The accuracy and reliability of the proposed method are verified by comparing the results of the literature and the finite element program ABAQUS. The free vibration characteristics including natural frequencies and mode shapes of ply drop-off laminated rectangular plates with various geometrical dimensions and boundary conditions are presented through numerical examples.