Free vibration analysis of laminated closed conical, cylindrical shells and annular plates with a hole using a meshfree method

Abstract

In this paper, a novel meshfree approach is proposed for the free vibration analysis of laminated closed conical, cylindrical shells and annular plate with a hole. The theoretical formulation for free vibration analysis is based on the first order shear deformation theory (FSDT) and the field functions are approximated by a Tchebychev-radial point interpolation method (TRIPM) shape function using various radial functions augmented with Tchebychev polynomials as the basis. A laminated closed shell with a hole is decomposed into five open shells without holes, and continuous conditions of displacement are applied at the interfaces between the open shells. The governing equations and boundary conditions for the laminated open shells without hole are derived using Hamilton’s principle. The boundary and continuous conditions are generalized by the introduction of an artificial spring technique, and the type of the conditions is selected according to the spring stiffness values. A comparison with the results of the literatures and finite element software ABAQUS is conducted to verify the accuracy and reliability of the proposed method. The investigation of the vibration characteristics of the laminated closed conical, cylindrical shells and annular plates with a hole according to various radial functions, geometric dimensions and boundary conditions is presented through numerical examples.