A new meshfree approach for three-dimensional free vibration analysis of thick laminated doubly-shell of revolution

Abstract In this paper, a new meshfree approach is proposed for the three-dimensional free vibration analysis of laminated composite elliptical and paraboloidal shells of revolution. The three-dimensional theory of elasticity has been applied to formulations for free vibration analysis of laminated composite elliptical and paraboloidal shells of revolution. The field function is approximated by a new Tchebychev-point interpolation method (TPIM) shape function that uses the Tchebychev polynomial as the basis for the point interpolation method (PIM) shape function. The governing equation and boundary conditions for laminated elliptical and paraboloidal shells are obtained by combining the governing equation and boundary conditions for individual layers using a continuous condition. The artificial spring technique is introduced to generalize the boundary and continuous conditions, and the type of boundary conditions is selected according to the stiffness of the spring. The accuracy and reliability of the proposed method is verified through comparison with the results of literature and ABAQUS software. Free vibration characteristics such as natural frequency and mode shape of laminated elliptical and paraboloidal shells of revolution under various boundary conditions are presented through numerical examples.