Three-dimensional free vibration analysis of thick laminated combination shell using a meshfree approach

In this paper, a novel meshfree approach is proposed for the three-dimensional free vibration analysis of laminated composite combination shells. The three-dimensional theory of elasticity is applied to the formulation for free vibration analysis of thick laminated elliptical-cylindrical and conical-cylindrical combination shells, and the field functions are approximated by a novel meshfree Tchebychev-point interpolation method shape function using Tchebychev polynomials as the basis. The governing equation and boundary conditions for the individual layers of the substructures of the laminated combination shell 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 proposed method with those of literature and finite element program ABAQUS. The free vibration characteristics including natural frequencies and mode shapes of thick combination shells with various geometries and boundary conditions are presented through numerical examples. (c) 2021 Author(s).All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0061090