A unified spectral-geometric model of FGM double conical/cylindrical/spherical shell coupled with annular plates

Abstract

This paper presents the analysis of the free and force vibration characteristics of FGM double layered cylindrical/conical/spherical shell and annular plate coupled structures under various boundary conditions and coupled connection conditions. The spectral geometry method is utilized to represent the displacement variable for FGM shell and annular plate structures in the uniform form, which overcomes the discontinuity or jump phenomenon at the boundary. To simulate the boundary conditions and coupling connection relationship between the FGM plate and shell substructures, the artificial virtual spring technique is implemented by adjusting the stiffness values of linear or rotational springs. Based on the Rayleigh-Ritz procedure, the unified dynamic equations of the FGM double layered cylindrical/conical/spherical shell and annular plate coupled structures are derived. Numerical examples are provided to demonstrate the convergence of the proposed model, and the accuracy and correctness of the proposed analytical model are verified by comparing the results with the vibration results obtained by the finite element method. Furthermore, parametric analysis is conducted to investigate the effect of material parameters, geometric parameters, and position parameters on the inherent characteristics and steady-state response of the FGM double layered coupled structure under various boundary conditions. Overall, this paper contributes to the understanding of the dynamic behavior of FGM double layered coupled structures and provides a useful analytical tool for the design and optimization of such structures.