A semi-analytical model for free and forced vibration analysis of axial directional FG-GPLRC spherical shell in thermal environment

Understanding the impact of novel gradient materials on the dynamic performance of aerospace thin-walled structures is crucial. This study develops a semi-analytical framework for the free and forced vibration analysis of axially functionally graded graphene platelet-reinforced composite (AFG-GPLRC) spherical shells in a steady-state thermal environment. Temperature-dependent material properties are evaluated using the Halpin-Tsai model and mixture rules, while an area-weighted normalization method is introduced to construct five axial GPL distribution patterns with the same total mass. Based on the first-order shear deformation theory (FSDT), Gegenbauer polynomials and Fourier functions are employed to approximate admissible functions. Virtual spring technology is applied to describe arbitrary boundary conditions, and the governing equations are derived from Lagrange equations. Modal superposition is utilized to obtain harmonic displacement responses and actual vibration shapes. Convergence studies demonstrate the stability and efficiency of the method, and comparisons with published reference and Abaqus simulations confirm its accuracy for both natural characteristics and forced responses. A single run of the proposed method requires approximately 1s. Furthermore, the effects of GPL distribution patterns, weight fraction, opening angle, temperature difference, and boundary conditions on the vibration performance are analyzed. The proposed model provides an efficient tool for the vibration analysis and gradient design of AFG-GPLRC spherical shells in a thermal environment.