Vibration Analysis of Functionally Graded Material (FGM) Double-Layered Cabin-like Structure by the Spectro-Geometric Method

This study presents a spectro-geometric vibration model for analyzing free as well as forced vibration properties for FGM cylindrical double-walled shells with internal structures. The boundary conditions and coupling effects are modeled using an artificial virtual spring approach, which allows for the simulation of arbitrary boundary and coupling conditions by varying the elastic spring stiffness coefficients. The spectral geometry method is employed to represent the displacement variables of the FGM substructure, overcoming the discontinuity phenomenon commonly observed when traditional Fourier series are used. The dynamic equations of the FGM cylindrical double-walled shell with an internal structure are derived using the first-order shear deformation assumption and the Rayleigh–Ritz method, and the corresponding vibration solutions are computed. The model’s reliability and prediction accuracy are confirmed through convergence checks and numerical comparisons. Additionally, parametric studies are conducted to examine the influence of material constants, position parameters, and geometric parameters on the shell’s inherent characteristics and steady-state response.