Improved Fourier Series-Ritz Method for Free Vibration Analysis of Hard Coating Damping Thin-Walled Cylindrical Shells with Thickness Variation Under Arbitrary Boundary Conditions

This work focuses on the free vibration characteristics of hard coating damping thin-walled cylindrical shells with thickness variation and arbitrary boundary conditions.

The analytical model is established on the basis of the Flügge thin shell theory. Secondly, the substrate thickness function is expanded uniformly into Fourier series form in order to integrate the thickness variation parameters into the Fourier coefficients accordingly, the artificial spring technique is used to simulate the arbitrary boundary conditions. Furtherly, the admissible functions are constructed by the improved Fourier series, the Rayleigh–Ritz method is employed to derive the dynamical equations for hard coating thin-walled cylindrical shells with thickness variation. Finally, the state space method with high efficiency is used to solve the calculation.

This study provides validated solutions of natural frequency and modal loss factors for hard coating damping thin-walled cylindrical shells with thickness variation under arbitrary boundary conditions. The rationality of the theoretical approach is verified by the published literature and finite element method (FEM). A comprehensive parametric analysis reveals the effects of multiple factors on the natural frequency and modal loss factors, including spring stiffness, boundary conditions, thickness of hard coating, elastic modulus of hard coating, length-to-diameter ratio and thickness variation location. These findings can provide valuable guidance for practical engineering design and shell structure optimization.