Semi-analytical modeling and thermomechanical coupling vibration analysis of hard-coating thin-walled cylindrical shell under thermal environments and arbitrary boundary conditions

This work focuses on investigating the thermomechanical coupling vibration characteristics of a hard-coating thin-walled cylindrical shell under different thermal environments and arbitrary boundary conditions. This study presents a semi-analytical dynamic model for the hard-coated thin-walled cylindrical shell based on the Rayleigh–Ritz method, which accounts for the temperature dependence of material properties, steady-state thermal fields, and thermal stress. Utilizing Love’s first approximation theory and von Kármán-type nonlinear strain–displacement relations, the governing equations of motion are derived. Admissible displacement functions are constructed using generalized Jacobi polynomials and boundary conditions are simulated with artificial spring techniques. By incorporating adaptive step-size adjustment, an extended Newton–Raphson method is developed for efficiently solving the thermomechanical coupling vibration equations of the shell. The model’s accuracy is verified by comparing the semi-analytical method (SAM) results with those from the finite element method (FEM) under clamped–free (C–F) and clamped–clamped (C–C) boundary conditions, using a thin-walled cylindrical shell coated with NiCoCrAlY as an example. The comparison shows that the relative error in natural frequencies between SAM and FEM does not exceed 1.69% for either boundary condition. These findings effectively validate the accuracy and rationality of the semi-analytical model across different boundary scenarios. A detailed analysis is conducted to investigate the thermomechanical coupling vibration characteristics, focusing on parameters such as spring stiffness, temperature, and coating thickness. These factors are systematically analyzed to understand their influence on the vibration mechanism and damping vibration reduction effects.