Nonlinear parametric vibration analysis of the rotating thin-walled functionally graded material hyperbolic beams

This paper presents a nonlinear model for analyzing the behavior of functionally graded material Euler-Bernoulli thin-walled beams with varying cross-sections, while considering periodic perturbations in the rotating speed. The study focuses on an analytical exploration of the natural frequency and amplitude frequency response associated with the nonlinear parametric vibrations within this system. Initially, the governing differential equations for the transverse vibrations of the beams are derived through Hamiltonian principle. Subsequently, the perturbation method is employed to solve the established equations, and Galerkin method is adopted to determine the mode shapes and frequencies. Furthermore, this research extensively examines the influence of significant parameters on the vibration characteristics of the system.