Nonlinear vibration analysis of flexible rotating beam using multiple scales method

This paper develops a comprehensive nonlinear dynamic model for rotating beams with a setting angle, incorporating centrifugal stiffening, nonlinear damping, and higher order geometric nonlinearities. By formulating the governing equation and applying the Method of Multiple Scales, analytical expressions are derived for the amplitude and phase modulation, nonlinear frequency shift, and the influence of the effective parameters. The resulting slow flow equations reveal that the system exhibits clear softening or hardening behavior depending on the balance between nonlinear stiffness and damping. The analytical predictions are rigorously validated through direct numerical simulations based on the fourth order Runge–Kutta method, showing excellent agreement. The results provide a unified framework for understanding and predicting nonlinear vibrational behavior in rotating beam like structures, offering practical insight for the design, analysis, and control of wind turbine blades, helicopter and turbomachinery components, and advanced flexible robotic systems.

Keywords:

Rotating beams , Nonlinear vibrations , Multiple scales method , Setting angle effects , Frequency response analysis