Nonlinear vibration of a composite flexible cantilever beam with a tip mass, subjected to uniform airflow and planar excitation forces

This study investigates the nonlinear vibration of a symmetrically laminated composite beam with a tip mass, subjected to uniform airflow and planar excitation forces. The beam is excited at its primary resonances, with auto-parametric internal resonance conditions between the flapwise-torsional and chordwise modes. The influence of uniform airflow in the flapwise direction on the beam's response is examined, extending previous research to include base excitation and tip mass. The multiple scales method is employed to analyze the non-linear equations and determine the stability of the steady-state amplitudes in both frequency and forced responses. The results show that the introduction of airflow significantly alters the system's behavior, eliminating Hopf bifurcations and reducing hardening-type behavior. Additionally, airflow induces a jump phenomenon at lower excitation frequencies and amplifies the effects of reduced damping on the system's amplitude. The findings demonstrate the importance of considering airflow in the analysis of vibration systems, particularly those with complex non-linear behavior.