Nonlinear resonance and chaotic vibration behavior of composite components in high-performance sports equipment

In this paper, considering the nonlinear governing equations including cubic and quadratic nonlinearity terms of the vibrational behavior of a composite plate, chaotic vibrations and primary frequency resonance (PFR) are analyzed. Moreover, the Runge–Kutta numerical method and the multiple scales method (MTM) are used to compute and generate the chaotic response and the PFR of composite plate subjected to the harmonic excitation respectively. The effects of excitation amplitude, damping coefficient and detuning factor are studied to investigate the chaotic condition and phenomenon of jumping and PFR of composite plate. The largest Lyapunov exponent diagrams are employed to compute the chaotic critical amplitude of excitation and the Poincaré map and phase plane are generated to present the chaotic and periodic behavior of the composite plate corresponding to the selected amplitude excitation. In addition, nonlinear PFR with the backward jumping phenomenon is generated to study the intensity of the influence of selected parameters on the instability of composite plate. The results show that as the excitation amplitude increases, the system’s peak response amplitude and instability regions rise by 50–100%.