Vibration Suppression of a Nonlinear Energy Sink with Nonlinear Damping Under Gaussian White Noise Excitation

Compared with linear absorber, nonlinear energy sink has gained significant attention due to its ability to enhance vibration absorption performance by broadening absorption bandwidth. Currently, in the research on stochastic nonlinear energy sinks, linear damping is mainly taken into account. Different from existing research, this paper studies vibration suppression effect of a nonlinear energy sink with nonlinear damping under Gaussian white noise excitation. First, based on generalized harmonic function technique and stochastic averaging method, FPK equation of the system is obtained. Second, analytical solutions are compared with numerical solutions obtained from Monte Carlo simulation to verify the validity of the proposed method. Results show that the proposed method has a high degree of consistency. Subsequently, the influences of mass ratio and Gaussian white noise intensity on system vibration suppression are discussed. With increase of mass ratio and noise intensity, vibration suppression effect of a nonlinear energy sink gradually weakens. Ultimately, the time histories of displacement of the main oscillator coupled and uncoupled a nonlinear energy sink are analyzed to verify the desired goal of vibration suppression. Results show that cubic stiffness coefficient of nonlinear energy sink has an optimal value. The influence of nonlinear damping on the main oscillator vibration suppression are also analyzed. Results show that nonlinear energy sink with nonlinear damping used in this paper plays a better vibration suppression effect.