Effects of weights on vibration suppression via a nonlinear energy sink under vertical stochastic excitations

A primary structure attached by a nonlinear energy sink (NES) moving vertically under a Gaussian white noise excitation is investigated. This paper demonstrates the stochastic responses and vibration suppression with emphasis on the effects of the weights. Four-dimensional state space equations which consider or ignore the weights in the vertical direction are given. Numerical probability density functions computed via the path integration method based on the Gauss-Legendre scheme are confirmed by Monte Carlo simulations. Probability density functions of the structure's responses are compared between two cases under various random excitation intensities. The root-mean-square (RMS) displacement of the primary structure or random vibration suppression is estimated through the path integration method. Results reveal that the NES is able to suppress broadband random vibration of the structure. As the stochastic excitation decreases, the NES weight has significant effects on both probability density functions of the structure's responses and RMS displacements of the primary structure. The NES parameters are discussed to explore random vibration suppression. For purpose of more accurate predictions, the effects of weights should be taken into consideration when the primary structure is excited by small random excitations or coupled with a large and reasonable NES mass. Simulations and discussions in this work provide theorical meanings to predict vibration suppression via a NES in stochastic environment.