Stochastic excitation of a simple system with impact damper

Abstract

An approximate analytical solution is obtained for the stationary response of a highly nonlinear auxiliary mass damper (impact damper) attached to a single‐degree‐of‐freedom oscillator that is subjected to an excitation with white power spectral density and Gaussian probability distribution. Experimental measurements with an electronic analogue computer verify the analytical findings both qualitatively and quantitatively. Results are given for the mean‐squared level and the power spectral density of the response. The effects of various damper parameters on the response of the primary system are determined. The impact damper under consideration is shown to be substantially more effective than the conventional dynamic vibration neutralizer in controlling the response of stochastically excited primary systems.

Analytical and experimental investigation on a multiple-mass-element pendulum impact damper for vibration mitigation

“…(2) and (3) describe the equilibrium in the two principal (inclined) directions of the motion for each lumped-mass element of the pendulum, as shown in Fig. 1b.…”

“…As explained in Section 3, λ is proportional to the ratio between the pulsation of the primary system and the local pulsation of one element of the pendulum, i.e., it can be used as an indirect measures of relative stiffness. The parameters of the damper, λ 2 and ζ 2 , are chosen as suggested in [2][3][4] to replicate a suitable average restitution coefficient at inelastic impact. The restitution coefficient is inversely proportional to ζ 2 , e.g., ζ 2 ¼ 0:2 corresponds to 50% restitution and ζ 2 ¼ 0:5 corresponds to 15% restitution [2,3].…”

“…The parameters of the damper, λ 2 and ζ 2 , are chosen as suggested in [2][3][4] to replicate a suitable average restitution coefficient at inelastic impact. The restitution coefficient is inversely proportional to ζ 2 , e.g., ζ 2 ¼ 0:2 corresponds to 50% restitution and ζ 2 ¼ 0:5 corresponds to 15% restitution [2,3]. Additional discussion on the restitution coefficient may be found in Section 5.…”

“…The fundamental theory on the mechanics of impact dampers devices has been examined by Masri and his research team. Starting from his pioneering work on the mechanical modeling of impact dampers [1][2][3], the research considered many problems and applications, which include "particle" dampers composed of either a single mass or multi-particle [4,5], studying both one-dimensional and three-dimensional motion of the particles [6,7]. More recently, Vakakis et al [8] analyzed the use of "impact dampers" for the suppression of aeroelastic instabilities on airplane wings (flutter during flight) and seismic vibration on buildings [9], by using a generalized concept of nonlinear energy sink (NES, [8]).…”

Response of Impact Dampers With Granular Materials Under Random Excitation

“…26 The dimensionless rms response curves of the base-excited singledegree-of-freedom system with an attached single-particle damper under random excitation are shown in Figure 9.…”