Response of a multi-degree-of-freedom system with a pounding vibration neutralizer to harmonic and random excitation

Abstract

Exact steady-state solutions are obtained for the motion of a multi-degree-of-freedom system (MDOF) that is provided, at an arbitrary location within the primary structure, with a highly-nonlinear auxiliary mass damper which resembles a conventional linear dynamic vibration neutralizer (DVN) whose relative motion with respect to the primary system is constrained to remain within a specified gap, thus operating as a “pounding DVN.” This configuration of a conventional DVN with motion-limiting stops could be quite useful when a primary structure with a linear DVN is subjected to transient loads (e.g., earthquakes) that may cause excessive relative motion between the auxiliary and primary systems. Under the assumption that the motion of the composite nonlinear MDOF system under harmonic excitation is undergoing steady-state motion with two symmetric impacts per period of the excitation, an exact, closed-form solution is obtained for the motion of the MDOF as well as the nonlinear damper. This solution is subsequently used to develop an approximate analytical procedure to estimate the stationary response of the pounding DVN when subjected to random excitation with white spectral density and Gaussian probability distribution. Since the vibration control effectiveness of auxiliary mass dampers, whether linear or not, deteriorates considerably when dealing with transient dynamic loads, an extensive investigation is provided for assessing the influence and interaction effects of the major nonlinear system parameters, so as to provide useful guidelines for quantifying the tradeoffs in selecting a suitable strategy to enhance the mitigation capabilities of the subject class of dampers, under stationary as well as nonstationary deterministic and random dynamic environments.