A Decrement Method for Quantifying Nonlinear and Linear Damping in Multidegree of Freedom Systems

Abstract

A method is presented which can estimate the linear and nonlinear damping parameters in a lightly damped multidegree of freedom system which allows the system to be decomposed into a set of single degree of freedom nonlinear systems. Only a single response measurement from a free decay test is required as input ensuring that the magnitude of the damping parameters is not compromised by phase distortion between measurements. The response is band-pass filtered in the time domain, around each of the natural frequencies. While this provides a free response measurement for each mode, it introduces a restriction as the natural frequencies must be distinct and separated. The instantaneous energy of each trace is used to describe the long-term evolution of the mode. This is achieved by using only the peak amplitudes in each period, and so the stiffness and inertial forces are effectively ignored, and only the damping forces are considered. Thus, the method is not unlike the familiar decrement method, which can estimate the viscous damping in linear systems. The method is developed for a weakly nonlinear, lightly damped two-degree-offreedom system, with both linear and Coulomb damping. Simulated response data is used to demonstrate the accuracy of the technique.