Table of Contents
ISRN Mechanical Engineering
Volume 2011, Article ID 659484, 7 pages
Research Article

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

School of Engineering, Trinity College, Dublin 2, Ireland

Received 18 January 2011; Accepted 13 February 2011

Academic Editors: S. Marchesiello and R. Nagaosa

Copyright © 2011 Craig Meskell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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-of-freedom system, with both linear and Coulomb damping. Simulated response data is used to demonstrate the accuracy of the technique.