A method is presented which can estimate the linear and non-linear damping parameters in a lightly damped multi-degree of freedom system. This in effect 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. This ensures 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, with the pass band centered on each of the natural frequencies. This provides a set of free response measurements, one for each mode. However, it does introduce a restriction in that the natural frequencies must be distinct and separated somewhat. The instantaneous energy of each trace is used to describe the long-term evolution of the mode. Practically this is achieved by using only the peak amplitudes in each period. In this way the stiffness and inertial forces are effectively ignored, and only the damping forces are considered. For this reason, the method is not unlike the familiar decrement method, which can be used to estimate the viscous damping in linear systems. The method is developed in the context of a weakly non-linear, lightly damping two degree-of-freedom system, with both linear and Coulomb damping. Simulated response data is used to demonstrate the accuracy of the technique.

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