Two key properties of a vibrating structure are the frequencies at which it resonates and its ability to absorb energy. For a linear structure, these properties are characterised by the natural frequencies and the damping ratios. For nonlinear systems, such properties may not exist and equivalents must be sought. A method of measuring equivalent properties has been developed for nonlinear systems by examining the decaying vibration time history following excitation of the system.
In a first stage, the time history is filtered to separate out a frequency range of interest. In the second stage, which is the main concern of this paper, instantaneous values of natural frequencies and damping ratios are extracted from the decaying time history by means of a curve fitting process. The curve fitting involves finding four parameters two of which are the instantaneous natural frequency and damping ratio and two more which account for the amplitude and phase. The curve fitting is a minimisation process which is divided into two stages. For each minimisation step, the amplitude and phase are extracted first. It is shown that this may be done in a one-step process. Next the frequency and damping are determined. This is found to be a straightforward although more difficult process. The key to simplifying the problem is to recast the model in a favourable form that reduces the curve fitting process from one of finding four parameters to finding just two. The procedure is found to be robust and capable of detailed investigation.
