Analysis of nonlinear damping using quadrature spectrum

Energy loss per cycle is one of the most common parameters to determine the magnitude of hysteresis damping. The measured hysteresis loops for materials during dynamic measurements are often irregular and general equations for defining the force-displacement-time relations of materials are unavailable in almost all cases. In order to analyze the complicate nature of the behavior of nonlinear hysteresis damping under non-sinusoidal loading, a new method was developed by the author for the damping characterization of materials subjected to any arbitrary dynamic loading. This method uses quadrature spectrum of displacement and restoring force signals to calculate the damping properties of materials at any frequency. It was proven that the quadrature spectrum method is an excellent tool for practical hysteresis damping measurement. The dynamic damping density function was also defined and discussed in this paper.