NON-LINEARITY IDENTIFICATION AND QUANTIFICATION USING AN INVERSE FOURIER TRANSFORM

Abstract

It is important to judge whether or not a linear model for a system or structure analysis is adequate. If it is thought that a linear model is not acceptable, a non-linear model should be considered for more accurate analysis even if it is more complicated and difficult to handle. There has been much work aimed at finding methods which identify the positions and degrees of non-linearity within a system or structure. The simplest method is to examine force state mapping and FRF plots. These plots are not satisfactory for quantifying and locating non-linearities. Tomlinson used the Hilbert transform of the FRF to quantify nonlinearity. In this work the inverse Fourier transform of the FRF method is used instead of the Hilbert transform to identify and quantify non-linearity. The ratio of non-causal power to total FRF power is defined as the NPR value. These values are calculated from the time domain data of the inverse Fourier transformed FRF. First, it is explained that a nonlinear system shows some non-causal power within its inverse Fourier transform of system FRFs. Then the NPR values are examined using numerical tests for varying excitation forces and non-linear types. It was found that the NPR value grows with increasing nonlinearity. The non-linearity position can be found by searching for the most sensitive degree of freedom in the NPR values at varying excitation force levels. This method reduces computation time when compared with the Hilbert transform technique.