IDENTIFICATION OF COUPLED NON-LINEAR MODES FROM FREE VIBRATION USING TIME-FREQUENCY REPRESENTATIONS

A new method based on time–frequency representations is presented for identifying the non-linear modal parameters of a multi-degree-of-freedom non-linear lightly damped mechanical system. The coupled non-linear modes are first introduced. It is shown that, by using the coupled non-linear modes, the free response can be expressed as a linear combination of frequency and amplitude modulated components. This suggests the use of time–frequency methods to characterize these modulation laws and then identify the coupled non-linear modes. These modulation laws are extracted by using an extended definition of the so-called “ridges” of the continuous Gabor transform, which enables a more accurate estimation. An identification procedure of the coupled non-linear modes is proposed and the validity of the whole process is confirmed by performing computer simulations of different types of non-linear elastic dynamic systems.