ABSTRACT
A number of studies have been carried out over recent years concerning the application of wavelet-based analytical techniques to the investigation and modelling of dynamical systems. Applications include the evaluation of dynamic properties and system characteristics, the modelling and control of dynamical behaviour, and the partitioning or decoupling of multiple responses. Early work worth consulting in this area is that by Staszewski (1997, 1998a), who employed a Morlet wavelet for the detection of system nonlinearities through the identification of damping and stiffness parameters for multi-degree-of-freedom (MDOF) dynamic systems during transient testing. This wavelet is very effective for this application as it has good support in both frequency and time, which allows the decoupling of the system’s various modes of vibration. Figure 5.1a shows one of the signals analyzed in the study resulting from the impulse response of a two-degrees-of-freedom model system. Figure 5.1b shows the ridges of the modulus plot and Figure 5.1c shows the wavelet
FIGURE 5.1 (a) Impulse response function for well separated modes. (b) Ridges of the wavelet transform scalogram. (c) Comparison of the real parts of the wavelet transform skeletons (dashed lines) obtained from the ridges given in the preceding figure and the theoretical impulse response function (solid line). Top trace: first mode (20 Hz); bottom trace: second mode (78 Hz). (From Staszewski, W. J., Journal of Sound and Vibration, 203(2), 283-305, 1997.) Reproduced with kind permission of Academic Press Ltd.
