| Summary: | The Conditioned Reverse Path (CRP) method introduced by Richards and Singh can be used to obtain the underlying linear dynamic compliance matrix in the presence of nonlinearities in Single Degree of Freedom (SDOF) and general Multi Degree of Freedom (MDOF) systems. The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations. There are number of small issues associated with the approach, the main one being the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion, which leads to an accumulation of errors. In the first part of this thesis study, the CRP method is discussed in its standard form; minor modifications to the algorithm are then suggested in order to improve the estimates of the coefficients of nonlinear model terms. Although CRP is known to work well in numerical simulations and experimental work, in this thesis also a more radical suggestion is made to replace the conditioned spectral analysis, which is the basis of the method, with an alternative time-domain decorrelation method. This new algorithm becomes the second main topic in this thesis. The suggested approach is called the Orthogonalised Reverse Path (ORP) method. This new method is explained in the context of a SDOF system, however, the analysis for MDOF systems works out in exactly the same manner. This new estimator is found to handle nonlinear interactions as well as the CRP and the estimates also appear to be free of the aforementioned artefacts. This is illustrated using data from simulations of nonlinear SDOF and MDOF systems, which are benchmarked to the results produced in CRP cases. Furthermore, the algorithm can be coded in an extremely transparent and compact form if an appropriate Gram-Schmidt module is available. The final part of this thesis presents the application of both CRP and ORP to experimental test set-ups; these are a nonlinear beam rig and an SDOF system mass isolator with damping nonlinearity (using a semi-active damper known as a magnetorheological shock absorber).
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