Backbone Curve Analysis of Nonlinear Mechanical Systems

Nonlinear dynamic behaviour has become increasingly significant due to the performance demands on modern mechanical structures that are increasingly lightweight and flexible, e.g. the geometric nonlinearity caused by the large detection. Also, numerous traditional mechanical applications are found to be able to achieve better performance when nonlinear characteristics are exploited. However, the application of any traditional linear analysis to nonlinear systems can only provide, at best, suboptimal solutions as the well-established linear techniques fail to capture the unique nonlinear features, e.g. modal interactions and bifurcations.
This thesis aims to improve the theoretical understanding of the smooth nonlinear dynamic behaviours of mechanical systems and apply the findings to develop innovative approaches for practical use. Backbone curve analysis is employed throughout the thesis as a tool to develop this understanding.
The resonant interactions only involving two modes of a three-lumped-mass nonlinear oscillator are investigated. It is demonstrated that the backbone curves of this example system can provide an interpretation of the underlying nonlinear dynamic behaviours, including stability and bifurcations. Then we consider two kinds of triple-mode resonant interactions in other 3-DoF systems, including 1:1:1 and 1:2:3 modal interactions. The effects of these multi-mode resonant interactions, e.g. the non-existent of single- and double-mode responses and the resonance between ‘non-resonant’ modes after involving extra modes, are demonstrated, and the mechanism is explored using backbone curves.
A nonlinear dynamic phenomenon, resonant frequency shift, is also considered. The power spectrum density results of a thin plate under multi-mode-multi-frequency excitations are used to demonstrate this nonlinear behaviour, which shows that the frequency shift can be caused by an interaction between any non-resonant modes. Based on a nonlinear reduced-order model, backbone curves are used to explain the mechanism of the non- resonant modal interaction, which is caused by the unconditionally resonant mixed-mode nonlinear terms. The understanding of the non-resonant modal interaction is then used to develop a practical approach for nonlinear system identification which employs the backbone curves as the parametric model. The proposed identification approach is applied to the example plate to demonstrate its accuracy and advantages.