Multimodal and transitional behaviour in second-order nonlinear systems

Second-order systems with amplitude-dependent nonlinearities can exhibit multirnodal behaviour. A method of finding the range of parameters for which this behaviour is observed is considered, and the method is then extended to predict the type of transients which occur in the system from a given set of initial conditions. The method is based on the describing function of the nonlinearity. The effect of the shape of the nonlinearity on the number of possible fundamental modes of response is discussed, and attention is given to the possibility of exciting subharmonic modes of response, the purpose being to find the range of parameters for which the analysis of the fundamental modes of response is valid.