A generalised frequency detuning method for multi-degree-of-freedom oscillators with nonlinear stiffness

In this paper, we derive a frequency detuning method for multi-degree-of-freedom oscillators with nonlinear stiffness. This approach includes a matrix of detuning parameters, which are used to model the amplitude dependent variation in resonant frequencies for the system. As a result, we compare three different approximations for modeling the affect of the nonlinear stiffness on the linearized frequency of the system. In each case, the response of the primary resonances can be captured with the same level of accuracy. However, harmonic and subharmonic responses away from the primary response are captured with significant differences in accuracy. The detuning analysis is carried out using a normal form technique, and the analytical results are compared with numerical simulations of the response. Two examples are considered, the second of which is a two degree-of-freedom oscillator with cubic stiffnesses.