It is possible to use numerical techniques to provide solutions to nonlinear dynamical systems that can be considered exact up to numerica ltolerances. However, often, this does not provide the user with sufﬁcient information to fully understand the behaviour of these systems. To address this issue, it is common practice to ﬁnd an approximate solution using an analytical method, which can be used to develop a more thorough appreciation of how the parameters of a system inﬂuence its response. This paper considers three such techniques – the harmonic balance, multiple scales, and direct normal form methods – in their ability to accurately capture the forced response of nonlinear structures. Using frequency detuning as a method of comparison, it is shown that it is possible for all three methods to give identical solutions, should particular conditions be used.
- normal form
- multiple scales