Two methods for the computation of nonlinear modes of vibrating systems at large amplitudes

The aim of this paper is to present two methods for the calculation of the nonlinear normal modes of vibration for undamped nonlinear mechanical systems: the time integration periodic orbit method and the modal representation method. In the periodic orbit method, the nonlinear normal mode is obtained by making the continuation of branches of periodic orbits of the equation of motion. The terms “periodic orbits” means a closed trajectory in the phase space, which is obtained by time integration. In the modal representation method, the nonlinear normal mode is constructed in terms of amplitude, phase, mode shape, and frequency, with the distinctive feature that the last two quantities are amplitude and total phase dependent. The methods are compared on two DOF strongly nonlinear systems.