Stability of similar nonlinear normal modes under random excitation

Two-DOF nonlinear system under stochastic excitation is considered. It is assumed that the system allows from two up to four nonlinear normal modes (NNMs) with rectilinear trajectories in the system configuration space. Influence of the random excitation to the NNMs stability is analyzed by using the analytical-numerical test, which is an implication of the well-known stability definition by Lyapunov. Boundary of the stability/instability regions is obtained in plane of the system parameters. Stability of the NNMs under deterministic chaos excitation is also considered.

Automated summary

This study focuses on a two-DOF nonlinear system under stochastic excitation, examining the influence of random excitation on the stability of nonlinear normal modes (NNMs). Utilizing an analytical-numerical test and the stability definition by Lyapunov, the boundary of stability/instability regions in the system parameter plane is obtained. Additionally, the stability of NNMs under deterministic chaos excitation is also considered.