Resonant Characterization of Nonlinear Structures in the Co-existence of Multiple Resonant Components

The study of nonlinear normal modes has become a very popular subdiscipline in the structural dynamics community. This is principally due to the fact that they allow for a practical generalization of the concept of spectral invariant manifolds in linear dynamics. There have been a lot of analytical successes achieved in this area through the application of the method of multiple scales which decomposes the response of a nonlinear oscillator into fast-changing dynamics occurring on a slowly varying manifold. Numerical calculations have also been carried out using a periodic ansatz (with resonance-based constraints). Most of such investigations in the past have focused on cases where a single nonlinear mode is studied in isolation. Although this alone provides very interesting results, such as invariant manifold characterization and internal resonance detection, these are usually not sufficient to study the coupling between multiple nonlinear modes. Recent experimental studies have shown that such coupling can lead to very nontrivial trends in the resonant characteristics, making it difficult to correlate computational realizations with experimental measurements. The present paper takes a computational approach frequency-domain numerical simulations conducted using quasi-periodic harmonic balance to obtain numerical insights into the steady-state multi-resonant behavior. These results are compared with signal processing conducted on transient ringdown responses to determine the ramifications of commonly employed signal processing techniques like frequency-domain filtering for mode isolation. Analytical results are also computed using multiple scales for comparisons. Results are presented for a simplified system with two kinds of nonlinearities: geometric and dry friction.