Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form. (June 2018) - Denis, V.; Jossic, M.; Giraud-Audine, C.; Chomette, B.; Renault, A.; Thomas, O.
Highlights: A framework is proposed for the identification of a single nonlinear mode. A nonlinear mode can be characterized with linear frequency and a single nonlinear cubic coefficient. The phase resonance can be measured in forced regime using a phase-locked loop. The phase-locked loop is a robust technique for measuring nonlinear forced responses and backbone curves. The proposed methodology is applied to a circular plate, a chinese gong and piezoelectric beam. Abstract: In this article, we address the model identification of nonlinear vibratory systems, with a specific focus on systems modeled with distributed nonlinearities, such as geometrically nonlinear mechanical structures. The proposed strategy theoretically relies on the concept of nonlinear modes of the underlying conservative unforced system and the use of normal forms. Within this framework, it is shown that without internal resonance, a valid reduced order model for a nonlinear mode is a single Duffing oscillator. We then propose an efficient experimental strategy to measure the backbone curve of a particular nonlinear mode and we use it to identify the free parameters of the reduced order model. The experimental part relies on a Phase-Locked Loop (PLL) and enables a robust and automatic measurement of backbone curves as well as forced responses. It is theoretically and experimentally shown that the PLL is able to stabilize the unstable part of Duffing-like frequency responses, thus enabling its robust experimental measurement. Finally, the whole procedure is tested on three experimental systems: a circular plate, a chinese gong and a piezoelectric cantilever beam. It enable to validate the procedure by comparison to available theoretical models as well as to other experimental identification methods.