Experimental assessment of polynomial nonlinear state-space and nonlinear-mode models for near-resonant vibrations. (September 2020) - Scheel, Maren; Kleyman, Gleb; Tatar, Ali; Brake, Matthew R.W.; Peter, Simon; Noël, Jean-Philippe; Allen, Matthew S.; Krack, Malte
Highlights: Two different nonlinear models are identified for two experimental test rigs. The models are used to predict dynamic behavior under sine (-sweep) excitations. The modal model is accurate for sine excitation close to resonance. The modal model is sensitive for uncontrolled sweeps if the excitation force drops. Polynomial nonlinear state-space models highly depend on the used training data. Abstract: In the present paper, two existing nonlinear system identification methodologies are used to identify data-driven models. The first methodology focuses on identifying the system using steady-state excitations. To accomplish this, a phase-locked loop controller is implemented to acquire periodic oscillations near resonance and construct a nonlinear-mode model. This model is based on amplitude-dependent modal properties, i.e. does not require nonlinear basis functions. The second methodology exploits uncontrolled experiments with broadband random inputs to build polynomial nonlinear state-space models using advanced system identification tools. The methods are applied to two experimental test rigs, a magnetic cantilever beam and a free-free beam with a lap joint. The respective models obtained by either method for both specimens are then challenged to predict dynamic, near-resonant behavior observed under different sine and sine-sweep excitations. The vibration prediction of the nonlinear-mode and state-space models clearly highlight capabilities and limitations. The nonlinear-mode model, by design, yields a perfect match at resonance peaks and high accuracy in close vicinity. However, it is limited to well-spaced modes and sinusoidal excitation. The state-space model covers a wider dynamic range, including transient excitations. However, the real-life nonlinearities considered in this study can only be approximated by polynomial basis functions. Consequently, the identified state-space models are found to be highly input-dependent, in particular for sinusoidal excitations where they are found to lead to a low predictive capability.