Experimental Quantification and Validation of Modal Properties of Geometrically Nonlinear Structures by Using Response-Controlled Stepped-Sine Testing

Abstract

Background Various nonlinear system identification methods applicable to distributed nonlinearities have been developed over the last decade. However, many of them are not eligible to accurately quantify a high degree of nonlinearity. Furthermore, there exist few studies that actually validate the identified nonlinear properties. Objective The main objective of this paper is the validation of a novel nonlinear system identification framework recently developed by the authors on a double-clamped thin beam structure that exhibits continuously distributed strong geometrical nonlinearity due to large amplitude oscillations and considerable damping nonlinearity due to micro-slip in the beam-base connections. Methods The identification framework consists of response-controlled stepped-sine testing (RCT) and the harmonic force surface (HFS) concept. The framework is implemented by using standard hardware and software in modal testing. The RCT approach is based on keeping the displacement amplitude of the driving point constant throughout the frequency sweep and its basic assumptions are well-separated modes and no internal resonance. Constant-force frequency response curves and backbone curves of the first nonlinear normal mode (NNM) are identified at multiple measurement points from HFSs constructed by using measured harmonic excitation force spectra. The NNM shapes of the first mode at various vibration levels are then constructed from the identified NNM backbone curves. On the other side, the response level-dependent modal parameters are identified by applying standard linear modal analysis techniques to frequency response functions (FRFs) measured at constant displacement amplitude levels throughout RCT. ResultsThe RCT-HFS framework quantifies about a 20% shift of the natural frequency and an order of magnitude change of the modal damping ratio (from 0.5% to 4%) for the first mode of the double-clamped beam, which indicates a considerably high degree of stiffness and damping nonlinearities in the vibration range of interest. The identified nonlinear modal parameters are successfully validated by comparing near-resonant constant-force frequency response curves synthesized from these parameters with the ones measured by constant-force stepped-sine testing and with the ones extracted from the HFSs. The HFSs are determined for the first time in an experiment at multiple measurement points other than the driving point. The NNM shapes determined from HFSs are also validated by comparing them with the ones obtained from the identified nonlinear modal constants. Conclusions The RCT-HFS framework is successfully validated for the first time on a structure that exhibits continuously distributed geometrical nonlinearity. This study is a humble contribution towards making nonlinear experimental modal analysis a standard engineering practice.

Continuation methods for lab experiments of nonlinear vibrations

“…Abeloos et al [1] replaced the fixed‐point iteration by adaptive FIR‐filters for further reduction of measurement times. Similar to S‐curves, Karaagacli and Özgüven [8,9] obtain the RCT‐curve by stepping through the frequency values. For tracking NLFR‐functions experimentally, a continuation algorithm with variable frequency is necessary comparable to numerical continuation.…”

“…Abeloos et al [1] replaced the fixed-point iteration by adaptive FIR-filters for further reduction of measurement times. Similar to S-curves, Karaagacli and Özgüven [8,9] NLFR-functions experimentally, a continuation algorithm with variable frequency is necessary comparable to numerical continuation. As the faster fixed-point iteration for S-curves is referred to as simplified method, see [16], we use the term full CBC for NLFR-continuation in the following.…”