Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration

Abstract

a b s t r a c tRealizing that nonlinearity is a frequent occurrence in engineering structures and that linear experimental modal analysis (EMA) is of limited usefulness in this context, the present paper is an attempt to develop nonlinear EMA by targeting the extraction of nonlinear normal modes (NNMs) from time series of nonlinear mechanical systems. Based on a nonlinear extension of phase resonance testing, the proposed methodology excites the structure to isolate a single NNM during the experiments. Thanks to the invariance principle, the energy dependence of that nonlinear mode (i.e., the NNM modal curves and their oscillation frequencies) can be extracted from the resulting free decay response using time-frequency analysis. This paper is devoted to the experimental demonstration and robustness of this procedure. To this end, an experimental cantilever beam with a geometrical nonlinearity is considered, and the ability of the proposed methodology to extract its NNMs from the measured responses is assessed.

Optimization of nonlinear structural resonance using the incremental harmonic balance method

“…These are all well known phenomena but emphasize the need for an efficient and robust method to predict and subsequently optimize the resonance peak in nonlinear vibration. [41,42]. A physical interpretation is that the external load compensates for the damping force.…”

Experimental Modal Analysis of Nonlinear Structures Using Broadband Data

“…6 and is identical to the experimentallyupdated model in Ref. [32] . It comprises 14 two-dimensional beam elements for the main beam and 3 elements for the thin beam.…”

“…It should be noted that the same case study was investigated to demonstrate the nonlinear phase resonance method developed in Refs. [31,32] .…”

“…This is realized by tuning the frequency of a stepped-sine excitation so as to induce of a single-NNM motion of the system. This step is facilitated by a generalized phase lag quadrature criterion, which can be translated into a force appropriation indicator equal to 1 at resonance [32] . NNM appropriation is illustrated in Fig.…”

Resonant response functions for nonlinear oscillators with polynomial type nonlinearities

“…Normal form transformations are a powerful technique for studying the response of nonlinear oscillators, which has it's origins in the work of Poincaré [7]. The techniques have a long history of development and application, and are particularly useful for identifying resonant interactions in oscillators -for example see [8,9,10,11,12,13] and the related approach of using nonlinear normal modes [14,15,16,17,18]. In addition, a comprehensive overview of normal form theory and related techniques can be found in [19,20,21,22], and a survey of recent developments is given by Stolovitch [23].…”