Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

Abstract

a b s t r a c tModal testing and analysis is well-established for linear systems. The objective of this paper is to progress toward a practical experimental modal analysis (EMA) methodology of nonlinear mechanical structures. In this context, nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the classical linear normal modes (LNMs). A nonlinear extension of force appropriation techniques is developed in this study in order to isolate one single NNM during the experiments. With the help of time-frequency analysis, the energy dependence of NNM modal curves and their frequencies of oscillation are then extracted from the time series. The proposed methodology is demonstrated using two numerical benchmarks, a two-degree-of-freedom system and a planar cantilever beam with a cubic spring at its free end.

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

“…In the presence of weak to moderate viscous damping, as shown in [17,20] and experimentally confirmed in this study, the damped dynamics can be interpreted based on the topological structure of the NNMs of the underlying conservative system. For large damping, it is important to note that the type of nonlinear behavior that is observed (e.g., hardening or softening) may be modified as shown in [24].…”

“…Because modal superposition is no longer valid, the methodology introduced in [17] for EMA of nonlinear structures is realized through a nonlinear phase resonance method (also called force appropriation), which relies on the extension of the phase lag quadrature criterion to nonlinear systems. Specifically, if the forced response across the structure is a monophase periodic motion in quadrature with the excitation, an NNM vibrates in isolation.…”

“…3, the NNM extraction is carried out in two steps: NNM force appropriation and NNM free decay. A detailed description of the overall methodology is given in [17]. The philosophy of the procedure and the related fundamental properties are briefly reviewed in this section.…”

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.…”

“…In this case, we consider two optimization problems by using equation (42). The first one is to minimize the superharmonic resonance with a fixed load amplitude without increasing the amount of material in the beam.…”