Experimental Identification of Backbone Curves of Strongly Nonlinear Systems by Using Response-Controlled Stepped-Sine Testing (RCT)

Abstract

In stepped-sine testing of strongly nonlinear structures with the classical force-control strategy, corrective force perturbations of a standard controller used to capture the reference signal in the proximity of turning points of frequency response curves may often lead to a premature jump before reaching the actual resonance peak. Accordingly, a classical force-control approach is not suitable to identify backbone curves of strongly nonlinear structures. This paper shows that currently available commercial modal test equipment can accurately identify backbone curves of strongly nonlinear structures by using Response-Controlled stepped-sine Testing (RCT) and the Harmonic Force Surface (HFS) concept, both recently proposed by the authors. These methods can be applied to systems where there are many nonlinearities at several different (and even unknown) locations. However, these techniques are not applicable to systems where internal resonances occur. In RCT, the displacement amplitude of the driving point, rather than the amplitude of the applied force, is kept constant during the stepped-sine testing. Spectra of the harmonic excitation force measured at several different displacement amplitude levels are used to build up a smooth HFS. Isocurves of constant amplitude forcing on the HFS lead to constant-force frequency response curves with accurately measured turning points and unstable branches (if there are any), which makes it possible to identify backbone curves of strongly nonlinear structures experimentally. The validation of the proposed approach is demonstrated with numerical and experimental case studies. A five degree-of-freedom (DOF) lumped system with five cubic stiffness elements, which create strong conservative nonlinearity, is used in the numerical example. Experimental case studies consist of a cantilever beam and a control fin actuation mechanism of a real missile structure. The cantilever beam is supported at its free-end by two metal strips constrained at both ends to create strong stiffening nonlinearity. The control fin actuation mechanism exhibits very complex and strong nonlinearity due to backlash and friction.

Experimental Modal Analysis of Geometrically Nonlinear Structures by Using Response-Controlled Stepped-Sine Testing

“…The accurate identification of turning points and unstable branches of frequency response curves, which is a considerable issue even for the new generation experimental continuation techniques, is the prominent feature of the HFS technique. This feature was successfully used in [16] to experimentally determine the backbone curves of strongly nonlinear structures.…”

Stepped and swept control-based continuation using adaptive filtering

“…Another method which uses feedback control to characterize the response of nonlinear structures is the so-called Response-Controlled stepped-sine Testing (RCT) [26,27]. CBC and RCT share an important conceptual similarity as both methods directly control the response of the system to achieve a particular response target.…”

“…FRCs, S-curves and RCT's constant-response FRFs are in fact the three possible ways in which the response manifold can be sliced. Data collected using RCT was interpolated using the Harmonic Force Surface (HFS) concept to successfully identify the nonlinearities of structures with stiffness [26], friction, and backlash [27] nonlinearities. However, RCT neglects the effects of nonfundamental harmonics, leaving the controller invasive and potentially affecting the identified orbits.…”

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

“…The main advantage of the RCT-HFS technique is the accurate extraction of turning points and unstable branches, if there are any, of these frequency response curves. This advantage helps to determine the NNM backbone curves of strongly nonlinear systems accurately by combining the resonance peaks of constantforce frequency response curves [24].…”

“…The RCT framework has been successfully applied so far to the T-beam benchmark, a real missile with considerable damping nonlinearity spread over the structure due to bolted connections [23] and on a real control fin actuation mechanism with complex and strong nonlinearity due to backlash and friction [24]. In a recent work [29], the identification of nonlinear modal parameters of a double-clamped beam that exhibits strong geometrical nonlinearity has been achieved successfully.…”