Identification of modal parameters, when a structure is under operational conditions is termed Operational Modal Analysis (OMA). Current OMA techniques are based on the assumption of linear time-invariant systems, and thus have limited applicability when applied to structures known to violate these assumptions. The present study investigates how the Random Decrement (RD) technique can improve robustness of OMA methods when friction-induced nonlinear damping is present in a system. This is done by estimating the amplitude dependent damping. A friction mechanism is introduced in a model of a structure, and by applying the RD technique at different amplitudes of simulated responses, RD signatures are produced, that represent the system vibrating with these amplitude levels. This allows the modal parameters to be estimated based on RD signatures computed with each amplitude level, using time domain parameter estimation methods, and the amplitude dependency of the damping is identified.
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Dynamic characteristics of structures in operational conditions are commonly identified from measured responses using Operational Modal Analysis (OMA). The OMA techniques are, however, confined to the principle of linearity. To overcome some of this limitation, this paper proposes a method for an OMAbased conditional linear approximation of a type of nonlinear systems, by which two or more sets of linear modes are estimated that together describe the behaviour of the true system. These sets of modes can be used to update a nonlinear numerical model that fits each linear estimate in relation to the associated conditions. Additionally, the method can alleviate the issue of varying approx. natural frequencies of nonlinear systems, when employing Structural Health Monitoring to detect damages based on changes of these. The method is demonstrated on both a numerical and an experimental study. Specifically, the numerical study consists of a cantilever beam with a clearance and a stopper at the tip, and it is shown, based on a single response measurement with multiple channels, that the method enables identification of both the underlying linear system and a linear system with modal properties affected by the nonlinearity. The experimental study consists of two simple, friction-coupled, offshore platform-like models, for which two sets of modes are estimated from one measurement, each set characterising the dynamic behaviour in coupled and uncoupled state, respectively. The paper also demonstrates that the proposed method can relieve the said complications of conducting Structural Health Monitoring of structures with changing natural frequencies due to nonlinearity.
The random decrement (RD) technique can be used to analyze the response signal from a system that has amplitude dependent modal parameters. The implementation of RD for this purpose is usually done by simply applying the technique at multiple amplitudes in the measured response signal. Modal parameters are then estimated based on RD signatures using well known time domain modal parameter estimation methods. This analysis procedure originates from the invention of the RD technique, and is described by several studies in the literature. However, the RD technique is developed for linear systems, and caution must be exercised when applying it to nonlinear systems. In this study, several aspects of applying of the RD technique on signals exhibiting nonlinear behavior are addressed. The principle of superposition does not apply for a nonlinear system. This means the averaging process in RD can yield corrupted results. The benefit of a sufficiently high sampling rate is described.
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