Output-Only Estimation of Amplitude Dependent Friction-Induced Damping
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
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Output-Only Estimation of Amplitude Dependent Friction-Induced Damping Karsten K. Vesterholm, Tobias Friis, Evangelos Katsanos, Rune Brincker, and Anders Brandt
Abstract 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. Keywords Random decrement · Random vibrations · Friction-induced Nonlinear damping · Operational modal analysis · Identification of nonlinearity
3.1 Introduction The Random Decrement (RD) technique was invented in the late 1960s and the early 1970s by Cole [1–3], as a way to extract the ‘signature’ of a vibration signal, while the signal was being measured. It was invented to detect when damage in a vibrating structure occurred. The idea was, that damage was difficult to detect from observing the raw vibration signal, but easy to see in the signature. The RD technique is now an established output-only method for evaluating modal parameters of structures under random force inputs. It is possible to apply the RD technique, with a certain triggering condition, at multiple amplitude levels in the same response signal, and producing RD signatures that represent the system vibrating at these amplitude levels. The RD signatures can be treated as correlation functions, and amplitude specific modal parameters of the system can be estimated using time domain parameter estimation methods. When the modal parameters, representing different amplitude levels, are estimated, it reveals amplitude dependent nonlinearities in the system. The system investigated here has the stick-slip friction nonlinearity. The purpose of this study is to propose a new method of estimating the amplitude dependency of the damping caused by this type of nonlinearity, using only the measured response of the system. Amplitude dependent nonlinearities are present in many systems, and can cause difficulties, and erroneous results, since the current OMA methods are designed for linear systems [4]. The idea of applying the RD technique at multiple amplitude levels in one response signal was described by Jeary [5], where it successfully uncovered the amplitude dependent damping in tall buildings. The damping was
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