Chapter 13 Operational Modal Analysis Based Stress Estimation in Friction Systems Marius Tarpø, Tobias Friis, Bruna Nabuco, Sandro Amador, Evangelos Katsanos, and Rune Brincker Abstract It is possible to estimate the strain response of a structure in unmeasured points by the use of operational modal analysis and modal expansion. Both techniques are based on the assumption that the system is linear. However, this is not always the case since nonlinear elements often violate this assumption. In this paper, the precision of estimating the strain response of a nonlinear system is investigated using the operational response of numerical simulations. Local nonlinearities are introduced by adding friction to the test specimen and this paper finds that this approach of strain estimation can still predict the strains with high precision. Keywords Operational modal analysis · Strain estimation · Modal expansion · Structural health monitoring · Non-linear dynamics 13.1 Introduction Fluctuating forces continuously influence offshore structures and it causes the structures to fatigue over time. Eventually, this load history leads to failure of the structure. In the design process of offshore structures, we account for the fatigue by a designed lifetime, which is based on approximations of this load history. However, the actual lifetime of the structure in operation is unknown and there is a significantly potential profit if we determine the remaining lifetime. Vibration based Structural Health Monitoring might provide a better access to the actual integrity than the design process could. Unfortunately, several issues complicate the monitoring of offshore structures [1, 2]. The environment is hostile and the structures are abstruse. The seawater corrodes and damages underwater sensors, which makes subsea monitoring difficult. Non-linear connectors between platforms can make the system response non-linear. The structural properties change over time and the structural response can become non-stationary due to temporary operational forces. We are able to estimate the full-field dynamic strain response of a linear structure in unmeasured points above sea level. Here, we use operational modal analysis to identify the modal parameters and we expand the measured response to the strain response of the entire structure. Different methods exist for the full-field strain estimation where the Modal Expansion[3–7] and the Kalman filter [7–9] are among the most used techniques. However, the mentioned techniques are based on linear systems whereas many actual structures have some amount of non-linearities. Various types of non-linearities introduce potential errors in the operational modal analysis based strain estimation. Zhang et al. checked the effect of non-linearities on operational modal analysis and they found output-only identification techniques can extract the modal parameter of non-linear systems [10]. In their tests the mode shapes and natural frequencies had low variance and bias whereas the damping ratios had a higher variance and bias. In this paper, we will use operational modal analysis and the modal expansion so we can estimate the strain response of a simulated system where we add friction in order to introduce non-linearity to the system. This paper is a part of an ongoing project regarding non-linearities in operational modal analysis and strain estimation [11, 12]. We are able to estimate the strain response in a non-linear friction system with high precision. In this test, the frequency domain decomposition and the modal expansion are unaffected by the local non-linearities caused by the friction. M. Tarpø Aarhus University, Aarhus, Denmark e-mail: martar@eng.au.dk T. Friis ( ) · B. Nabuco · S. Amador · E. Katsanos · R. Brincker Technical University of Denmark, Kongens Lyngby, Denmark e-mail: brunan@byg.dtu.dk; sdio@byg.dtu.dk; vakat@byg.dtu.dk; runeb@byg.dtu.dk © The Society for Experimental Mechanics, Inc. 2019 G. Kerschen (ed.), Nonlinear Dynamics, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-319-74280-9_13 143
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