Chapter 5 Importance of Virtual Sensing and Model Reduction in the Structural Identification of Bolted Assemblies Sina Safari and Julian M. Londoño Monsalve Abstrac t Creating mathematical models of mechanical structures with bolted joints is still a challenging topic, which is the base of ongoing research efforts to develop methods to characterize and quantify nonlinearities in mechanical structures. An approach to efficiently handle the identification of large nonlinear structural systems using measured data is to formulate the identification problem in a low-dimensional space, that is, nonlinear modal reduced order model (NMROM). This chapter discusses the effects of truncating the order of reduced order model in their prediction accuracy and its impact on the nonlinear model identification process that uses the reduced order model. This chapter also presents results of a virtual sensing strategy that is used alongside to the model reduction to lift the necessity of direct measurement of the degrees of freedom where the active nonlinear element is located. An experimental setup of a bolted joint structure is used to demonstrate the application of reduced order modeling for identification purpose. The results quantify the accuracy of the selected model in predicting global responses of the structure such as amplitude-dependent frequencies and damping ratios. Keyword s Damping nonlinearity · Structural identification · Bolted joints · Virtual sensing · Model reduction 5.1 Introduction Efficient and lightweight structures developed for the industrial application like aerospace exhibit levels of nonlinearity during vibration test. The development of effective system identification techniques applicable to nonlinear systems is a major demand by dynamitists [1]. In this context, nonlinear characterization and quantification regarded as nonlinear model selection and parameter estimation using measured data is still a challenging task [2]. Although it is possible to build lowdimensional parametric models via nonlinear modal reduced order modeling (NMROM), these techniques usually demand high number of modal bases to accurately approximate the responses of large structural models when modal couplings are present [1]. This issue often compromises the efficiency of model reduction for nonlinear structures and consequently nonlinear identification. This chapter explores ways to efficiently determine the minimum number of modal bases needed to successfully perform the nonlinear identification problem. This is accomplished through a data-driven methodology for the structural identification of nonlinear assemblies with mechanical joints (localized nonlinearities) in which model reduction and virtual sensing are employed to allow identifying nonlinearities in known but inaccessible-to-measure locations. 5.2 Methodology Consider a multi-degree-of-freedom mechanical system of the form below in the physical domain .M¨q(t) +C˙q(t) +Kq(t) + r i=1 ρ T i fnli ρiq(t), ρi ˙q(t) =F(t) (5.1 ) S. Safari ( ) · J. M. Londoño Monsalve Faculty of Environment, Science and Economy (ESE), University of Exeter, Exeter, UK e-mail: ss1072@exeter.ac.uk © The Society for Experimental Mechanics, Inc. 2024 M. R. W. Brake et al. (eds.), Nonlinear Structures & Systems, Volume 1 , Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-36999-5_5 33
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