Chapter 7 Model Updating of Nonlinear Structures Güvenç Canbalog˘lu and H. Nevzat Özgüven Abstract There are always certain discrepancies between modal data of a structure obtained from its mathematical model and experimentally measured ones. Therefore it is a general practice to update the theoretical model by using experimental measurements in order to have a more accurate model. Since in several real life engineering problems there exist structural nonlinearities, model updating of nonlinear structures come into prominence. To be able to apply one of the well-established model updating methods, the linear FRFs of a nonlinear structure are to be measured. Although it may be possible to obtain linear FRFs of a nonlinear structure experimentally with a certain approximation by using low level forcing in FRF measurement, when there is frictional type of nonlinearity, this is not possible. In this study a model updating method for nonlinear structures is proposed. A noble method developed recently by the authors to obtain linear FRFs of nonlinear structures having multiple nonlinearities including friction type of nonlinearity is used in the nonlinear model updating approach proposed. The method is validated by applying the method developed to a nonlinear test system. Keywords Nonlinear model updating • Model updating • Nonlinear structures • Nonlinearity • Friction nonlinearity 7.1 Introduction Numerical structural modeling is a common practice to obtain dynamic response of engineering structures, and finite element (FE) method has established itself as the most common numerical method. Since FE methods have certain inaccuracies due to modeling errors, experimental and FE method results do not always match perfectly. In order to correct the mathematical model so that these discrepancies will be eliminated, some of the parameters used in the FE models need to be changed by using model updating techniques. In literature, various model updating methods were proposed in order to have accurate numerical structural models. However; most of these methods are for linear systems. Sidhu and Ewins [1] used the error matrix equation to correlate FE model and test results of an aerospace structure better. Dascotte and Vanhonacker [2] developed an automatic updating procedure based on natural eigenfrequency sensitivity. Brughmans and Lembregts [3] studied the effect of experimental modal parameter estimation techniques for normal mode shapes on an optimization procedure for FE mass and stiffness matrices. Nalitolela et al. [4] presented a method which is based on exact model reduction and perturbation of both the actual structure and its analytical model by adding mass or stiffness to produce accurate dynamic models. In order to update FE models Roy et al. [5] proposed direct energy approach which uses the expanded set of experimental modes to relate the kinetic and strain energies of each part of a FE model to the experimental data. Visser and Imregun [6] investigated the use of FRFs for model updating, and discussed the requirement for minimum measured data for successful implementation of the technique. Brughmans et al. [7] discussed the application of a FE model updating technique, based on a forward sensitivity formulation, to a twin propeller commuter aircraft. Ibrahim et al. [8] developed direct updating technique for G. CanbaloMglu ( ) Department of Mechanical Engineering, Middle East Technical University, 06800 Ankara, Turkey MGEO Division, ASELSAN Inc., 06750 Ankara, Turkey e-mail: gcanbal@aselsan.com.tr H.N. Özgüven Department of Mechanical Engineering, Middle East Technical University, 06800 Ankara, Turkey G. Kerschen (ed.), Nonlinear Dynamics, Volume 2: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04522-1__7, © The Society for Experimental Mechanics, Inc. 2014 69
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