A Hybrid Static and Dynamic Model Updating Technique for Structures Exhibiting Geometric Nonlinearity Mahesh Nagesh, Randall J. Allemang, and Allyn W. Phillips Abstract Finite element methods (FEM) are commonly used to analyze the behavior of various dynamic systems. Several model updating techniques are available that can be used for linear or nonlinear dynamic systems and help reduce discrepancies between characteristics obtained from the FE models and their experimental counterparts. Linear model updating techniques employ eigen solutions or the frequency response functions (FRF) to reduce errors between the discretized mass [M], damping [C], and stiffness [K] terms or FRF terms directly. However, model updating of structures exhibiting nonlinear behavior is seldom straightforward and requires special consideration of various terms contributing to the nonlinear responses when modeling the system. This paper investigates a hybrid static and dynamic model updating technique for structures exhibiting geometric nonlinearity. The static model updating minimizes errors in stiffness modeling and the dynamic model updating minimizes errors in modeling non-stiffness terms of the FE model. Keywords Model updating · Geometric nonlinearity · Hybrid techniques 1 Introduction Finite element model updating (FEMU) in structural dynamics uses one or more techniques to reduce the discrepancy between modal parameters and response characteristics obtained from a finite element model (FEM) and a corresponding experimental data obtained for the system. This topic has gained more prominence in recent years with the introduction of extremely light structural components with complex and varying geometries, material characteristics, etc. Well-established FEMU techniques are popularly used for structures behaving under the linear assumption. Friswell and Mottershead [1, 2] provide the earliest detailed description of both direct and iterative methods using modal data and frequency response function (FRF) data for FEMU. One such popular iterative modal method is the inverse eigen sensitivity method (IESM) formulated by Lin et al. [3, 4]. Methods that formulate the model updating using FRF data include the response function method formulated by Grafe, Lin, and Ewins [5–7]. A comprehensive listing of the further improvements and advancements since is found in [8] along with a comparative study of both methods available in [9]. More recent works on the sensitivity method include [10] where the importance of equation conditioning and quality of model updating is elaborated. Other techniques utilize some form of computational intelligence for FEMU [11] and a few other have utilized popular linear FEMU and then used various other techniques to update nonlinear models as well [12–15]. Most FEMU techniques have their own merits and demerits. These techniques generally formulate a sensitivity analysis problem that is solved using a least-squares approach. A common problem encountered is the balance between total number of variables that require updating and the total available data since most techniques rely only on FRFs obtained during experimental modal analysis and/or modal parameters estimated from these FRFs [16–19]. In order to overcome this issue, an earlier work by the authors [20] discusses a hybrid static and dynamic model updating technique for linear dynamic systems, which updates the linear stiffness matrix of the FE model based on static tests, i.e., update at zero frequency followed by a mass updating performed on this static updated model to obtain a complete model that works for both static and dynamic type tests. Static tests are generally employed prior to a dynamic test to determine linearity of a system, verify global parameters, detect type of nonlinearity in a system, etc. [21–23]. Some FRF-based methods are also used for static M. Nagesh ( ) · R. J. Allemang · A. W. Phillips Structural Dynamics Research Laboratory (SDRL), Department of Mechanical and Materials Engineering, College of Engineering and Applied Sciences, University of Cincinnati, Cincinnati, OH, USA e-mail: nageshmh@mail.uc.edu; allemarj@ucmail.uc.edu; philliaw@ucmail.uc.edu © The Society for Experimental Mechanics, Inc. 2022 G. Kerschen et al. (eds.), Nonlinear Structures & Systems, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-77135-5_17 151
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