Chapter 29 Dynamics of Geometrically-Nonlinear Beam Structures, Part 2: Experimental Analysis D. Anastasio, J. Dietrich, J. P. Noël, G. Kerschen, S. Marchesiello, J. Häfele, C. G. Gebhardt, and R. Rolfes Abstract System identification is a key tool to gather information about dynamical structures. In the last decades, important steps have been made to perform this task in the presence of localized nonlinearities. However, the continual interest in improving structural performance has created the need of designing light and flexible elements in several engineering fields. These elements are usually characterized by moderate and large deformations, exhibiting distributed nonlinearities. System identification of structures with distributed nonlinear features remains particularly challenging, especially when dealing with experimental data. This work proposes a method to perform such a task, relying on a convenient basis reduction of the measured signals. The identification is then performed using the nonlinear subspace identification method (NSI) in the reduced domain together with a closed-form nonlinear description. This methodology is validated on an experimental structure, consisting of a very thin steel beam that is clamped at both ends. Excited with a multisine, the beam undergoes large amplitude oscillations. A final objective of the identification is to exploit its response through the correct identification of the parameters that define the nonlinearity. Results show a high level of accuracy, which validates the effectiveness of the methodology and paves the way toward the identification of more complex real-life structures exhibiting large deformations. Keywords Nonlinear system identification · Subspace identification · Geometrical nonlinearity · Nonlinear beam · Large deformation 29.1 Introduction Large-amplitude vibrations of mechanical structures have been studied for decades, and many efforts have been made in order to mathematically represent their characteristics [1]. However, their importance has increased in the last years, driven by the need for designing flexible and light structures [2]. Generally, geometrical nonlinearity arises when a structure undergoes large amplitude vibrations, resulting in nonlinear strain-displacement relations. In this framework, a nonlinear model is very often obtained relying on a convenient basis reduction [3]. Linear normal modes (LNMs) are the most common choice when dealing with linear systems, but they have some limitations when nonlinearities are present [4]. Yet, their implementation is fairly easy especially when dealing with experimental data, and they are still capable of giving a nonlinear dynamical description when moderately large amplitude vibrations are considered [5]. In this work, a method is presented to identify a distributed nonlinear behavior from experimental data, relying on such a reduction. The identification is then performed using the nonlinear subspace identification (NSI) method [6–8] in the reduced domain using a closed-form nonlinear description. This approach has already been tested on numerical data [9], and it is now validated on experimental measurements acquired on a very thin clamped-clamped beam, undergoing large amplitude vibrations. D. Anastasio ( ) · S. Marchesiello Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, Italy e-mail: dario.anastasio@polito.it J. Dietrich · J. Häfele · C. G. Gebhardt · R. Rolfes Institute of Structural Analysis, Leibniz Universität Hannover, Hannover, Germany J. P. Noël · G. Kerschen Space Structures & Systems Lab., Bldg B52/3, Department of Aerospace and Mechanical Engineering, University of Liège, Liège, Belgium © Society for Experimental Mechanics, Inc. 2020 G. Kerschen et al. (eds.), Nonlinear Structures and Systems, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12391-8_29 217
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