Chapter 24 Techniques for Nonlinear Identification and Maximizing Modal Response D. Roettgen, B. R. Pacini, and R. Mayes Abstract Recent research has shown that weakly nonlinear structures can be modeled as a combination of nonlinear pseudomodal models. These modal models consist of a linear spring, mass, and damper with the addition of a nonlinear element often identified using a restoring force surface technique. This approach is limited by force level achieved when exciting the system for identification. Extrapolation leads to poor results when predicting the nonlinear response; thus, there is a need to maximize the modal amplitude excited in these weakly nonlinear structures. Previous works have compared hammer testing to shaker testing using windowed sinusoidal input forces. This appeared to be a promising technique to increasing the excited modal amplitude. In this work the windowed sinusoidal technique is further investigated to understand how window parameters (such as window width) can be optimized to maximize the modal amplitude obtained during the identification process. Keywords Nonlinear system identification · Experimental techniques · Structural dynamics · Modal analysis · Nonlinear testing methods 24.1 Introduction Many industries design and manufacture mechanical structures with bolted joints. The frictional interfaces that occur due to these joints often introduce nonlinearity into an otherwise linear system. Two main approaches exist to account for these nonlinearities: local physical models and pseudo-modal modeling [1–3]. Local physical modeling attempts to capture the physics happening at each local joint. While physically insightful, this method can be computationally expensive, and the constituative models require expensive calibration for every structural joint. Nonlinear pseudo-modal modeling is computationally inexpensive, and nonlinear parameters can be identified from a quick experiment focused on each nonlinear mode. In this work, a weakly nonlinear system is studied which exhibited small shifts in frequency with large changes in damping. In previous works [4, 5] pseudo-modal modeling was found to be a practical approach for this type of nonlinear system. Nonlinear pseudo-modal models take a form analogous to a standard modal model except augmenting a single degreeof-freedom (DOF) system with a nonlinear forcing element. This element has taken many forms, from an Iwan element [6] to simple polynomial springs and dampers [5]. This approach relies on two primary assumptions. First, the modes of the system must remain uncoupled in the amplitude range of interest. Second, the mode shapes of the system must not change with amplitude. These assumptions allow for the use of a modal filter to obtain single degree-of-freedom signals in order to identify a nonlinear model. Like most nonlinear modeling techniques, the model is only accurate in the amplitude range used in parameter identification, so maximizing this amplitude range is of great interest. In previous works [4, 7], the achievable structural response was not limited by mechanical factors but by the maximum allowable voltage output by the shaker amplifier. The objective of this work is to maximize the modal response using the Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. D. Roettgen ( ) · B. R. Pacini · R. Mayes Department of Structural Dynamics, Sandia National Laboratories, Albuquerque, NM, USA e-mail: drroett@sandia.gov © 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_24 173
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