Challenges of Characterizing Geometric Nonlinearity of a Double-Clamped Thin Beam Using Nonlinear Modal Testing Methods Mahesh Nagesh, Randall J. Allemang, and Allyn W. Phillips Abstract Phase-locked loop (PLL) controllers are increasingly employed for obtaining nonlinear frequency response curves (FRC) and backbone curves. Such controllers provide a specific phase lag between the response obtained and the excitation signal and isolate the nonlinear mode under consideration. The use of such feedback controllers provides many advantages against traditional sine-sweep methods and helps better characterize nonlinear behavior of dynamic systems. This paper briefly discusses about obtaining the nonlinear frequency response curves (FRC) and backbone curves of both symmetric and asymmetric modes of a double-clamped thin beam exhibiting geometric nonlinearity including a qualitative analysis such as stability and other prominent issues that arise during nonlinear modal testing particularly when the technique is applied to athinandlight structure. A comparison of nonlinear modal testing using PLL controllers as against other traditional methods such as sine-sweep methods is also demonstrated. Keywords Nonlinear modal testing · Phase-locked loop · Nonlinear frequency response · Geometric nonlinearity 1 Introduction Analysis of dynamic systems that exhibit nonlinear force-response relationships is very challenging. In particular, experimental characterization of such behavior is extremely challenging and requires adequate understanding of all aspects of experimentation while interpreting the experimental data. Nonlinearity is readily encountered in extremely thin and light structures, and widely available experimental modal analysis and modal parameter estimation techniques used for generally linear structures [1–5] cannot be applied to such thin and light structures. Current widespread use of such structures must be accompanied by adequate understanding of the complex phenomenon associated with them, such as variations of natural frequencies, deflection characteristics, damping, and other important parameters with variations in forcing levels and other relevant factors. In addition to the characteristics of the test structure, also of foremost importance during experimentation with thin and light structures is the use of traditional modal shakers to obtain such characteristics. While modal shakers are robust devices capable of various operations, their applications to thin and light structures are often limited and sometimes lead to incorrect characterization. Detailed theoretical analysis and modeling of dynamic behavior of nonlinear structures is widely available [6–8]. Experimental techniques for analysis of such nonlinear structures are widely available and well documented in [7–10]; common issues of applying linear modal analysis techniques to nonlinear structures are detailed in [11]. The variation of frequencies and other important parameters with variations in forcing levels applied to nonlinear structures is traditionally characterized using sine-sweep methods [7, 9, 10]. These methods provide frequency response curves (FRC) that show variations of characteristics at constant force level. A FRC is used for nonlinear analysis that provides actual response at a given force level instead of using a traditional frequency response function (FRF) approach used in linear systems that is generally force normalized. Lately, control-based phase resonance testing of nonlinear structures has gained widespread popularity. Two such techniques are widely available and in current use by researchers, viz. phase-locked loop (PLL) and control-based continuation [12–16]. 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_20 179
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