Using Transmissibility measurements for Nonlinear Identification A Carrella1, DJ Ewins1, L Harper2 1 University of Bristol, Faculty of Engineering, Bristol, BS8 1TR, 2 AgustaWestland UK, Yeovil, BA20 2YB Abstract In order to improve the predictive capability of the mathematical or numerical models of engineering structures, there is a need to capture their physical behaviour based on experimental measurements. In dynamics, this is accomplished with specific vibration tests, such as the Ground Vibration Test (GVT) used in aerospace applications. Currently, it seems that the engineering community lacks appropriate tools for the detection and quantification of dynamic nonlinearities during vibration tests. Of the nonlinear identification methods developed during the past 30 years, only a few are suitable for application on practical engineering structures. One of these has the particular advantage of requiring standard measurement techniques and sensors and is based on the analysis of Frequency Response Function (FRF) data. However, in many practical applications, structures are required to be tested by excitation of the base, so that transmissibilities are measured in place of FRFs. In this paper an existing identification method based on FRF data is shown to be applicable also when transmissibility is measured. Numerical simulations are used to demonstrate the applicability of the method. INTRODUCTION In many engineering applications, numerical analysis based on mathematical models is becoming a major feature of the design stage. The main purpose of the model, most commonly a Finite Element (FE) model, is to enable the designers to predict a system’s dynamic under different structural and loading conditions. It can be argued that in order to increase the accuracy and the prediction capability of the numerical models, nonlinear effects cannot be neglected. The validation process aims at ameliorating the quality of the model by comparing the numerical analysis results with experimental data and applying the necessary changes to the model in order to minimise the difference between simulations and experiments. For a more reliable and accurate model, there is thus a need for being able to extract nonlinear parameters from measured data. The modal parameters (natural frequencies, modal damping and mode shapes) extracted using standard - and nowadays very advanced - techniques, are in many cases accurate enough for structural dynamic design purposes. However, there are instances in which the nonlinear effects cannot be ignored. A nonlinear behaviour can results in drastic changes of natural frequency or damping. Furthermore, these modal quantities can be dependent on several variables, i.e. the nature of the nonlinearities is due, for example, to amplitude of vibration, frequency of excitation, temperature, etc. There is a need for a structured procedure, or Non Linear Modal Testing (NLMT), which allow engineers and dynamicists to identify and quantify the structural nonlinearities in standard testing environment. The reference textbook, and arguably the only book on the subject, on identification and quantification of nonlinearities in structural dynamics was published in 2001 by Worden and Tomlinson [1]. Some years later, Kershen et al [2] have contributed to the subject by publishing a review paper in which 446 references were cited. As these authors stated, their review has inevitably missed some works on the subject. Probably for reasons of commercial interest, there is a scarcity of works published on NLMT that refers to industrial research and/or practice. Some methods that the authors of this paper deem of practical applicability are the Restoring Force Surface (RFS), [3], the Inverse Method [4] and the Linearity Plots, T. Proulx (ed.), Modal Analysis Topics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series 6, 479 DOI 10.1007/978-1-4419-9299-4_39, © The Society for Experimental Mechanics, Inc. 2011
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