Chapter 7 A Modal Model to Simulate Typical Structural Dynamic Nonlinearity Randall L. Mayes, Benjamin R. Pacini, and Daniel R. Roettgen Abstract Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions. Keywords Nonlinear system identification • Nonlinear simulation • Structural dynamics • Modal model Nomenclature d(t) Decay function for damping as function of time Modal damping ratio ! Frequency in radians per second H Hilbert transform (t) Phase as a function of time ¦ Iwan parameter related to power law damping ‰ Modal filter vector F Subscript for Fourier transform C Superscript indicating the Moore-Penrose pseudo-inverse of a matrix A Amplitude c Damping coefficient d Subscript for damped dof Degree of freedom f Frequency in cycles/sec F Force FRF Frequency response function H Frequency response function matrix k Stiffness coefficient Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy National Nuclear Security Administration under Contract DE-AC04-94AL85000. R.L. Mayes ( ) • B.R. Pacini Structural Dynamics X-Ray/NDE Department, Sandia National Laboratories, P.O. Box 5800 – MS0557, Albuquerque, NM 87185, USA e-mail: rlmayes@sandia.gov; brpacin@sandia.gov D.R. Roettgen Engineering Mechanics Department, University of Wisconsin – Madison, Madison, WI, USA e-mail: droettgen@wisc.edu © The Society for Experimental Mechanics, Inc. 2016 M. Allen et al. (eds.), Dynamics of Coupled Structures, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29763-7_7 57
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