Chapter 3 Prediction of Nonlinear Forced Response on Ancillary Subsystem Components Attached to Reduced Linear Systems Sergio E. Obando, Peter Avitabile, and Jason Foley Abstract Industrial size FE models often times involve multiple interconnected linear components with very high fidelity resolution and very refined mesh. The prediction of the dynamic characteristics of this type of system can be costly and inefficient, in particular, when localized nonlinearities are present due to coupling elements such as hard contacts, isolation mounts, gap springs, bilinear springs, etc. Reduction methodologies are currently employed in this setting to decrease the set of active degrees of freedom in the FEM and efficiently compute the nonlinear system response. For complete multicomponent systems with complicated nonlinear subcomponent configurations, the dynamic response of the system will have the embedded characteristics of the appended/ancillary subcomponents but the fidelity of the model will be highly dependent on the quality and resolution of the model. Therefore, sufficient substructure information is needed for an accurate prediction of the response of the appendage and/or its coupling structure. In this work, analytical models of a multi-component beam system with nonlinear contact interactions were created to investigate the prediction of the dynamic response of ancillary subsystem components. The ancillary structure will be assumed to be dynamically active but will not contain any degrees of freedom in the reduced model. The models will be created first at full space as a reference and then reduction techniques will be used to determine the necessary information in order to accurately predict the displacement at the appendage. The dynamic characteristics of the ancillary component will be extracted using the subcomponent information available from the system. The solution is obtained from piecewise linear approximations of the reduced order model and expansion is used to obtained system level response at all DOF. Keywords Forced nonlinear response • Reduced order modeling • Cascaded components Nomenclature Symbols fXng Full Set Displacement Vector fXag Reduced Set Displacement Vector fXdg Deleted Set Displacement Vector [Ma] Reduced Mass Matrix [Mn] Expanded Mass Matrix [Ka] Reduced Stiffness Matrix [Kn] Expanded Stiffness Matrix [Ua] Reduced Set Shape Matrix [Un] Full Set Shape Matrix [Ua] g Generalized Inverse [T] Transformation Matrix [TU] SEREP Transformation Matrix S.E. Obando ( ) • P. Avitabile Structural Dynamics and Acoustic Systems Laboratory, University of Massachusetts Lowell, One University Avenue, Lowell, MA 01854, USA e-mail: sergio.e.obando@gmail.com J. Foley Air Force Research Laboratory, Munitions Directorate, Fuzes Branch, Eglin Air Force Base, 306 W. Eglin Blvd, Bldg 432, Eglin AFB, Valparaiso, FL 32542-5430, USA © The Society for Experimental Mechanics, Inc. 2016 G. Kerschen (ed.), Nonlinear Dynamics, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-15221-9_3 23
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