The linear dynamics of many structural systems is characterized by multiple internal resonances. Such systems may exhibit a high sensitivity of the eigenproperties with respect to a set of significant mechanical parameters. This condition is recognized as the source of relevant phenomena, as frequency veering and mode localization or hybridization. The leading idea of the present work consists in systematically treating nearly-resonant Hamiltonian systems as perturbations of a reference, unknown a priori, resonant system. Given a nearly-resonant experimental system, a multiparameter perturbation method is presented in order to, first, identify in the parameter space a close resonant system (inverse problem), and, second, use the identified resonant system as suited initial point to approximate the eigensolution of the systems originated by a generic multi-parameter perturbation (direct problem). The conditions of existence and uniqueness of the inverse problem solution, as well as the subsequent validity of the perturbation-based sensitivity analysis are discussed

"Multi-parameter perturbation methods for the eigensolution sensitivity in discrete systems exhibiting multiple frequency veering"

LEPIDI, MARCO;
2009

Abstract

The linear dynamics of many structural systems is characterized by multiple internal resonances. Such systems may exhibit a high sensitivity of the eigenproperties with respect to a set of significant mechanical parameters. This condition is recognized as the source of relevant phenomena, as frequency veering and mode localization or hybridization. The leading idea of the present work consists in systematically treating nearly-resonant Hamiltonian systems as perturbations of a reference, unknown a priori, resonant system. Given a nearly-resonant experimental system, a multiparameter perturbation method is presented in order to, first, identify in the parameter space a close resonant system (inverse problem), and, second, use the identified resonant system as suited initial point to approximate the eigensolution of the systems originated by a generic multi-parameter perturbation (direct problem). The conditions of existence and uniqueness of the inverse problem solution, as well as the subsequent validity of the perturbation-based sensitivity analysis are discussed
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/503525
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