By Alexander F. Vakakis
The papers during this quantity handle complicated nonlinear themes within the normal parts of vibration mitigation and approach id, equivalent to, equipment of study of strongly nonlinear dyanmical structures; suggestions and methodologies for studying complicated, multi-frequency transitions in damped nonlinear responses; new methods for passive vibration mitigation in response to nonlinear distinctive power move (TET) and the linked suggestion of nonlinear power sink (NES); and an outline and evaluate of present nonlinear process id strategies.
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Extra info for Advanced Nonlinear Strategies for Vibration Mitigation and System Identification
The coefficient of the nonlinear term can be modified by proper rescaling of the dependent variables and the forcing amplitude; the value (4H / 3) is chosen for the sake of convenience. We will analyze the steady state periodic responses of (1) by the complexification – averaging (CX-A) methodology. To this end, we apply the following coordinate transformations, denoting the center-of-mass and relative displacements of the system, v y1 H y2 w y1 y2 (2) and then switch the analysis to complex variables: M1 exp( jt ) v jv M2 exp( jt ) w jw (3) By (3) we partition the dynamics into slow and fast components, and make the additional ansatz that the sought steady state responses are in the form of fast oscillations exp( jt ) modulated by slowly-varying complex amplitudes Mi (t ) .
Gendelman* and Y. Starosvetsky* Faculty of Mechanical Engineering Technion – Israel Institute of Technology Haifa 32000 Israel Abstract. We show that the steady state response of a primary system under harmonic excitation with an attached nonlinear energy sink (NES) exhibits not only common steady – state and weakly modulated responses, but also strongly modulated responses (SMRs), which may be regarded as the extension of the targeted energy transfer (TET) phenomenon to structures under periodic excitation.
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