Download Advanced Nonlinear Strategies for Vibration Mitigation and by Alexander F. Vakakis PDF

By Alexander F. Vakakis

The papers during this quantity handle complex nonlinear themes within the common parts of vibration mitigation and approach identity, comparable to, tools of study of strongly nonlinear dyanmical platforms; strategies and methodologies for reading complicated, multi-frequency transitions in damped nonlinear responses; new methods for passive vibration mitigation in keeping with nonlinear specific power move (TET) and the linked suggestion of nonlinear power sink (NES); and an outline and overview of present nonlinear process identity thoughts.

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9H7< 5 5B8 G7<9A5H=7 6 C: H<9 H97HIF9G 5F9 7CBFA98 6M =;IF9G  5B8  H<9 K5J9@9H GD97 HF5 C: H<9 CCF 8=GD@579A9BHG F9@5H=J9 HC ;FCIB8 G

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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 ) .

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