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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Kluwer Academic Publishers

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DOI

10.1002/uog.6384

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1573-269X

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SteadyState dynamics of a linear structure weakly

Authors: Pramod Malatkar Ali H Nayfeh
Publish Date: 2006/09/13
Volume: 47, Issue: 1-3, Pages: 167-179
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Abstract

We present a theoretical study of the dynamics of the coupled system of Jiang McFarland Bergman and Vakakis It comprises a harmonically excited linear subsystem weakly coupled to an essentially nonlinear oscillator We explored the rich dynamics exhibited by this coupled system by determining its periodic responses and their bifurcations Not surprisingly we found a lot of interesting dynamics over a broad frequency range cyclicfold Hopf symmetrybreaking and perioddoubling bifurcations phaselocked motions regions with multiple coexisting solutions hysteresis and chaos We did not find any occurrence of energy transfer via modulation also known as zerotoone internal resonance theoretically the possibility of its occurrence was ruled out for systems with weak nonlinearity and damping Finally we investigated the ef fectiveness of the socalled nonlinear energy sink NES in vibration attenuation of forced linear structures We found that the NES results in an increase in the vibration amplitude of the linear subsystem especially when the damping is low contrary to the claim made by Jiang et al Also we did not find any indication of nonlinear energy pumping or localization of energy in the NES away from the directly forced linear subsystem indicating that the NES is not ef fective for controlling the vibrations of forced linear structures

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