Journal
JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME
Volume 123, Issue 3, Pages 324-332Publisher
ASME-AMER SOC MECHANICAL ENG
DOI: 10.1115/1.1368883
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We study the inducement of passive nonlinear sinks in linear vibrating systems. These are substructures that absorb-vibrational energy in a one-way, irreversible fashion. The systems considered are composed of strongly coupled, grounded damped linear oscillators with a strongly nonlinear attachment at the end. Applying a complex averaging technique we derive a set of modulation equations that is directly amenable to physical interpretation, and provides insight into the energy pumping phenomenon. For the case of a two DOF system we show that nonlinear energy pumping occurs when a certain frequency of envelope modulation crosses through zero; then the dynamics of the envelope modulation of the motion resemble the dynamics of a forced rigid body. For the case of an impulsively loaded multi-DOF chain with a nonlinear attachment at the end, we show that after some initial transients the response of the nonlinear attachment sets to a motion dominated by a fast frequency identical to the lower bound of the propagation zone of the linear chain. This feature reduces the steady of energy pumping in the chain to a two DOF equivalent problem. The applications of the energy pumping phenomenon to practical engineering problems are discussed.
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