Abstract
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 study 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.
Original language | English (US) |
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Pages (from-to) | 324-332 |
Number of pages | 9 |
Journal | Journal of Vibration and Acoustics, Transactions of the ASME |
Volume | 123 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2001 |
ASJC Scopus subject areas
- Acoustics and Ultrasonics
- Mechanics of Materials
- Mechanical Engineering