Inducing Passive Nonlinear Energy Sinks in Vibrating Systems

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.

Particle impact dampers: Past, present, and future

“…In other words, the goal of reducing the vibration for a wide range of frequencies can be attained by NES. [90][91][92] On the basis of the traditional TMD, Li and Song et al [18][19][20] added the impact energy dissipation and put forward the pounding TMD. In the design, the vibration energy can be dissipated through heat generated by the impact or pounding between a tuned mass block and a delimiter covered with viscous-elastic material.…”

Vibratory energy exchanges between a system with a chain of Saint-Venant elements and a nonlinear energy sink

“…1: It consists of two oscillators. The first one with mass, stiffness and damping as M, k 0 andλ, respectively which possesses a set of Saint-Venant elements in parallel with characteristics ask j and α j , j = 1, 2, ..., n. The second oscillator, namely NES has the mass, stiffness and damping as m (0 < = m M 1),c l andλ 1 . The potential of the NES is considered to be nonlinear in general.…”

“…One of these nonlinear system (mainely cubic) is names as nonlinear energy sink (NES) and the phenomenon is called energy pumping [1,2]. Non-smooth nonlinear systems due their efficiency and feasibilities in fabrications and design are of highly interests in industrially [3].…”

Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment

“…It has been proved that by endowing nonlinear innate of some special light attachments, namely Nonlinear Energy Sink (NES), it is possible to localize the vibratory energy of important oscillators which are mainly linear [1]. This localization, which is called energy pumping or targeted energy transfer, can be operated for control and/or energy harvesting.…”