O. V. Gendelman 1 Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, 32000 Israel e-mail: ovgend@tx.technion.ac.il G. Sigalov College of Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 L. I. Manevitch Institute of Chemical Physics, RAS, Kosygin str. 4, Moscow, Russia M. Mane A. F. Vakakis L. A. Bergman College of Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 Dynamics of an Eccentric Rotational Nonlinear Energy Sink The paper introduces a novel type of nonlinear energy sink, designed as a simple rotating eccentric mass, which can rotate with any frequency and; therefore, inertially couple and resonate with any mode of the primary system. We report on theoretical and experimental investigations of targeted energy transfer in this system. [DOI: 10.1115/1.4005402] 1 Introduction The nonlinear energy sink (NES) has been defined as a single- degree-of-freedom (SDOF) structural element with relatively small mass and weak dissipation, attached to a primary structure via essentially nonlinear coupling [1–3]. If the primary structure is excited by a shock whose energy is above a certain critical thresh- old, the NES can act as broadband passive and adaptive controller by absorbing vibration energy from the primary structure in an almost irreversible manner. This process is referred to as passive targeted energy transfer (TET) [4,5]. Targeted energy transfer nor- mally occurs via transient resonance captures, made possible by the essential (nonlinearizable) stiffness nonlinearity of the NES which prevents a preferential resonance frequency. In previous works it has been shown theoretically, numerically and experi- mentally that the NES can efficiently protect a primary structure against impulsive excitations [6], harmonic (narrowband) loads [7,8], and seismic excitations [9], and it has also been applied to passively suppress aeroelastic instabilities [10,11] and drill-string instabilities [12]. A detailed discussion of the concepts of NES, TET and related issues is presented in a recent monograph [12]. Theoretically, the type of nonlinearity involved in the NES may be rather diverse. In the first papers devoted to the subject [1,2] pure cubic nonlinearity was considered. Later more involved types of nonlinear stiffness were incorporated, including general nonpolynomial [13] monotonic functions, NES with multiple states of equilibrium [14], as well as nonsmooth and vibro-impact NES [15]. Experimentally, only a handful of nonlinear stiffness functions were built and tested. Nonlinear stiffness close to purely cubic was realized with the help of elastic strings or springs with minimal pretension [12,16]. The nonsmooth NES was realized by combining linear elastic and vibro-impact elements [17]. Targeted energy transfer in acoustic systems has been achieved by use of a modified commercial loudspeaker [18]. All these designs allow demonstration and investigation of TET and related phenomena under laboratory conditions, but their long-term performance under actual operating conditions has not yet been shown. How- ever, both for scientific and engineering purposes, it would be de- sirable to develop alternative concepts for NES designs. The basic idea of TET is the ability of the NES to undergo exci- tation over a broad range of frequencies, ultimately related to its essential nonlinearity. Arguably, the simplest system which can be excited at any frequency is a simple, free rotator—quite obviously, the rotation frequency can be arbitrary. Needless to say, this simple system has been widely studied in literature; in particular, it was proposed as a vibration absorber for harmonically excited oscillator [19]. In the current paper, we demonstrate theoretically and experi- mentally that such a rotator can be efficiently used as the NES. 2 Description of the Model and Numerical Demonstration of TET Let us consider the dynamical system schematically presented in Fig. 1. A simple, free eccentric rotator of mass m and radius r 0 is mounted inside a primary oscillator with mass M and linear stiff- ness C. We assume linear viscous damping about the axis of the ro- tator with coefficient c. We mention here that no gravity is taken into account (for instance, the system is mounted horizontally) and the attachment is allowed to freely rotate; so this design should not be confused with the well-known torsional vibration absorber [20]. The Lagrangian of this system (without including dissipation) is expressed as: L ¼ 1 2 ðM þ mÞ _ x 2 þ 1 2 mr 2 0 _ h 2  mr 0 _ x _ h sin h  1 2 Cx 2 (1) where x(t) is the displacement of the primary mass and h(t) is the rotation angle of the eccentric. Damping is taken into account via the Rayleigh dissipation function 1 Corresponding author. Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 11, 2011; final manu- script received May 24, 2011; published online December 13, 2011. Editor: Robert M. McMeeking. Journal of Applied Mechanics JANUARY 2012, Vol. 79 / 011012-1 Copyright V C 2012 by ASME Downloaded 14 Dec 2011 to 132.68.17.202. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm