Nonlinear Dynamics 33: 87–102, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. Steady State Passive Nonlinear Energy Pumping in Coupled Oscillators: Theoretical and Experimental Results XIAOAI JIANG Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, 104 S. Wright Str., Urbana, IL 61801, U.S.A.; E-mail: jiangxa@umich.edu D. MICHAEL MCFARLAND and LAWRENCE A. BERGMAN Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign. 104 S. Wright Str., Urbana, IL 61801, U.S.A.; E-mail: {dmmcf,lbergman}@uiuc.edu ALEXANDER F. VAKAKIS ⋆ Division of Mechanics, National Technical University of Athens, P.O. Box 64042, GR-157 10 Zografos, Athens, Greece; E-mail: vakakis@central.ntua.gr; and Department of Mechanical and Industrial Engineering (adjunct), University of Illinois at Urbana-Champaign, 1206 W. Green Str., Urbana, IL 61801, U.S.A.; E-mail: avakakis@uiuc.edu (Received: 23 July 2002; accepted: 31 March 2003) Abstract. We study theoretically and experimentally the effect that a nonlinear energy sink (NES) has on the steady state dynamics of a weakly coupled system. The NES possesses essentially nonlinear (nonlinearizable) stiffness nonlinearity of the third degree. We find that, in contrast to the classical linear vibration absorber, the NES is capable of absorbing steady state vibration energy from the linear oscillator over a relatively broad frequency range. This results in localization of the steady state vibration in the NES, away from the directly forced subsystem. For a forward frequency sweep the localized branch of steady state motions is suddenly eliminated by a jump to a linearized low-amplitude motion, whereas, for a backward frequency sweep a reverse jump occurs. The difference in the frequencies of the two jumps introduces a nonlinear hysteresis loop. This work extends to the steady state case of earlier transient passive energy pumping results. The notion of passively transferring vibration energy to an a priori determined NES, weakly attached to a main structure, is novel. The use of nonlinear energy sinks for passively absorbing energy from a linear main structure can form the basis of relatively simple and modular vibration and shock isolation designs of mechanical systems. Keywords: Nonlinear localization, steady state motions. 1. Introduction Vibration isolation has been a very important issue in engineering since a long time ago. Simply posed, the objective of a vibration isolation design is to prevent unwanted vibrations (disturbances) generated at a system from being transmitted to other neighboring connected systems. It represents an area of engineering with many and broad applications, ranging from industrial problems to applications in our daily life. To name a few, isolation of space- and aero-structures, vibrating machinery, or buildings, packaging, noise transmission cancellation, isolation of household appliances, and vehicle suspensions. In many applications the use of active controllers for vibration isolation is not feasible, for reasons including, cost, added weight or required independent energy supply. Hence, designs ⋆ Author for correspondence.