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Designing a New Type of Energy Trap: A Classical Analog of Quantum Landau-Zener Tunneling

[+] Author Affiliations
Alexander F. Vakakis, Grigori Sigalov, Mercedes Mane, Lawrence A. Bergman

University of Illinois at Urbana-Champaign, Urbana, IL

Leonid I. Manevitch, Yury A. Kosevich

Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia

Paper No. DETC2011-47690, pp. 361-367; 7 pages
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5478-5
  • Copyright © 2011 by ASME


We present a novel type of energy trap providing targeted energy transfer (TET) in a system of weakly coupled pendulums. Our approach is based on the analogy, presented in [1, 2], between the behavior of two weakly coupled classical parametric pendulums and nonadiabatic Landau-Zener tunneling (LZT) in a two-state quantum system. The two systems, however dissimilar, turn out to be described by the same asymptotic equations. Well-known properties of LZT allow us to predict the possibility of efficient irreversible transfer of vibration energy from one subsystem to another in mechanical systems. The TET takes place when the eigenfrequency of a subsystem changes in time so that the coupled subsystems pass through internal resonance. The existence of such a phenomenon is not restricted to coupled pendulums but is inherent to a wide class of both linear and nonlinear parametric oscillatory systems. This opens up the possibility of designing new types of energy traps and absorbers for the dynamic protection of various mechanical systems. Experimental data obtained in this work corroborate theoretical predictions.

Copyright © 2011 by ASME



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