Designing a new type of energy trap: A classical analog of quantum Landau-Zener tunneling

Alexander F. Vakakis, Grigori Sigalov, Mercedes Mane, Lawrence A. Bergman, Leonid I. Manevitch, Yury A. Kosevich

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
Pages361-367
Number of pages7
EditionPARTS A AND B
DOIs
StatePublished - Dec 1 2011
EventASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 - Washington, DC, United States
Duration: Aug 28 2011Aug 31 2011

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
NumberPARTS A AND B
Volume1

Other

OtherASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
CountryUnited States
CityWashington, DC
Period8/28/118/31/11

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ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

Cite this

Vakakis, A. F., Sigalov, G., Mane, M., Bergman, L. A., Manevitch, L. I., & Kosevich, Y. A. (2011). Designing a new type of energy trap: A classical analog of quantum Landau-Zener tunneling. In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 (PARTS A AND B ed., pp. 361-367). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 1, No. PARTS A AND B). https://doi.org/10.1115/DETC2011-47690