Towards a new type of energy trap: Classical analog of quantum Landau-Zener tunneling

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

Research output: Contribution to journalArticle

Abstract

We present a novel type of an energy trap providing targeted energy transfer in a system of weakly coupled pendulums. Our approach is based on the analogy we revealed between the behavior of two weakly coupled classical parametric pendulums (in linear approximation) and the nonadiabatic Landau-Zener tunneling in a two-state quantum system. This analogy leads us to the prediction of an efficient irreversible transfer of vibration energy from one subsystem to another, when the eigenfrequency of at least one of them changes in time, so that the coupled subsystems pass through an 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.

Original languageEnglish (US)
Pages (from-to)247-252
Number of pages6
JournalInternational Journal of Non-Linear Mechanics
Volume46
Issue number1
DOIs
StatePublished - Jan 1 2011

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Pendulum
Pendulums
Trap
Analogue
Analogy
Subsystem
Energy
Internal Resonance
Eigenfrequency
Absorber
Linear Approximation
Energy Transfer
Mechanical Systems
Quantum Systems
Energy transfer
Vibration
Prediction

Keywords

  • Coupled parametric pendulums
  • Energy trap
  • Landau-Zener tunneling
  • Targeted energy transfer

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

Towards a new type of energy trap : Classical analog of quantum Landau-Zener tunneling. / Manevitch, Leonid I.; Kosevich, Yury A.; Mane, Mercedes; Sigalov, Grigori; Bergman, Lawrence; Vakakis, Alexander F.

In: International Journal of Non-Linear Mechanics, Vol. 46, No. 1, 01.01.2011, p. 247-252.

Research output: Contribution to journalArticle

Manevitch, Leonid I. ; Kosevich, Yury A. ; Mane, Mercedes ; Sigalov, Grigori ; Bergman, Lawrence ; Vakakis, Alexander F. / Towards a new type of energy trap : Classical analog of quantum Landau-Zener tunneling. In: International Journal of Non-Linear Mechanics. 2011 ; Vol. 46, No. 1. pp. 247-252.
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