Targeted energy transfer between dynamical components due to essential nonlinearities: A stochastic perspective

T. P. Sapsis, Alexander F Vakakis, L. A. Bergman

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

Abstract

The problem ofTargeted EnergyTransfer (TET) from a linear mechanical medium to a nonlinear attachment is considered in the presence of stochasticity. We consider a generic linear system connected with an essentially nonlinear attachment in the presence of stochastic excitation to both the linear system and the nonlinear attachment. Then we transform the full problem to a single, stochastic, nonlinear, intergro-differential equation that captures the full dynamics and contains the complete probabilistic information of the problem. By approximating the dynamics in the early time regime we are able to describe the nonlinear interactions and energy transfers in terms of a Fokker-Planck equation that captures the evolution of the pdf.We analyze the form of the stochastic response and illustrate the interplay between the non-Gaussian properties, the nonlinear energy transfers, and the positive Lyapunov exponents.

Original languageEnglish (US)
Title of host publicationSafety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013
Pages1921-1928
Number of pages8
StatePublished - Dec 1 2013
Event11th International Conference on Structural Safety and Reliability, ICOSSAR 2013 - New York, NY, United States
Duration: Jun 16 2013Jun 20 2013

Publication series

NameSafety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013

Other

Other11th International Conference on Structural Safety and Reliability, ICOSSAR 2013
CountryUnited States
CityNew York, NY
Period6/16/136/20/13

Fingerprint

Energy transfer
Linear systems
Fokker Planck equation
Differential equations

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Safety, Risk, Reliability and Quality

Cite this

Sapsis, T. P., Vakakis, A. F., & Bergman, L. A. (2013). Targeted energy transfer between dynamical components due to essential nonlinearities: A stochastic perspective. In Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013 (pp. 1921-1928). (Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013).

Targeted energy transfer between dynamical components due to essential nonlinearities : A stochastic perspective. / Sapsis, T. P.; Vakakis, Alexander F; Bergman, L. A.

Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013. 2013. p. 1921-1928 (Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013).

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

Sapsis, TP, Vakakis, AF & Bergman, LA 2013, Targeted energy transfer between dynamical components due to essential nonlinearities: A stochastic perspective. in Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013. Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013, pp. 1921-1928, 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013, New York, NY, United States, 6/16/13.
Sapsis TP, Vakakis AF, Bergman LA. Targeted energy transfer between dynamical components due to essential nonlinearities: A stochastic perspective. In Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013. 2013. p. 1921-1928. (Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013).
Sapsis, T. P. ; Vakakis, Alexander F ; Bergman, L. A. / Targeted energy transfer between dynamical components due to essential nonlinearities : A stochastic perspective. Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013. 2013. pp. 1921-1928 (Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013).
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