Damped transition of a strongly nonlinear system of coupled oscillators into a state of continuous resonance scattering

David Andersen, Xingyuan Wang, Yuli Starosvetsky, Kevin Remick, Alexander F Vakakis, Mercedes Mane, Sean Hubbard, Lawrence Bergman

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

Abstract

We examine analytically and experimentally a new phenomenon of 'continuous resonance scattering' in an impulsively excited, two-mass oscillating system. This system consists of a grounded damped linear oscillator with a light, strongly nonlinear attachment. Previous numerical simulations revealed that for certain levels of initial excitation, the system engages in a special type of response that appears to track a solution branch formed by the so-called 'impulsive orbits' of this system. By this term we denote the periodic (under conditions of resonance) or quasi-periodic (under conditions of non-resonance) responses of the system when a single impulse is applied to the linear oscillator with the system being initially at rest. By varying the magnitude of the impulse we obtain a manifold of impulsive orbits in the frequency-energy plane. It appears that the considered damped system is capable of entering into a state of continuous resonance scattering, whereby it tracks the impulsive orbit manifold with decreasing energy. Through analytical treatment of the equations of motion, a direct relationship is established between the frequency of the nonlinear attachment and the amplitude of the linear oscillator response, and a prediction of the system response during continuous scattering resonance is provided. Experimental results confirm the analytical predictions.

Original languageEnglish (US)
Title of host publicationASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
Pages839-845
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
Volume4

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

Andersen, D., Wang, X., Starosvetsky, Y., Remick, K., Vakakis, A. F., Mane, M., Hubbard, S., & Bergman, L. (2011). Damped transition of a strongly nonlinear system of coupled oscillators into a state of continuous resonance scattering. In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 (PARTS A AND B ed., pp. 839-845). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 4, No. PARTS A AND B). https://doi.org/10.1115/DETC2011-47950