Response characteristics of systems with two-harmonic parametric excitation

Fatemeh Afzali, Gizem D. Acar, Brian F. Feeny

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Floquet theory is combined with harmonic balance to study parametrically excited systems with two harmonics of excitation, where the second harmonic has twice the frequency of the first one. An approximated solution composed of an exponential part with unknown exponents and a periodic term consisting of a truncated Fourier series is considered. When applied to a two-harmonic Mathieu equation the analysis shows that the second harmonic alters stability characteristics, particularly in the primary and superharmonic instabilities. We also look at the initial conditions response and its frequency content. The second excitation harmonic in the system with parametric damping is seen to disrupt the coexistence phenomenon which is observed in the single-harmonic case.

Original languageEnglish
Title of host publication14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
ISBN (Electronic)9780791851838
DOIs
StatePublished - 2018
EventASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2018 - Quebec City, Canada
Duration: 26 Aug 201829 Aug 2018

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume6

Conference

ConferenceASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2018
Country/TerritoryCanada
CityQuebec City
Period26/08/1829/08/18

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