Computing effective properties of nonlinear structures exposed to strong high-frequency loading at multiple frequencies

Jon Juel Thomsen (Invited author)

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Effects of strong high-frequency excitation at multiple frequencies (multi-HFE) are analyzed for a class of generally nonlinear systems. The effects are illustrated for a simple pendulum system with a vibrating support, and for a parametrically excited flexible beam. For the latter, theoretical predictions are supported by preliminary experimental results. The main effect of strong multi-HFE is to change the effective or apparent stiffness in a manner similar to that of mono-HFE, provided the HFE frequencies are well separated and non- resonant. Then the change in effective stiffness is proportional to the mean-square velocity of the excitation velocities, and the corresponding changes in equilibriums, equilibrium stability, and natural frequencies can be computed as for the mono-HFE case. When there are two or more close excitation frequencies, an additional contribution of slowly oscillating stiffness appears. This may cause strong parametrical resonance at conditions that might not appear obvious, i.e. when the difference in two HFE-frequencies is near twice an effective natural frequency of the system, which due to the HFE itself is shifted away from the natural frequency without HFE. Also, it is shown that strong multi-HFE can stabilize otherwise unstable equilibriums, but only if the frequencies are well separated; thus continuous broadband and random HFE does not have a stabilizing effect paralleling that of mono-HFE, or multi-HFE with non-close frequencies. The general results may be used to investigate general effects, or as a short cut to calculate effective properties for specific systems, or to calculate averaged equations of motion that may be much faster to simulate numerically.
Original languageEnglish
Title of host publicationCD-ROM proceedings of the III European Conference on Computational Mechanics
Place of PublicationLisbon
Publication date2006
Pages1-20
Publication statusPublished - 2006
Event3rd European Conference on Computational Mechanics: Solids, Structures and Coupled Problems in Engineering - Lissabon, Portugal
Duration: 5 Jun 20068 Jun 2006
Conference number: 3

Conference

Conference3rd European Conference on Computational Mechanics
Number3
Country/TerritoryPortugal
CityLissabon
Period05/06/200608/06/2006

Keywords

  • high-frequency excitation, multiple frequency excitation, nonlinear structures, dynamic stiffening, effective properties

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