Nonlinear vibration of a thin-plate workpiece during high speed milling under 1:1 internal resonance condition

Wei Zhang, Rui Zhou, Jean W. Zu, Qian Wang

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

1 Scopus citations

Abstract

In this paper, the nonlinear vibration of a thin-plate workpiece during milling process is investigated. The thin-plate workpiece is modeling as a cantilevered thin plate. The equations of motion for the thin-plate workpiece are derived based on the Kirchhoff-plate theory and the von Karman strain-displacement relations by using the Hamilton's principle. By applying the Galerkin's approach, the resulting equations are reduced to a two-degree-of-freedom nonlinear system with external excitations. Considering the case of 1:1 internal resonance, the method of Asymptotic Perturbation method is utilized to obtain the averaged equations of the cantilevered thin-plate workpiece. Numerical method is used to study nonlinear dynamics of the cantilevered thin plate and get the two-dimensional phase portraits, waveforms phase, three-dimensional phase and frequency spectrum phase. The result shows that the cantilevered thin-plate workpiece exhibits the complex dynamic behavior with the increase of the amplitude of the forcing excitation.

Original languageEnglish
Title of host publicationASME 2012 International Mechanical Engineering Congress and Exposition, IMECE 2012
Pages1891-1903
Number of pages13
EditionPARTS A, B, AND C
DOIs
StatePublished - 2012
EventASME 2012 International Mechanical Engineering Congress and Exposition, IMECE 2012 - Houston, TX, United States
Duration: 9 Nov 201215 Nov 2012

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)
NumberPARTS A, B, AND C
Volume3

Conference

ConferenceASME 2012 International Mechanical Engineering Congress and Exposition, IMECE 2012
Country/TerritoryUnited States
CityHouston, TX
Period9/11/1215/11/12

Keywords

  • Cantilever thin plate
  • Chaos
  • Nonlinear dynamics
  • Numerical simulation

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