On the Lateral Vibrations of a Vertically Moving String With a Harmonically Varying Length

Nick Gaiko, Wim van Horssen

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

Abstract

In this paper, the free lateral vibrations of a vertically translating continuum modeled as a taut string with variable length are studied. The time-varying length of the cable is described by a harmonically varying function about a constant mean length. This model can be used to describe the lateral vibrations of an elevator cable with changing length. A Fourier series approach is used to predict resonant frequencies arising because of the length fluctuation. The amplitudes of vibrations are represented by the infinitely dimensional system of coupled ordinary differential equations. This system is studied by Galerkin’s truncation method for the lowest resonant frequency. The obtained results are in agreement with the energy analysis, but the truncation technique leads to inaccurate approximations on long timescales. Hence, an alternative analytical method is proposed promising an accurate approximation of the response on long timescales for the general resonant frequency.
Original languageEnglish
Title of host publicationProceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE2015
PublisherASME
Pages1-7
Number of pages7
Volume4B
ISBN (Print)978-0-7918-5740-3
DOIs
Publication statusPublished - 2015
EventASME 2015 International Mechanical Engineering Congress and Exposition - Houston, United States
Duration: 13 Nov 201519 Nov 2015

Conference

ConferenceASME 2015 International Mechanical Engineering Congress and Exposition
CountryUnited States
CityHouston
Period13/11/1519/11/15

Keywords

  • String
  • Vibration

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