Revisiting the moving force problem

A. V. Pesterev, B. Yang, L. A. Bergman, C. A. Tan

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of the vibration of a beam subject to a travelling force is considered. The purpose of the study is to develop simple tools for finding the maximum deflection of a beam for any given velocity of the travelling force. It is shown that, for given boundary conditions, there exists a unique response-velocity dependence function. A technique to determine this function is suggested, which is based on the assumption that the maximum beam response can be adequately approximated by means of the first beam mode. To illustrate this, the maximum response function is calculated analytically for a simply supported (SS) beam and constructed numerically for a clamped-clamped beam. The effect of the higher modes on the maximum response is investigated, and the relative error of the one-mode approximation for a SS beam is constructed. The estimates obtained substantiate the assumption about adequacy of the one-mode approximation in a wide range of velocities; in particular, the relative error in the neighborhood of the velocity that results in the largest response is less than one percent.

Original languageEnglish (US)
Pages (from-to)75-91
Number of pages17
JournalJournal of Sound and Vibration
Volume261
Issue number1
DOIs
StatePublished - Mar 13 2003

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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