Analytical dynamics of a spinning Timoshenko beam subjected to a moving load

Ray P.S. Han, Jean Wu Zheng Zu

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

The dynamics of a simply supported, spinning Timoshenko beam subjected to a moving load is solved analytically using a modal analysis technique. In addition to obtaining the system transient response, this method also yields eigenquantities such as natural frequencies and mode shapes. Unlike the spinning Euler-Bernoulli and the simply supported spinning Rayleigh beams which have only one pair of natural frequencies corresponding to each mode shape, simply supported spinning Timoshenko beams possess two pairs of natural frequencies. It is also shown that the coupled differential equations are of the eighth-order which for most cases, can be reduced to a set of uncoupled fourth-order equations without introducing any significant errors. Closed-form expressions for natural frequencies and the system transient response are presented using this simplified theory. A linearized expression for the computation of natural frequencies, which retains the essential features of the Timoshenko beam theory is also proposed here.

Original languageEnglish
Pages (from-to)113-129
Number of pages17
JournalJournal of the Franklin Institute
Volume330
Issue number1
DOIs
StatePublished - Jan 1993

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