Free vibrations of general elastically restrained nonuniform Timoshenko beams

Sen-Yung Lee, Shueei Muh Lin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

The free vibration of a general elastically restrained symmetric nonuniform Timoshenko beam resting on a nonuniform elastic foundation and subjected to axial loads is studied. The relation between the flexural displacement and the angle of rotation due to bending is derived. The two coupled governing characteristic differential equations are reduced into one complete fourth-order ordinary differential equation with variable coefficients in the angle of rotation due to bending. The frequency equation is expressed in terms of the four normalized fundamental solutions of the differential equation. If the closed form fundamental solutions of the governing characteristic differential equation are not available, then the approximate fundamental solutions can be obtained through a simple and efficient algorithm. The limiting cases such as uniform Timoshenko beams, nonuniform Rayleigh and Bernoulli-Euler beams are examined. Several examples are given to illustrate the validity and accuracy of the analysis.

Original languageEnglish
Title of host publicationRecent Advances in Structural Mechanics - 1992
PublisherPubl by ASME
Pages101-109
Number of pages9
ISBN (Print)079181131X
Publication statusPublished - 1992 Dec 1
EventWinter Annual Meeting of the American Society of Mechanical Engineers - Anaheim, CA, USA
Duration: 1992 Nov 81992 Nov 13

Publication series

NameAmerican Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP
Volume248
ISSN (Print)0277-027X

Other

OtherWinter Annual Meeting of the American Society of Mechanical Engineers
CityAnaheim, CA, USA
Period92-11-0892-11-13

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

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