Studies on dynamic behaviour of a beam with symmetrically varying thickness

doi:10.1016/0045-7949(93)90376-O

Computers & Structures

Volume 47, Issue 2, 17 April 1993, Pages 265-274

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Abstract

A detailed study has been conducted on the effect of different types of variation in profile and thickness on the amplitude and the dynamic bending stress of a beam under a point harmonic load. The end conditions considered are clamped or simply supported at both the ends. The response has been calculated for the first three modes of vibration. In each case the results obtained for different types of thickness variation are compared with those obtained for a uniform thickness beam. It is observed that a considerable reduction in amplitude and bending stress can be achieved by proper selection of thickness variation.

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Cited by (1)

Lateral-torsional dynamic instability of uniform and double-tapered rectangular beams under harmonic shear deformation
2017, Engineering Structures
Citation Excerpt :
Therefore free vibrations will be analyzed first. In-plane free vibrations for double-tapered beams with rectangular cross section and fixed ends were studied in [2–5]. Results for lateral free vibrations for the same type of beams but with pinned ends with respect to the weak direction can be obtained from [6,7].
This paper analyzes lateral-torsional dynamic instability of elastic beams with rectangular cross section having constant thickness, with the depth symmetric with respect to the midpoint and either uniform or tapered linearly in each half. Free vibrations are also investigated. The ends of the beam are prevented from twisting and are pinned with respect to bending in the weak direction. In the strong direction, one end of the beam is fixed and the other is subjected to transverse harmonic motion. This problem was motivated by “butterfly-shaped links” proposed for use in seismic mitigation. Uniform torsion is assumed. Frequencies of free vibration are computed, critical excitation frequencies for lateral-torsional instability are determined, and critical combinations of excitation amplitude and frequency are obtained. The effects of geometric parameters of double-tapered beams on instability are presented. Lateral-torsional instability may occur for very small amplitudes of the moving end of the beam, as is typical for such problems involving parametric resonance.

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Studies on dynamic behaviour of a beam with symmetrically varying thickness

Abstract

J. Sound. Vibr.

J. Sound. Vibr.

J. Sound. Vibr.