Existence of Periodic Solution for Beams With Harmonically Variable Length-Reference-Cited by-同舟云学术

Existence of Periodic Solution for Beams With Harmonically Variable Length

Published:1997-07-01 Issue:3 Volume:119 Page:485-488
ISSN:1048-9002
Container-title:Journal of Vibration and Acoustics
language:en
Short-container-title:

Author:

Esmailzadeh E.¹,Nakhaie-Jazar G.¹,Mehri B.²

Affiliation:

1. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

2. Mathematical Sciences, Sharif University of Technology, Tehran, Iran

Abstract

The transverse oscillatory motion of a simple beam with one end fixed while driven harmonically at the other end along its longitudinal axis is investigated. For a special case of zero value for the rigidity of beam, the problem reduces to that of a vibrating string with its corresponding equation of motion. The sufficient condition for the periodic solution of the beam was determined using the Green’s function and Schauder’s fixed point theorem. The criterion for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

Publisher

ASME International

Subject

General Engineering

Link

http://asmedigitalcollection.asme.org/vibrationacoustics/article-pdf/119/3/485/5664850/485_1.pdf

Reference14 articles.

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2. Cartmell, M., 1990, Introduction to Linear, Parametric and Nonlinear Vibrations, Chapman and Hall.

3. Eflmov, A. V., Zolotarev, Y. G., and Terpigoreva, V. M., 1985, Mathematical Analysis, 2nd vol., Mir Publishers.

4. Lanczos, C., 1961, Linear Differential Operators, Van Nosrand.

5. Love, A. E. H., 1927, A Treatise on the Mathematical Theory of Elasticity, Dover Publications.

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