UGC Approved Journal no 63975(19)

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Published in:

Volume 5 Issue 9
September-2018
eISSN: 2349-5162

UGC and ISSN approved 7.95 impact factor UGC Approved Journal no 63975

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Published Paper ID:
JETIRA006343


Registration ID:
189178

Page Number

132-136

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Title

CONTINUUM FORMULATION FOR LARGE AMPLITUDE FREE VIBRATION OF UNIFORM FIXED-HINGED BEAM

Abstract

A simplified continuum formulation using the classical Rayleigh-Ritz method is proposed to study the large amplitude vibrations of uniform fixed-hinged beam. The Rayleigh-Ritz method requires the assumption of admissible functions for the axial displacement and lateral deflection. Though simple accurate single term admissible functions for the lateral deflection and the axial displacement are used, the Rayleigh-Ritz method gives two nonlinear algebraic equations that have to be solved to obtain the nonlinear frequency. This complex task can be simplified if one of the displacement function can be expressed in terms of the other. This is achieved in this paper by using the property of constant tension that is developed in the beam due to large deflections, when both the ends of the beam are restrained to move axially. Using the property of constant tension, the axial displacement distribution along the beam can be obtained in terms of the lateral deflection function and the problem contains a single undetermined coefficient, which can be solved easily to obtain the nonlinear frequency. The application of this procedure in conjunction with the harmonic balance method is demonstrated to study the large amplitude vibration of beams. Using the proposed formulation, the ratio of the nonlinear to linear radian frequencies for various maximum amplitude ratios for the practically important fundamental mode, are obtained that compare very well with those available in the literature.

Key Words

continuum method, fixed-hinged beam, simple harmonic motion, duffing equation, uniform beam.

Cite This Article

"CONTINUUM FORMULATION FOR LARGE AMPLITUDE FREE VIBRATION OF UNIFORM FIXED-HINGED BEAM", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 9, page no.132-136, September-2018, Available :http://www.jetir.org/papers/JETIRA006343.pdf

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2349-5162 | Impact Factor 7.95 Calculate by Google Scholar

An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 7.95 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator

Cite This Article

"CONTINUUM FORMULATION FOR LARGE AMPLITUDE FREE VIBRATION OF UNIFORM FIXED-HINGED BEAM", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 9, page no. pp132-136, September-2018, Available at : http://www.jetir.org/papers/JETIRA006343.pdf

Publication Details

Published Paper ID: JETIRA006343
Registration ID: 189178
Published In: Volume 5 | Issue 9 | Year September-2018
DOI (Digital Object Identifier):
Page No: 132-136
Country: -, -, - .
Area: Engineering
ISSN Number: 2349-5162
Publisher: IJ Publication


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