Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

Sarkar, Korak and Ganguli, Ranjan (2014) Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams. In: MECCANICA, 49 (6). pp. 1469-1477.

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Abstract

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.

Item Type:	Journal Article
Publication:	MECCANICA
Publisher:	SPRINGER
Additional Information:	copyright for this article belongs to SPRINGER, VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS
Keywords:	Rotating beams; Timoshenko beams; Free vibration; Test functions
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	24 Jun 2014 05:53
Last Modified:	24 Jun 2014 05:53
URI:	http://eprints.iisc.ac.in/id/eprint/49295

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