Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition

Sarkar, Korak and Ganguli, Ranjan (2014) Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition. In: COMPOSITES PART B-ENGINEERING, 58 . pp. 361-370.

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Abstract

In this paper, we study the free vibration of axially functionally graded (AFG) Timoshenko beams, with uniform cross-section and having fixed-fixed boundary condition. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, there exists a fundamental closed form solution to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions having simple polynomial variations, which share the same fundamental frequency. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of non-homogeneous Timoshenko beams. They can also be useful for designing fixed-fixed non-homogeneous Timoshenko beams which may be required to vibrate with a particular frequency. (C) 2013 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Publication:	COMPOSITES PART B-ENGINEERING
Publisher:	ELSEVIER SCI LTD
Additional Information:	copyright for this article belongs to ELSEVIER SCI LTD,ENGLAND
Keywords:	Mechanical properties; Vibration; Analytical modeling; Finite element analysis (FEA); Axially functionally graded material (AFGM)
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	16 Mar 2014 11:20
Last Modified:	16 Mar 2014 11:20
URI:	http://eprints.iisc.ac.in/id/eprint/48622

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