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Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

Sarkar, Korak and Ganguli, Ranjan (2014) Tailoring the second mode of Euler-Bernoulli beams: an analytical approach. In: STRUCTURAL ENGINEERING AND MECHANICS, 51 (5). pp. 773-792.

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In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to the TECHNO-PRESS, PO BOX 33, YUSEONG, DAEJEON 305-600, SOUTH KOREA
Keywords: Euler-Bernoulli beam; free vibration; modal tailoring; inverse problem; closed-form solution
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 29 Dec 2014 05:13
Last Modified: 29 Dec 2014 05:13
URI: http://eprints.iisc.ac.in/id/eprint/50540

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