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Closed-form solutions for non-uniform axially loaded Rayleigh cantilever beams

Sarkar, Korak and Ganguli, Ranjan and Elishakoff, Isaac (2016) Closed-form solutions for non-uniform axially loaded Rayleigh cantilever beams. In: STRUCTURAL ENGINEERING AND MECHANICS, 60 (3). pp. 455-470.

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Official URL: http://dx.doi.org/10.12989/sem.2016.60.3.455


In this paper, we investigate the free vibration of axially loaded non-uniform Rayleigh cantilever beams. The Rayleigh beams account for the rotary inertia effect which is ignored in Euler-Bernoulli beam theory. Using an inverse problem approach we show, that for certain polynomial variations of the mass per unit length and the flexural stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation for Rayleigh beams. The derived property variation can serve as test functions for numerical methods. For the rotating beam case, the results have been compared with those derived using the Euler-Bernoulli beam theory.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the TECHNO-PRESS, PO BOX 33, YUSEONG, DAEJEON 305-600, SOUTH KOREA
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 21 Dec 2016 07:24
Last Modified: 21 Dec 2016 07:24
URI: http://eprints.iisc.ac.in/id/eprint/55531

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