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Structural Engineering and Mechanics Volume 60, Number 3, November10 2016 , pages 455-470 DOI: https://doi.org/10.12989/sem.2016.60.3.455 |
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Closed-form solutions for non-uniform axially loaded Rayleigh cantilever beams |
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Korak Sarkar, Ranjan Ganguli and Isaac Elishakoff
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| Abstract | ||
| 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. | ||
| Key Words | ||
| Rayleigh beam; free vibration; inverse problem; closed-form solution; test functions | ||
| Address | ||
| Korak Sarkar, Ranjan Ganguli: Department of Aerospace Engineering, Indian Institute of Science, Bangalore-560012, India Isaac Elishakoff: Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991, USA | ||