Sarkar, Korak and Ganguli, Ranjan (2013) Closed-form solutions for non-uniform Euler-Bernoulli free-free beams. In: Journal of Sound and Vibration, 332 (23). pp. 6078-6092.
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In this paper, the free vibration of a non-uniform free-free Euler-Bernoulli beam is studied using an inverse problem approach. It is found that the fourth-order governing differential equation for such beams possess a fundamental closed-form solution for certain polynomial variations of the mass and stiffness. An infinite number of non-uniform free-free beams exist, with different mass and stiffness variations, but sharing the same fundamental frequency. A detailed study is conducted for linear, quadratic and cubic variations of mass, and on how to pre-select the internal nodes such that the closed-form solutions exist for the three cases. A special case is also considered where, at the internal nodes, external elastic constraints are present. The derived results are provided as benchmark solutions for the validation of non-uniform free-free beam numerical codes. (C) 2013 Elsevier Ltd. All rights reserved.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier Science.|
|Department/Centre:||Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)|
|Date Deposited:||29 Oct 2013 05:37|
|Last Modified:||29 Oct 2013 05:37|
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