Closed-form solutions for non-uniform Euler-Bernoulli free-free beams

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.

Administration's fiscal year 1984 budget proposals--II : hearings before the Committee on Finance, United States Senate, Ninety-eighth Congress, first session, June 15, 16, 22, 23, 28 and 29, 1983.

Item 1038-A, 1038-B (microfiche)

Conference Report of the First Meeting of the Native American and Indigenous Studies Association, 21-23 May 2009, Department of American Indian Studies, University of Minneapolis, Minesota, United States of America

Report provided back by Bronwyn Fredericks on her participation at the First Native American and Indigenous Studies Association Meeting held 21-23 May 2009 in Minnesota, United States of America.