Apparently first closed-form solution for vibrating: Inhomogeneous beams
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Article
Publication/Event/Conference Title
International Journal of Solids and Structures
Publication Status
Version of Record
Abstract
Free vibration of non-uniform beams, which possess non-homogeneous material density and elastic modulus along their axis, are studied under various boundary conditions. Closed-form expressions for the fundamental natural frequency are derived. It is shown that there is an infinite number of beams that share the same natural frequency. Moreover, it is proved that some coefficients describing the density and elastic modulus functions can be deterministic or random, yet, remarkably, in special circumstances, the fundamental natural frequencies turn out to be deterministic quantities. Extensive numerical analysis is performed to substantiate this seemingly paradoxical finding by the Monte Carlo method, Boobnov-Galerkin method and the finite-element method. © 2001 Elsevier Science Ltd. All rights reserved.
First Page
3411
Last Page
3441
DOI
10.1016/S0020-7683(00)00266-3
Publication Date
3-30-2001
Recommended Citation
Elishakoff, I. and Candan, S., "Apparently first closed-form solution for vibrating: Inhomogeneous beams" (2001). Faculty Scholarship. 452.
https://digitalcommons.fau.edu/faculty_papers/452