Apparently the first closed-from solution of inhomogeneous elastically restrained vibrating beams

Author Type

Faculty

Co-Author Type 1

Faculty

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Journal of Sound and Vibration

Publication Status

Version of Record

Abstract

In this paper we consider free vibration of inhomogeneous Bernoulli-Euler beam which is clamped at one end and elastically restrained at the other. The closed-form solution is obtained for the beam of constant material density and constant cross-section but of modulus of elasticity, which varies in a polynomial manner. The semi-inverse method is utilized; namely, the fundamental mode of vibration is postulated as a polynomial too. It turns out that such a formulation leads to infinite number of solutions; one can obtain an unique solution by introducing an additional requirement inherent in vibration tailoring: namely, designing the system that possesses the pre-specified natural frequency. It is shown that if in addition to the fundamental mode shape the natural frequency is also specified, the unique solution is derived. © 2006 Elsevier Ltd. All rights reserved.

First Page

439

Last Page

445

DOI

10.1016/j.jsv.2006.05.028

Publication Date

11-22-2006

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