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

✍ Scribed by Issac Elishakoff; Demetris Pentaras

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 141 KB
• Volume: 298
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/j.jsv.2006.05.028

✦ Synopsis

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.