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Journal of Vibration and Control
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An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

Ali H Nayfeh

Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

S.A. Emam

Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

Sergio Preidikman

Departamento de Ingenieria Mecanica, Universidad Nacional de Rio Cuarto, Ruta Nacional 36 km 601, 5800 - Rio Cuarto, Argentina

D.T. Mook

Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

Key Words: Flexible beams • rigid-body motion • linear vibrations

Journal of Vibration and Control, Vol. 9, No. 11, 1221-1229 (2003)
DOI: 10.1177/1077546304030692
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