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Chinese Journal of Engineering
Volume 2013 (2013), Article ID 624658, 10 pages
Research Article

Free Vibrations of Beam System Structures with Elastic Boundary Conditions and an Internal Elastic Hinge

1Departamento de Ingeniería, Instituto de Mecánica Aplicada, (IMA), Universidad Nacional del Sur, (UNS), 8000FTN Bahía Blanca, Argentina
2Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), C1033AAJ Buenos Aires, Argentina

Received 31 August 2013; Accepted 23 September 2013

Academic Editors: M. Chen and I. Smith

Copyright © 2013 Alejandro R. Ratazzi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The study of the dynamic properties of beam structures is extremely important for proper structural design. This present paper deals with the free in-plane vibrations of a system of two orthogonal beam members with an internal elastic hinge. The system is clamped at one end and is elastically connected at the other. Vibrations are analyzed for different boundary conditions at the elastically connected end, including classical conditions such as clamped, simply supported, and free. The beam system is assumed to behave according to the Bernoulli-Euler theory. The governing equations of motion of the structural system in free bending vibration are derived using Hamilton's principle. The exact expression for natural frequencies is obtained using the calculus of variations technique and the method of separation of variables. In the frequency analysis, special attention is paid to the influence of the flexibility and location of the elastic hinge. Results are very similar with those obtained using the finite element method, with values of particular cases of the model available in the literature, and with measurements in an experimental device.