Journal of Applied Mathematics
Volume 2003 (2003), Issue 10, Pages 503-516

Eigenfrequencies of generally restrained beams

Ricardo Oscar Grossi and Carlos Marcelo Albarracín

ICMASA, Facultad de Ingeniería, Universidad Nacional de Salta, Avenida Bolivia 5150, Salta 4440, Argentina

Received 13 March 2002; Revised 15 May 2003

Copyright © 2003 Ricardo Oscar Grossi and Carlos Marcelo Albarracín. 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.


We deal with the exact determination of eigenfrequencies of a beam with intermediate elastic constraints and generally restrained ends. It is the purpose of this paper to use the calculus of variations to obtain the equations of motion and the natural boundary conditions, and particularly those at the intermediate constraints. Numerical values for the first five natural frequencies are presented in a tabular form for a wide range of values of the restraint parameters. Several particular cases are presented and some of these cases have been compared with those available in the literature.