Natural Frequencies of a Timoshenko Beam: Exact Values by Means of a Generalized Solution

Abstract

The present paper deals with the determination of the natural frequencies of vibration of a Timoshenko beam with an alternative method to the classical approach. Here a generalized solution is used to achieve the exact values of the frequencies. The methodology is based upon the use of minimizing sequences made up of Fourier series. THe problem is then reduced to solve a single simple equation. A theoretical appendix with the demonstration of
the exactness of the eigenvalue is included. Cases of beams with various end conditions are numerically solved as examples, showing the rate of convergence of the method.