FREE VIBRATION ANALYSIS OF ELASTICALLY SUPPORTED TIMOSHENKO BEAMS

Abstract

In this study, free vibration of elastically supported beams is investigated based on Timoshenko beam theory (TBT). The Lagrange equations are used to examine the free vibration characteristics of Timoshenko beams. In the study, for applying the Lagrange equations, trial functions denoting the deflection and the rotation of the the cross-section of the beam are expressed in the power series form. By using the Lagrange equations, the problem is reduced to the solution of a system of algebraic equations. The influence of stiffnesses of the supports on the free vibration characteristics of Timoshenko beams is investigated. For this purpose, the first three eigenvalues of the Timoshenko beams are calculated for various rigidity values of translational and rotational springs, and obtained results are not only tabulated, but also presented in three-dimensional plots. It is thought that the tabulated results will prove useful to designers and provide a reference against which other researchers can compare their results.