FREE VIBRATION ANALYSIS OF TIMOSHENKO BEAMS UNDER VARIOUS BOUNDARY CONDITIONS

Abstract

Free vibration of Timoshenko beams having different boundary conditions is analyzed. The Lagrange equations are used to examine the free vibration characteristics of Timoshenko beams. The constraint conditions of supports are taken into account by using Lagrange multipliers. In the study, for applying the Lagrange equations, trial functions denoting the deflection and the rotation of the cross-section of the beam are expressed in the polynomial form. By using the Lagrange equations, the problem is reduced to the solution of a system of algebraic equations. The first eight eigenvalues of Timoshenko beam are calculated and tabulated for different thickness-to-length ratios. It is believed that the tabulated results will prove useful to designers and provide a reference against which other researchers can compare their results.