FREE VIBRATION ANALYSIS OF BEAMS SUBJECTED TO AXIAL LOAD UNDER VARIOUS BOUNDARY CONDITIONS

In this study, free vibration of beams subjected to axial loads and having different boundary conditions is analyzed within the frame of the Bernoulli-Euler beam theory. The Lagrange equations are used to examine the free vibration characteristics of the beams. The constraint conditions of the supports are taken into account by using very stiff linear spring constants. For applying the Lagrange equations, trial functions denoting the deflection of the beam is expressed in the form of power series. By using the Lagrange equations, the problem is reduced to the solution of a system of algebraic equations. The first six eigenvalues of the beams are calculated and tabulated for different values of the axial load. It is thought that the tabulated results will prove useful to designers and provide a reference against which other researchers can compare their results.