Solution of the problem on the vibrations of beams with a variable cross section using the finite-difference method

We present a numerical calculation of the frequencies of natural vibrations of beams with a cross section varying linearly in height under different conditions of fixing their ends. The differential equation is derived using the finite difference method. The eigenvalues of the equation and the frequency parameters are determined. The results are obtained in several various steps of nodes of the approximation, with their refinement being performed using the extrapolation method. The accuracy of the results is confirmed by comparison with the analytical solution for the case of a beam with a uniform cross section.