Application of variational iteration method to free vibration analysis of a tapered beam mounted on two-degree of freedom subsystems

In this paper, the modified variational iteration method (VIM) is applied to solve the free vibration problem of a tapered Euler-Bernoulli beam mounted on two-degrees of freedom mass-spring-damper subsystems. Both conical and wedge beams are investigated. The efficiency of the technique is demonstrated via several numerical examples. The natural frequencies and mode shapes of both uniform and tapered beams with attached subsystems are obtained. Several cases are presented as verification examples by comparison with published literature. Moreover, new results of the studied model are introduced, taking into account the effect of taper ratio and subsystem parameters variation. It is shown that by adjusting the number of iterations, highly accurate results are obtained that are identical to the results got from the exact solution method until the eighth figure. The numerical results prove that the variational iteration method demonstrates the efficiency and accuracy in solving the free vibration problem of non-uniform and integrated beam systems.