A perturbation method for the accurate estimation of the vibration spectrum for the Timoshenko beam

In the stabilization and control of the vibration of flexible structures, a knowledge of the systemʹs vibration spectrum is crucial. In the past, we developed a perturbation approach that, when coupled with the asymptotic wave propagation method of Keller and Rubinow, yields highly accurate estimates for the vibration spectra of certain beam problems. Here, we extend this method to a stand-alone method, applied to the Timoshenko beam problem; it is seen that the wave propagation method is a special case of this method, as are all other asymptotic results that we have found in the literature.