Abstract: It is of importance to study the influence of small changes of support location on vibration mode shapes because of its necessary role in structural optimization and model correction using the generalized variational principle, the first-order purturbation equations of vibration eigenproblem are derived. In order to solve these equations two difficulties are dealt with, one is associated with the incompleteness of the unperturbed eigenfunctions, the other the truncation of the higher modes. A hybrid expansi...