The transverse vibration of a rotating beam with tip mass: The method of integral equations

Abstract

An integral equation method is used to obtain improvable lower bounds for the second eigenvalue of the second-order “reduced” problem obtained from the problem described in the title by singular perturbation methods. These lower bounds are compared with results obtained directly by invariant embedding. The computational aspects of the integral equation method are stressed. The method is shown to be quite general and can be applied to a variety of boundary-value problems including those in which the eigenvalue parameter appears in the boundary conditions as well as in the differential operator.