On an elastic dissipation model for a cantilevered beam

In this paper we will study an elastic dissipation model for a cantilevered beam. This problem for a cantilevered beam has been formulated by D.L. Russell as an open problem in [1, 2]. To determine the relationship between the damping rates and the frequencies we will use a recently developed, adapted form of the method of separation of variables. It will be shown that the dissipation model as proposed by D.L. Russell for the cantilevered beam will not always generate damping. Moreover, it will be shown that some solutions can become unbounded.