On the frequency response function of a damped cantilever simply supported in-span and carrying a tip mass

This paper deals with the determination of the frequency response function of a cantilevered Bernoulli-Euler beam which is viscously damped by a single damper. The beam is simply supported in-span and carries a tip mass. The frequency response function is obtained through a formula that was established for the receptance matrix of discrete linear systems subjected to linear constraint equations, by considering the simple support as a linear constraint imposed on generalized co-ordinates. The comparison of the numerical results obtained via a boundary value problem formulation justifies the approach used here.