Determination of some critical flutter loads in the presence of arbitrarily small velocity dependent forces

Abstract

With the aid of certain asymptotic expansions, conditions are derived for the purpose of determining the exact value of the critical flutter load parameter, Q d of uniform beam subjected to a non-conservative force in the limit as the value of a parameter associated with certain velocity dependent forces tends to zero through positive values. These conditions, which complement the frequency equation for the given system without velocity dependent forces, involve integrals over the length of the beam of the products of the deflection functions and derivatives of the deflection functions for the original system without velocity dependent forces and its adjoint system in the cases of either internal damping or the Coriolis fore and involve a product of the integrals of these deflection functions in the case of magnetic damping. Some numerical results are presented for a uniform cantilever resting on an elastic foundation, having slight internal damping, carrying a tip mass, and subjected to a follower force at its free end.