Some phenomena for lateral flutter of beams under follower load

Simple model of a slender beam loaded by a transverse follower force and undergoing a lateral flutter is used to demonstrate the following phenomena: 1. If an analysis does not include any damping, an extraction of only two lowest eigenvalues can lead to a wrong conclusion that the critical load is infinite. This is so because, when the ratio of two principal rigidities of a beam is not small, the eigenvalue with a positive real part emerges first not at the very beginning of the spectrum. 2. For the Kelvin-type material, and with no external damping, the critical load becomes infinitely small when the damping in the normal stress vanishes while the shear stress damping is finite. 3. When the external damping is increased, the critical load approaches the value calculated with no internal damping. The nonlinear equilibrium is presented in the closed form and the eigenvalues of the torsional–flexural dynamic perturbed equations are found by the finite element approach and subdomain collocation method