Dynamic stability of viscoelastic columns loaded by a follower force

Abstract

This paper analyses the motion of a linear viscoelastic column using the dynamic approach. The viscoelastic material is mathematically represented by the four-element model. Using this model as a recursion equation, the elastic, one-, two-, three- and four-element models are solved and their results compared. The stability analyses of these systems are investigated by studying the eigenvalues of the characteristic equations for the solution to the boundary value problems. The stability analyses determined the smallest value of the follower load beyond which the system, under a suitable disturbance, will perform oscillations with increasing amplitudes. The dynamic instability is found to occur in the form of flutter. The effect of damping on the critical follower load is also examined. Three damping parameters are considered that affect the results. They are the damping coefficients related to a Maxwell unit, to a Kelvin unit and one appropriate to a combination of the two. The destabilization effects of viscosity are discussed.