Viscoelastic Stability of Columns on Continuous Support

Abstract

The stability of a viscoelastic beam subjected to an axial compression resting on a viscoelastic medium is studied using a dynamic method. The governing differential equation of the problem is derived from the condition of equilibrium along with the use of viscoelastic material laws for the beam and the continuous support. To examine the long‐time and short‐time effects of the materials, the critical axial loads are obtained for the cases of creep buckling and instantaneous buckling. The results obtained herein can be expressed in a form identical to those for the elastic case, provided proper moduli are used for the column and support. Several special cases are studied to confirm the validity of the present approach.