The dynamical stability of a homogeneous, simple supported column, subjecte
d to a periodic axial force, is investigated. The viscoelastic material is
assumed to obey the Leaderman nonlinear constitutive relation. The equation
of motion was derived as a nonlinear integro-partial-differential equation
, and was simplified into a nonlinear integro-differential equation by the
Galerkin method. The averaging method was employed to carry out the stabili
ty analysis. Numerical results are presented to compare with the analytical
ones. Numerical results also indicate that chaotic motion appears.