According to the constitutive model expressed by convolution method for viscoelastic solids with damage, the dynamic behaviors of a homogeneous, simple supported beam column, subjected to a periodic axial force is investigated under the case of small deflections. The equations of motion were derived as a set of linear integro-partial-dinferential equations, and were simplified into a set of linear integro-differential equations by the Galerkin method. The numerical methods in nonlinear dynamics, such as phase-trajectory diagrams, Poincare sections, time-path curves and bifurcation figures were used to solve the simplified system. It could be seen that there are plenty of dynamic properties for this kind of viscoelastic beam column under transverse harmonic loads. The influences of the material on the dynamic behavior of viscoelastic beam column with voids were investigated.
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