Theoretical and numerical investigations on dynamic stability of viscoelastic columns with semi-rigid connections

Dynamic stability of structures is an essential topic in civil engineering analysis and design because collapse of critical structures due to dynamic excitations would cause loss of properties or even fatalities. This paper conducts theoretical analysis and numerical simulation investigations on both stability and responses of viscoelastic columns with semi-rigid connections/supports subjected to axial parametric loads. The equation of motion for the viscoelastic column is derived and decoupled into an ordinary differential equation with periodic coefficients by describing the viscoelasticity as the linear Kelvin-Voigt model. Theoretical analysis is performed by the method of harmonic balance and the approximate boundaries of dynamic stability are obtained. A novel numerical simulation method is proposed to investigate both dynamic stability and vibration responses of viscoelastic columns with semi-rigid connections. The approximate boundaries are calibrated by the numerical results. The effects of the material's viscoelasticity, the supports' rigidity, damping, and the static and dynamic component loads on the column stability are investigated through the numerical analysis. Two key findings of the study are that the greater the rigidity of the supports, the larger both the natural frequency and the critical dynamic load; and the viscosity of materials has a great positive impact on the dynamic stability of viscoelastic columns. The proposed method can be extended to systems under arbitrary periodic parametric excitations.