Study of dynamic stability of columns under harmonic loading

In this study a simple model of a column is presented and analyzed under harmonic loadings with various frequencies. Additionally, dynamic stability criteria are examined for the model. For this end, column is modeled with a series of elements with axial rigidity connected to each other by nonlinear rotational springs and linear dampers. By carrying out dynamic equations for each element and combining them, a system of coupled second-order nonlinear differential equations is obtained. Fourth order Runge-Kutta numerical method which is proven to be stable is used to carry out solutions for these equations. Furthermore, by solving system characteristic equations for various natural frequencies, rotational stiffness and damping are obtained. the rotational springs are supposed to be elastic-perfect plastic. It is demonstrated that material nonlinearity doesn't have a significant effect on dynamic instability regions of column under harmonic loading. Although the amplitude of vibration of the column in elastic-perfect plastic model are more realistic in comparison with linear model.

کلیدواژه ها:

dynamic stability ، nonlinear dynamic analysis ، Runge-Kutta method ، harmonic loading ، column