Dynamic simulation of columns considering geometric nonlinearity

Abstract

Dealing with slender structural columns will make the use of classic elastic dynamic analysis of structures untrustworthy. This will emphasize the importance of developing a method for dynamic analysis of structures taking geometric nonlinearities into consideration. In order to achieve this the equations of motions are formulated, based on finite strain formula and virtual work method. To solve the equation of motion, the usual central difference method is used. The developed method is applied to two cases of columns with different slenderness ratio. The effect of introducing the nonlinear approach for different slenderness ratios of columns is investigated on natural frequency of the first three modes. Also, the relationship between the maximum displacement for a known time step and loading frequency is studied. To find the suitable slenderness ratio threshold when the effect of nonlinearity becomes significant, the relationship between slenderness ratio and the maximum displacement ratio for a known loading frequency is studied. The results show that columns with higher ratio of axial loading over slenderness ratio provide a higher rate of decrease in natural frequencies. It is also found that the effect of taking geometric nonlinearity into consideration will be significant while dealing with higher slenderness ratio and smaller loading frequency. For a specific situation, these results are discussed and the slenderness ratio threshold is found equal to 110. It means that for slenderness ratios higher than 110 the effects of geometric nonlinearity becomes significant and should be taken into consideration.