Analysis of Dynamic Elastic Stability of Framed Structures Considering the Effect of Damping and Forced Vibration

In this paper authors deal with the dynamic instability of the framed structures in two cases, in which the effect of damping is considered and it is supposed that the frequency of loads is close to the natural frequencies of the structures, and show the method of analysis of them and the effect of damping and forced vibration. In former case, it is supposed that the damping force proportional to a derivative of the displacement with respect to time is considered and damping matrix can be diagonalized by modal matrix. The boundary values of the regions of instability of columns and arches are estimated by applying the proposed method, which agree with them of column simply supported at both sides.