DYNAMIC INSTABILITY OF COLUMN SUBJECTED TO PERIODIC AXIAL LOAD

Abstract

Geometric effects cause structural instability failure in elastic structures. Nonlinearities are introduced by the geometry of deformation which amplify the stresses calculated based on the initial undeformed configuration of the structure. Different definitions of stability are used for different problems. However, dynamic stability definition is applicable to all structural stability problems. The structures appear stable from static buckling analysis when subjected to dynamic axial loads but actually they fail due to ever increasing amplitude of vibration. This is correctly detected by dynamic analysis. The new phenomena are existence of solution for all values of the frequency rather than only for a set of characteristic values and dependence of amplitude on frequency. In this project the simply supported column, uniform in cross-section along the length subjected to periodic longitudinal force. The stability boundaries are derived which are periodic solution of second order differential equation with period T and 2T to the Mathieu equation. Usual assumptions are made i.e. Hooke’s law is valid and plane sections remain plane. Different zones of instability of column under periodic axial loading are plotted and instability of different points on amplitude frequency curve are studied through phase portraits.