COMPUTATION OF THE DYNAMIC INSTABILITY REGION OF STRUCTURES BY THE FINITE ELEMENT METHOD.

This paper presents a method for obtaining the boundaries of the first region of dynamic instability of a structure loaded by large axial forces. The structure is divided into finite elements, and its matrix of rigidity is written approximately as the sum of two matrices: K equals K//E plus K//G. K//E is the ordinary elastic matrix of rigidity obtained from the elastic analysis, and K//G is the geometric stiffness matrix. An analysis of the differential equation of motion can provide the boundaries for all the regions of dynamic instability, but for practical problems, only the boundaries of the first region are important. These boundaries are found by relating them to the natural frequencies of the same structure loaded with a system of fictitious axial forces. All calculations are presented as a computer program DINSS (Dynamic Instability of Structure).