Dynamic stiffness analysis of follower force

Abstract

The dynamic stiffness method can predict an infinite number of natural modes of a conservative structure by means of a finite number of co-ordinates. The method is extended to non-conservative systems characterized by follower forces in this paper. Skeletal frame structures are taken as examples. The resulting matrix equations are solved by the parametric inverse iteration method with the intensity of the follower forces as parameter. The influences of shear deformation and rotatory inertia on the flutter instability are considered. The higher order flutter mode critical follower forces for a slender cantilever are found to be (2n−0·5)²π²EI/l² approximately. The flutter frequency and flutter load are calculated directly by a Newtonian method with a Romberg algorithm for the determinant derivatives. It is found that flutter may occur by coalescence of non-adjacent linear modes.