Dynamic Stability Analysis of Truss Structures under Nonconservative Constant and Pulsating Follower Forces

Abstract

The aim of this study is to investigate the dynamic stability behaviors of truss structures under nonconservative constant and pulsating follower forces through the finite element formulation and the multiple scales perturbation method. In physical phenomena, we may face the problem of truss structures subjected to wind loadings in sinusoidal types. This system can be modeled as truss systems subjected to constant and pulsating follower forces. So the truss system may lost its instability due to the so-called sum type combination resonance or difference type combination resonance just as a liquid-filled projectile under a thrust does [1],[2]. Herein a definition direct approach is used to derive the constant and pulsating follower load stiffness matrix of a truss element. This non-conservative load matrix is contributed by constant and pulsating follower forces acting on the nodes on the truss element. Using Euler finite rotation formula and the principle of virtual work, the constant and pulsating follower forces acting on the nodes of truss element can be related to the degrees of freedom of the truss element in a simple close form, then an explicit form of the nonconservative load stiffness matrix can be derived. A simple matrix from to present the nonconservative force effect in the element is purposed in this paper. Then it is assembled with the associated matrices that contain mass stiffness matrix and elastic stiffness matrix. Finally the equations of motion of the truss systems under pulsating follower forces are formulated and solved by the multiple scales perturbation method. The dynamic stability diagrams that show the resonant frequencies of summation type or the resonant frequencies of difference type of the system are also discussed in this paper.