Flexibility Effects—Estimation of the Stiffness Matrix in the Dynamics of a Large Structure

Abstract

In this paper, an estimation of the stiffness matrix for a mechanical tree-like structure is presented. The coefficients of the stiffness matrix are evaluated based on Kane’s equations together with the finite segment modeling technique and matrix structure analysis. The procedure developed is used to evaluate the stiffness coefficients in the case where the flexibility effects are modeled by uniform beam elements with springs and dampers at the connecting joints. The method presented in this paper is very useful in the study of the dynamics, vibration, and control of a large tree-like structure undergoing large motions. An illustration of how the method is used in extracting the natural frequencies and their corresponding mode shapes is presented. The set of equations developed in this paper are the complement equations used to monitor the transient response of the structure undergoing a rigid-body motion.