Forced Vibration Analysis of a Straight-Line Beam Structure with Nonlinear Support Elements : 2nd Report, Suggestion of Stability Analysis by Using Reduction Model and Numerical Computational Results

Abstract

By applying the incremental transfer stiffness coefficient method suggested in the previous report to a large-scale nonlinear structure, the stable and unstable solutions can be computed without distinction. Therefore, the stability of the solution obtained has to be analyzed. It is, however, very difficult to analyze the stability of the solution of the large-scale nonlinear structure. In order to overcome the difficulty, the method to reduce the dimensions of the structure without the decrease of accuracy is developed by applying the concept of the modal analysis to the stability analysis of the variational equation. Two types of modal matrices are considered in the reduction of dimension, and the method is proposed to select rationally the modes that dominate the stability of the solution. The validity of the incremental transfer stiffness coefficient method and the method of stability analysis using reduction model is confirmed by the numerical computational results.