A Study on the Increase of Numerical Stability and Accuracy of the Transfer Matrix Method

Abstract

Problem Statement: The transfer matrix method is a very useful tool for the static and dynamic analysis of structures. There are a number of issues though that worsens the numerical stability and the accuracy of this method. Approach: This study proposed a simple technique that can be used to handle these numerical difficulties and overcome the problems they give. Its main idea was to apply the method twice starting from two far ends of the structure. Results: An example from the calculation of the sensitivity function between two points in a dynamic system is presented. The results presented the very big potential of the proposed method. The improvement of the stability was clear in the graphs of the results. An initial study on the limitations of the proposed technique was also briefly given, together with some initial thoughts on how to overcome them. Finally, an idea of a possible use of the method for the maintenance studies of a high-speed rotor is presented, showing the very big variety of applications this methodology can be applied into. Conclusions: The proposed technique was very simple and effective, and hence it should be applied whenever the transfer matrix method was used.