By Using the Lie-group SL(4,R) Method to Solve the Free Vibration Problems of the Elastic Beam
Date Issued
2012
Date
2012
Author(s)
Lin, Chih-Yi
Abstract
The vibration problem of beam is an important issue in engineering, and it can be expressed as the fourth-order differential equation. In this article, we construct an SL(4,R)-based Lie-group shooting method to find the eigenvalues which are natural frequencies. By using the group preserving scheme (GPS) and the closure property of the Lie group, we develop one-step Lie-group transformation between two ends. Together with the generalized mid-point rule, we have derived an SL(4,R) shooting method. In which, we can develop the analytical characteristic equation to solve the eigenvalues.
Last but not least, in this article, several numerical examples show that the mentioned method is feasible, efficient and easy to use.
Subjects
Free Vibration Problems of the Elastic Beam
Fourth-order Generalized Sturm-Liouville Problem
Eigenproblem
Eigenvalues
Characteristic Equation
SL(4,R)-based Lie-group Shooting Method
Type
thesis
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