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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
