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| A symplectic midpoint scheme for structural dynamic response problems in Birkhoffian form |
| Received:September 03, 2023 Revised:October 10, 2023 |
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| DOI：10.7511/jslx20230903001 |
| KeyWord:structural dynamic response problem Birkhoffian equation midpoint scheme symplectic algorithm perturbation method |
| Author | Institution |
| 邱志平 |
北京航空航天大学 航空科学与工程学院, 北京 |
| 邱宇 |
北京航空航天大学 航空科学与工程学院, 北京 ;北京航空航天大学 沈元学院, 北京 |
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| Abstract: |
| Structural dynamic response prediction is the foundation of structural design and serves as a prerequisite for structural vibration control and load identification.In this paper, we address structural dynamic response problems within the symplectic framework and propose a symplectic midpoint scheme in Birkhoffian form.The state variables are first introduced and the structural dynamic response equations are transformed into the form of linear autonomous Birkhoffian equations based on the perturbation method.The central difference is further used to derive the midpoint scheme of the linear autonomous Birkhoffian equation, which is proved to be symplectic.This scheme does not require the coefficient matrix of the Birkhoffian equation to be non-singular and is therefore suitable for odd-dimensional systems.The results from two distinct numerical test cases provide ample validation of the excellence of the method presented in this paper, highlighting the significant advantages it possesses over traditional algorithms in terms of computational accuracy and stability. |