用于柔性结构耦合动态分析的能量守恒矩阵扰动理论

IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computers & Structures Pub Date : 2024-10-30 DOI:10.1016/j.compstruc.2024.107572
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引用次数: 0

摘要

针对力-形耦合系统时变特征值的再分析问题,本文提出了一种能保持系统基本物理特性的能量保护矩阵扰动理论(EPMPT)。经典的矩阵扰动方法采用插值形状函数,在连续扰动过程中无法及时评估和处理解误差。这一局限性导致了理论上的 "特征值漂移 "问题,而这一缺陷自 40 年前原始方法问世以来就一直存在。相比之下,本文提出的方法利用动态刚度法一次性获得系统特征值和特征向量,并提供了时变特征值问题的扰动解。进一步结合 Wittrick-Williams 算法中的 J 计数测试技术,开发出了一种可以 "自我检查和自我修正 "解的能量保护方法。提出了 "连续扰动应在频域内保持力形动态自洽性 "的观点,避免了长期数值模拟造成的能量分散和由此产生的失真问题。为了说明 EPMPT 的优势,研究了包含力-形耦合效应的航空航天结构热诱导振动和包含刚-柔耦合效应的柔性空间太阳能电池阵列振动。案例研究表明,EPMPT 能够显著提高与广义特征值和响应再分析问题相关的计算效率。与传统的逐步积分法相比,EPMPT 的计算效率至少提高了 70%,在某些情况下甚至高达 90%。
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Energy-preserving matrix perturbation theory for coupling dynamic analysis of flexible structures
Aiming at the reanalysis problem of time-varying eigenvalues of force-shape coupled systems, this paper proposes an energy-preserving matrix perturbation theory (EPMPT) that can maintain the essential physical properties of the system. The classical matrix perturbation method, which employs interpolated shape functions, fails to evaluate and address solution errors promptly during the continuous perturbation process. This limitation has led to the theoretical issue of “eigenvalue drift”, a flaw that has persisted in the original method since its introduction 40 years ago. In contrast, the presented method uses the dynamic stiffness method to obtain the system eigenvalues and eigenvectors at one time, and provides a perturbation solution to the time-varying eigenvalue problem. Further combined with the J count test technology in the Wittrick-Williams algorithm, an energy-preserving method that can “self-check and self-correct” the solution was developed. The idea that “continuous perturbation should maintain force-shape dynamic self-consistency in the frequency domain” is proposed, and avoiding the energy dispersion and resulting distortion problems caused by long-term numerical simulation. To illustrate the advantage of the EPMPT, a thermally induced vibration of an aerospace structure including force-shape coupling effect, and the vibration of a flexible space solar power arrays including rigid-flexible coupling effect are investigated. Case studied elucidates that EPMPT possesses the capability to notably enhance the computational efficiency associated with generalized eigenvalue and response reanalysis problems. When juxtaposed against conventional step-by-step integration methods, EPMPT has been found to augment computational efficiency by a margin of at least 70 %, and in some instances, up to 90 %.
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来源期刊
Computers & Structures
Computers & Structures 工程技术-工程:土木
CiteScore
8.80
自引率
6.40%
发文量
122
审稿时长
33 days
期刊介绍: Computers & Structures publishes advances in the development and use of computational methods for the solution of problems in engineering and the sciences. The range of appropriate contributions is wide, and includes papers on establishing appropriate mathematical models and their numerical solution in all areas of mechanics. The journal also includes articles that present a substantial review of a field in the topics of the journal.
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