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大范圍轉動彈性梁柔性動力學建模與攝動解耦
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國家重點研發(fā)計劃項目(2017YFB1303502、2018YFB1308900)和天津市自然科學基金面上項目(18JCYBJC87900,、17JCYBJC18300)


Flexible Dynamics Modeling and Perturbation Decoupling of Elastic Beam in Large Overall Rotation
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    摘要:

    為實現(xiàn)大空間轉動彈性梁的高速,、高精度平穩(wěn)控制,,首先需解決彈性梁的非線性動力學建模問題,,并完成動力學解耦,。假設柔性連桿為歐拉-伯努利梁,,應用假設模態(tài)法進行坐標離散,,采用Galerkin法和Hamilton最小變微分原理建立彈性梁柔性動力學模型;基于攝動理論構建正則攝動式,,應用多尺度法對攝動式進行改進,,對比分析了常規(guī)正則攝動法、改進后攝動法的解耦精度,,應用四階Runge-Kutta法驗證了所提出方法的有效性與可行性,。數(shù)值仿真結果表明,改進后的攝動法解耦精度高,,解耦誤差比常規(guī)正則攝動誤差降低一個數(shù)量級,,解決了低階正則攝動法解耦精度低的問題,避免了采用高階攝動來提高解耦精度而產(chǎn)生龐大計算量的弊端,。

    Abstract:

    In order to realize the stable and precision control of elastic beams in large overall rotation at high speed, its nonlinear dynamic model must be built and the decoupling work should be completed. Flexible rod was assumed by Euler-Bernoulli beam. The approach of assumed modes was applied to discrete the coordinates, and the Galerkin method and Hamilton principle were adopted to establish the flexible dynamic model. The regular perturbation formula was deduced with perturbation theory. Multiscale method was used to improve the perturbation formula by separating two-time parameters. The decoupling accuracy was deeply analyzed for the regular perturbation method and the improved perturbation method.The validity and feasibility of the proposed method were verified by Runge-Kutta method. The simulation data indicated that the improved perturbation solution owned high decoupling accuracy, little computation and good rapidity. The problem of low decoupling accuracy was solved compared with the common regular perturbation method which was limited by effective time series. The proposed decoupling method also avoided much calculation caused by high-order perturbation to improve the computation’s accuracy. It provided an important theoretical basis and data support for dynamic decoupling about complex multi-body flexible systems.

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趙磊,趙新華,李彬,周海波,楊玉維,劉涼.大范圍轉動彈性梁柔性動力學建模與攝動解耦[J].農(nóng)業(yè)機械學報,2020,51(1):391-397. ZHAO Lei, ZHAO Xinhua, LI Bin, ZHOU Haibo, YANG Yuwei, LIU Liang. Flexible Dynamics Modeling and Perturbation Decoupling of Elastic Beam in Large Overall Rotation[J]. Transactions of the Chinese Society for Agricultural Machinery,2020,51(1):391-397.

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  • 收稿日期:2019-05-14
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  • 在線發(fā)布日期: 2020-01-10
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