EI、Scopus 收录
中文核心期刊
Quick Search Issue Search Advanced Search
Volume 54 Issue 1
Jan.  2022
Turn off MathJax
Article Contents
Abstract
References
Related Articles
Du Chaofan, Zheng Yanlong, Zhang Dingguo, Zhou Xiaoting. High-order rigid-flexible coupled dynamic model of rotating Mindlin plate based on radial point interpolation method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 119-133. DOI: 10.6052/0459-1879-21-362
Citation: Du Chaofan, Zheng Yanlong, Zhang Dingguo, Zhou Xiaoting. High-order rigid-flexible coupled dynamic model of rotating Mindlin plate based on radial point interpolation method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 119-133. DOI: 10.6052/0459-1879-21-362
shu

HIGH-ORDER RIGID-FLEXIBLE COUPLED DYNAMIC MODEL OF ROTATING MINDLIN PLATE BASED ON RADIAL POINT INTERPOLATION METHOD

  • *.

    College of Architectural Science and Engineering, Yangzhou University, Yangzhou 225000, Jiangsu, China

  • †.

    School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China

  • Received Date: July 27, 2021
  • Accepted Date: November 28, 2021
  • Available Online: November 29, 2021
    Graphical Abstract
    • Abstract
  • The radial point interpolation method (RPIM) is proposed for dynamic analysis of rotating hub-Mindlin plates. Considering the shear deformation and non-linear coupling deformation which means the in-plane longitudinal shortening terms caused by transverse deformation, retaining all of the high-order terms related to the non-linear coupling deformation in the kinetic energy, the high-order rigid-flexible coupled (HOC) dynamic model is established via employing Lagrange’s equations of the second kind with floating coordinate system and the first-order shear deformation theory which means Mindlin plate theory. This model can avoid the shear locking issue by constructing high-order shape functions. And it can not only deal with thin plate problems but also thick plate problems. The high-order shape functions can be constructed easily by adding high-order polynomial basic functions in RPIM. The static results show that it is enough to avoid shear locking issue by adding 15 polynomial basic functions for RPIM. The simulation results for dynamic analysis of a rotating hub-rectangular plate are compared with those obtained by using first-order approximation coupled (FOAC) dynamic model and zero-order approximation coupled (ZOAC) dynamic model. The results show that the ZOAC dynamic model can only be applied to the case with low rotating speed because of its theoretical defects (neglecting the non-linear coupling deformation), the FOAC and HOC dynamic models can be applied to both low rotating speed and high rotating speed cases. It also shows the results using HOC are more accurate and have wider scope of application, especially in the situation of large deformation. The results are also compared with those obtained by assumed mode method (AMM) and finite element method (FEM), which shows the accuracy of RPIM. It is also demonstrated that the RPIM as a flexible discrete method has more advantages in the same computational condition and can be extended in the field of multibody system dynamics.
    • FullText(HTML)
    • References (33)
  • [1]
    Chen ZQ, Qian LF. Nonlinear dynamics characteristics analysis of planar flexible rotating beams with clearance joint. Journal of the Brazilian Society of Mechanical Science and Engineering, 2020, 42(6): 333 doi: 10.1007/s40430-020-02388-1
    [2]
    Asgarikia M, Kakavand F. Minimum diameter of optimally located damping wire to maximize the fundamental frequencies of rotating blade using Timoshenko beam theory. International Journal of Structural Stability and Dynamics, 2021, 21(7): 2150090 doi: 10.1142/S0219455421500905
    [3]
    Xu J, Yang ZC, Yang J, et al. Influence of the boundary relaxation on the free vibration of rotating composite laminated Timoshenko beams. Composite Structures, 2021, 266: 113690 doi: 10.1016/j.compstruct.2021.113690
    [4]
    Dokainish MA, Rawtani S. Vibration analysis of rotating cantilever plates. International Journal for Numerical Methods in Engineering, 1971, 3(2): 233-248 doi: 10.1002/nme.1620030208
    [5]
    Wei Z, Li L, Zhao F. First-order approximate rigid-flexible coupled dynamics analysis of a simple aero-engine blade model with dynamic stiffening effect. Journal of Mechanical Science and Technology, 2021, 35: 2997-3003 doi: 10.1007/s12206-021-0623-z
    [6]
    Yoo HH, Chung J. Dynamics of rectangular plates undergoing prescribed overall motion. Journal of Sound and Vibration, 2001, 239(1): 123-137 doi: 10.1006/jsvi.2000.3111
    [7]
    刘又午, 王建明, 张大钧等. 作大范围运动的矩形板动力分析. 振动与冲击, 1998, 17(1): 38-43 (Liu Youwu, Wang Jianming, Zhang Dajun, et al. Dynamic analysis of rectangular plates undergoing large overall motion. Journal of Vibration and Shock, 1998, 17(1): 38-43 (in Chinese)
    [8]
    刘锦阳, 洪嘉振. 作大范围运动矩形薄板的建模理论和有限元离散方法. 振动工程学报, 2003, 16(2): 175-179 (Liu Jinyang, Hong Jiazhen. Dynamic modeling theory and finite element method for a rectangular plate undergoing large overall motion. Journal of Vibration Engineering, 2003, 16(2): 175-179 (in Chinese) doi: 10.3969/j.issn.1004-4523.2003.02.009
    [9]
    Li L, Zhang DG. Free vibration analysis of rotating functionally graded rectangular plates. Composite Structures, 2016, 136: 493-504 doi: 10.1016/j.compstruct.2015.10.013
    [10]
    Vu TV, Nguyen NH, Khosravifard A, et al. A simple FSDT-based meshfree method for analysis of functionally graded plates. Engineering Analysis with Boundary Elements, 2017: 791-812
    [11]
    黎亮, 章定国, 洪嘉振. 作大范围运动FGM矩形薄板的动力学特性研究. 动力学与控制学报, 2013, 11(4): 329-335 (Li Liang, Zhang Dingguo, Hong Jiazhen. Dynamic of rectangular functionally graded thin plates undergoing large overall motion. Journal of Dynamics and Control, 2013, 11(4): 329-335 (in Chinese) doi: 10.6052/1672-6553-2013-042
    [12]
    Chung J, Yoo HH. Dynamic analysis of a rotating cantilever beam by using the finite element method. Journal of Sound and Vibration, 2002, 249(1): 147-164 doi: 10.1006/jsvi.2001.3856
    [13]
    Sanborn GG, Shabana AA. A rational finite element method based on the absolute nodal coordinate formulation. Nonlinear Dynamics, 2009, 58(3): 565-572 doi: 10.1007/s11071-009-9501-4
    [14]
    杜超凡, 章定国, 洪嘉振. 径向基点插值法在旋转柔性梁动力学中的应用. 力学学报, 2015, 47(2): 279-288

    Du Chaofan, Zhang Dingguo, Hong Jiazhen. A meshfree method based on radial point interpolation method for the dynamic analysis of rotating flexible beams. Chinese Jounal of Theoretical and Applied Mechanics, 2015, 47(2): 279-288 (in Chinese)
    [15]
    蒋建平, 李东旭. 大范围运动板动力刚化分析. 动力学与控制学报, 2005, 3(1): 10-14 (Jiang Jianping, Li Dongxu. Dynamic analysis of rectangular plate undergoing overall motion. Journal of Dynamics and Control, 2005, 3(1): 10-14 (in Chinese) doi: 10.3969/j.issn.1672-6553.2005.01.003
    [16]
    杨兴, 刘仁伟, 侯鹏等. 基于一阶剪切板理论的FGM板刚柔耦合动力学建模与仿真. 动力学与控制学报, 2020, 18(4): 33-43 (Yang Xing, Liu Renwei, Hou Peng, et al. Dynamic modeling and simulation of functionally graded materials plates based on first order shear plate theory. Journal of Dynamics and Control, 2020, 18(4): 33-43 (in Chinese)
    [17]
    潘科琪, 刘锦阳. 计及剪切变形复合材料梁的刚/柔耦合动力学特性. 上海交通大学学报, 2009, 43(8): 1293-1297 (Pan Keqi, Liu Jinyang. Rigid-flexible coupling dynamics of composite beam considering shear deformation. Journal of Shanghai Jiaotong University(Science) , 2009, 43(8): 1293-1297 (in Chinese) doi: 10.3321/j.issn:1006-2467.2009.08.022
    [18]
    李彬, 刘锦阳, 洪嘉振. 计及剪切变形的Timoshenko梁的刚-柔耦合动力学. 计算力学学报, 2006, 23(4): 419-422 (Li Bin, Liu Jinyang, Hong Jiazhen. Coupling dynamics of Timoshenko beam with shear deformation. Chinese Journal of Computational Mechanics, 2006, 23(4): 419-422 (in Chinese) doi: 10.3969/j.issn.1007-4708.2006.04.007
    [19]
    Yuan J, Pao YH, Chen W. Exact solutions for free vibrations of axially inhomogeneous Timoshenko beams with variable cross section. Acta Mechanica, 2016, 227(9): 2625-2643 doi: 10.1007/s00707-016-1658-6
    [20]
    陈思佳, 章定国, 洪嘉振. 大变形旋转柔性梁的一种高次刚柔耦合动力学模型. 力学学报, 2013, 45(2): 251-256 (Chen Sijia, Zhang Dingguo, Hong Jiazhen. A high-order rigid-flexible coupling model of a rotating flexible beam under deformation. Chinese Jounal of Theoretical and Applied Mechanics, 2013, 45(2): 251-256 (in Chinese) doi: 10.6052/0459-1879-12-221
    [21]
    Fang JS, Zhou D. Free vibration analysis of rotating Mindlin plates with variable thickness. International Journal of Structural Stability and Dynamics, 2017, 17: 1750046 doi: 10.1142/S0219455417500468
    [22]
    Fan JH, Zhang DG, Shen H. Discretization methods of a rotating flexible rectangular thin plate. Journal of Shanghai Jiaotong University(Science) , 2020, 25(1): 118-126 doi: 10.1007/s12204-019-2129-8
    [23]
    Liu G, Chen GF, Cui FS, et al. Nonlinear vibration analysis of composite blade with variable rotating speed using Chebyshev polynomials. European Journal of Mechanics-A/Solids, 2020, 82: 103976 doi: 10.1016/j.euromechsol.2020.103976
    [24]
    Liew KM, Ng TY, Wu YC. Meshfree method for large deformation analysis — A reproducing kernel particle approach. Engineering Structures, 2002, 24: 543-551 doi: 10.1016/S0141-0296(01)00120-1
    [25]
    Atluri SN, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, 1998, 22: 117-127 doi: 10.1007/s004660050346
    [26]
    Li DM, Featherston CA, Wu ZM. An element-free study of variable stiffness composite plates with cutouts for enhanced buckling and post-buckling performance. Computer Method in Applied Mechanics and Engineering, 2020, 371: 113314 doi: 10.1016/j.cma.2020.113314
    [27]
    Wang JG, Liu GR. A point interpolation meshless method based on radial basis functions. International Journal for Numerical Methods in Engineering, 2002, 54(11): 1623-1648 doi: 10.1002/nme.489
    [28]
    Qin X, Shen YJ, Chen W, et al. Bending and free vibration analyses of circular stiffened plates using the FSDT mesh-free method. International Journal of Mechanical Sciences, 2021, 202: 106498
    [29]
    Rodrigues DES, Belinha J, Dinis LMJS, et al. The numerical analysis of symmetric cross-ply laminates using the natural neighbor radial point interpolation method and high-order shear deformation theories. Engineering Structures, 2020, 225: 111247 doi: 10.1016/j.engstruct.2020.111247
    [30]
    Hosseini S, Rahimi G, Anani Y. A meshless collocation method based on radial basis functions for free and forced vibration analysis of functionally graded plates using FSDTT. Engineering Aanlysis with Boundary Elements, 2021, 125: 168-177 doi: 10.1016/j.enganabound.2020.12.016
    [31]
    Du CF, Zhang DG, Zhang JS, et al. Predicting dynamics behavior of rotating Mindlin plate using radial point interpolation method. International Journal of Structural Stability and Dynamics, 2019, 19(7): 1950070 doi: 10.1142/S0219455419500706
    [32]
    Chen YZ, Guo X, Zhang DG, et al. A novel radial point interpolation method for thin plate in the frame of absolute nodal coordinate formulation. Journal of Sound and Vibration, 2020, 469(17): 115132
    [33]
    Liu GR. Mesh Free Methods: Moving beyond the Finite Element Method. CRC Press, 2002: 496-497
    • Related Articles

  • Related Articles

    [1]Mo Shuai, Huang Zurui, Liu Yiheng, Zhang Wei. NON-LINEAR DYNAMICS OF AERONAUTICAL NON-ORTHOGONAL OFFSET GEAR SPLIT FLOW SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1110-1122. DOI: 10.6052/0459-1879-23-232
    [2]Mo Shuai, Zeng Yanjun, Wang Zhen, Zhang Wei. NONLINEAR DYNAMIC ANALYSIS OF HIGH SPEED AND HEAVY LOAD HERRINGBONE GEAR TRANSMISSION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(10): 2381-2392. DOI: 10.6052/0459-1879-23-166
    [3]Chen Kefan, Li Yuan, He Shuanhai, Song Yifan, Xu Keyao. MODELLING AND ANALYSIS OF THE IN-PLANE DYNAMICS OF CABLE-STAYED BRIDGES CONSIDERING THE PYLON-CABLE-BEAM COUPLING EFFECT[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(9): 2010-2026. DOI: 10.6052/0459-1879-23-236
    [4]Han Fei, Duan Zunyi. RESEARCH ON DYNAMIC RESPONSE ANALYSIS AND CABLE FORCE IDENTIFICATION METHOD OF SUBMERGED ANCHOR CABLES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(4): 921-928. DOI: 10.6052/0459-1879-21-583
    [5]Li Xiaoyu, Yue Baozeng. STUDY ON THE RIGID-LIQUID COUPLING DYNAMICS OF A CYLINDRICAL-TANK SPACECRAFT IN TRANSLATION BASED ON MUTI-SCALE METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1448-1454. DOI: 10.6052/0459-1879-19-111
    [6]Zhang Shu, Xu Jian. REVIEW ON NONLINEAR DYNAMICS IN SYSTEMS WITH COULPLING DELAYS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 565-587. DOI: 10.6052/0459-1879-17-123
    [7]Gu Huaguang. COMPLEX DYNAMICS OF THE NERVOUS SYSTEM FOR INFORMATION PROCESSING AND ABNORMAL FUNCTIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 410-420. DOI: 10.6052/0459-1879-16-315
    [8]Du Chaofan, Zhang Dingguo, Hong Jiazhen. A MESHFREE METHOD BASED ON RADIAL POINT INTERPOLATION METHOD FOR THE DYNAMIC ANALYSIS OF ROTATING FLEXIBLE BEAMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(2): 279-288. DOI: 10.6052/0459-1879-14-334
    [9]Jing Lu, Junfeng Li, Tianshu Wang, Baozeng Yue. Analytic study on 1:1:1 internal resonance nonlinear dynamics of a liquid-filled spacecraft with elastic appendages[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(6): 804-812. DOI: 10.6052/0459-1879-2007-6-2006-497
    [10]A METHOD FOR DETERMINING THE PERIODIC SOLUTION AND ITS STABILITY OF A DYNAMIC SYSTEM WITH LOCAL NONLINEARITIES 1)[J]. Chinese Journal of Theoretical and Applied Mechanics, 1998, 30(5): 572-579. DOI: 10.6052/0459-1879-1998-5-1995-163

Catalog

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (626) PDF downloads (110) Cited by()
    Related

    Download Center

    Author Center

    Copyright © Editorial Office of the Chinese Journal of Mechanics   京ICP备05039218号-1

    Address：15 Beishihuan Xi Lu, Haidian District, Beijing, China   China Pos：100190

    Tel：010-62536271

    Email：lxxb@cstam.org.cn

    微信公众号
    RSS

    Supported by: Beijing Renhe Information Technology Co., Ltd.  Baidu Analytics

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return