Abstract
Purpose
Considering the manipulators applied in the space missions, a flexible hub-beam model with a hollow tapered cross section is concerned based on the classic hub-beam model in this paper.
Method
The dynamic equations describing the coupling behaviors between the rotation of the hub and the vibration of the flexible beam with a hollow tapered cross section are proposed first. Then, combining the symplectic precise integration method for the rotation of the hub and the approximate multi-symplectic method for the transverse vibration of the flexible hollow tapered cross-section beam, a complex structure-preserving iteration approach is constructed to investigate the dynamic response of the concerned coupling dynamic system.
Results and Conclusions
The effects of the taper ratio and the hollow ratio of the beam on the dynamic response of the coupling system are investigated in the numerical simulations in detail. From the numerical results presented in this paper, it can be found that, with the increase of the taper ratio or the decrease of the hollow ratio of the beam, both the stable rotation angular speed of the hub and the stable vibration amplitude of the beam decrease, which provide some guidance for the structural design and the structural optimization of the manipulator employed in space structure when the dynamic properties of the system is taken into account. The above numerical results are verified by the tiny relative errors of the total energy of the system indirectly.
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Data availability
Data will be made available on request.
References
Zhao Y, Bai ZF (2011) Dynamics analysis of space robot manipulator with joint clearance. Acta Astronaut 68(7–8):1147–1155. https://doi.org/10.1016/j.actaastro.2010.10.004
Sabatini M, Gasbarri P, Monti R, Palmerini GB (2012) Vibration control of a flexible space manipulator during on orbit operations. Acta Astronaut 73:109–121. https://doi.org/10.1016/j.actaastro.2011.11.012
Fujii HA, Uchiyama K, Yoneoka H, Maruyama T (1996) Ground-based simulation of space manipulators using test bed with suspension system. J Guid Control Dyn 19(5):985–991. https://doi.org/10.2514/3.21736
Caron M, Modi VJ, Misra AK (1998) Order-N formulation and dynamics of multi-unit flexible space manipulators. Nonlinear Dyn 17(4):347–368. https://doi.org/10.1023/a:1008314211138
Meng D, She Y, Xu W, Lu W, Liang B (2018) Dynamic modeling and vibration characteristics analysis of flexible-link and flexible-joint space manipulator. Multibody SysDyn 43(4):321–347. https://doi.org/10.1007/s11044-017-9611-6
Xiang W, Yan S (2020) Dynamic analysis of space robot manipulator considering clearance joint and parameter uncertainty: Modeling, analysis and quantification. Acta Astronaut 169:158–169. https://doi.org/10.1016/j.actaastro.2020.01.011
Li K, Zhang Y, Hu Q (2019) Dynamic modelling and control of a tendon-actuated lightweight space manipulator. Aerosp Sci Technol 84:1150–1163. https://doi.org/10.1016/j.ast.2018.11.018
Ma S, Liang B, Wang T (2020) Dynamic analysis of a hyper-redundant space manipulator with a complex rope network. Aerospace Sci Technol https://doi.org/10.1016/j.ast.2020.105768
Li Y, Hao X, She Y, Li S, Yu M (2021) Constrained motion planning of free-float dual-arm space manipulator via deep reinforcement learning. Aerospace Sci Technol https://doi.org/10.1016/j.ast.2020.106446
Yang H, Hong JZ, Yu ZY (2003) Dynamics modelling of a flexible hub-beam system with a tip mass. J Sound Vib 266(4):759–774. https://doi.org/10.1016/s0022-460x(02)01332-9
Cai GP, Lim CW (2008) Dynamics studies of a flexible hub-beam system with significant damping effect. J Sound Vib 318(1–2):1–17. https://doi.org/10.1016/j.jsv.2008.06.009
You C, Hong J, Cai G (2006) Modeling study of a flexible hub-beam system with large motion and with considering the effect of shear deformation. J Sound Vib 295(1–2):282–293. https://doi.org/10.1016/j.jsv.2006.01.047
Liu Z, Liu J (2017) Experimental validation of rigid-flexible coupling dynamic formulation for hub-beam system. Multibody SysDyn 40(3):303–326. https://doi.org/10.1007/s11044-016-9539-2
Zhao Z, Liu C, Ma W (2016) Characteristics of steady vibration in a rotating hub-beam system. J Sound Vib 363:571–583. https://doi.org/10.1016/j.jsv.2015.11.007
Wen H, Chen T, Jin D, Hu H (2017) Passivity-based control with collision avoidance for a hub-beam spacecraft. Adv Space Res 59(1):425–433. https://doi.org/10.1016/j.asr.2016.09.013
An SQ, Zou HL, Deng ZC, Hu WP (2019) Dynamic analysis on hub-beam system with transient stiffness variation. Int J Mech Sci 151:692–702. https://doi.org/10.1016/j.ijmecsci.2018.12.025
Hu W, Xu M, Song J, Gao Q, Deng Z (2021) Coupling dynamic behaviors of flexible stretching hub-beam system. Mech Syst Signal Process https://doi.org/10.1016/j.ymssp.2020.107389
Hu W, Huai Y, Xu M, Feng X, Jiang R, Zheng Y, Deng Z (2021) Mechanoelectrical flexible hub-beam model of ionic-type solvent-free nanofluids. Mech Syst Signal Process https://doi.org/10.1016/j.ymssp.2021.107833
Cai GP, Hong JZ, Yang SX (2005) Dynamic analysis of a flexible hub-beam system with tip mass. Mech Res Commun 32(2):173–190. https://doi.org/10.1016/j.mechrescom.2004.02.007
Hu W, Xu M, Zhang F, Xiao C, Deng Z (2022) Dynamic analysis on flexible hub-beam with step-variable cross-section. Mech Syst Signal Process https://doi.org/10.1016/j.ymssp.2022.109423
Ditarant RA (1974) Lateral vibrations of a damped laminated hollow circular cross-section beam. J Eng Industry Transact ASME 96(3): 845–852 https://doi.org/10.1115/1.3438451
Gounaris G, Anifantis N, Dimarogonas AD (1991) Dynamics of cracked hollow beams. Eng Fract Mech 39(6):931–940. https://doi.org/10.1016/0013-7944(91)90101-6
Choi SB, Park YK, Kim JD (1993) Vibration characteristics of hollow cantilevered beams containing an electrorheological fluid. Int J Mech Sci 35(9):757–768. https://doi.org/10.1016/0020-7403(93)90023-n
Eisenberger M (1995) Dynamic stiffness matrix for variable cross-section Timoshenko beams. Commun Numer Methods Eng 11(6):507–513. https://doi.org/10.1002/cnm.1640110605
Zheng DY, Fan SC (2003) Vibration and stability of cracked hollow-sectional beams. J Sound Vib 267(4):933–954. https://doi.org/10.1016/s0022-460x(02)01605-x
Wu JS, Chiang LK (2004) Free vibrations of solid and hollow wedge beams with rectangular or circular cross-sections and carrying any number of point masses. Int J Numer Meth Eng 60(3):695–718. https://doi.org/10.1002/nme.981
Ece MC, Aydogdu M, Taskin V (2007) Vibration of a variable cross-section beam. Mech Res Commun 34(1):78–84. https://doi.org/10.1016/j.mechrescom.2006.06.005
De Rosa MA, Auciello NM, Lippiello M (2008) Dynamic stability analysis and DQM for beams with variable cross-section. Mech Res Commun 35(3):187–192. https://doi.org/10.1016/j.mechrescom.2007.10.010
Sapountzakis EJ, Dikaros IC (2013) Nonlinear flexural-torsional dynamic analysis of beams of variable doubly symmetric cross section-application to wind turbine towers. Nonlinear Dyn 73(1–2):199–227. https://doi.org/10.1007/s11071-013-0779-x
Asadi H, Aghdam MM (2014) Large amplitude vibration and post-buckling analysis of variable cross-section composite beams on nonlinear elastic foundation. Int J Mech Sci 79:47–55. https://doi.org/10.1016/j.ijmecsci.2013.11.017
Boiangiu M, Ceausu V, Untaroiu CD (2016) A transfer matrix method for free vibration analysis of Euler-Bernoulli beams with variable cross section. J Vib Control 22(11):2591–2602. https://doi.org/10.1177/1077546314550699
Hajhosseini M, Rafeeyan M (2016) Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting. Appl Math Mechan English Edition 37(8):1053–1066. https://doi.org/10.1007/s10483-016-2117-8
Murin J, Goga V, Aminbaghai M, Hrabovsky J, Sedlar T, Mang HA (2017) Measurement and modelling of torsional warping free vibrations of beams with rectangular hollow cross-sections. Eng Str 136:68–76. https://doi.org/10.1016/j.engstruct.2016.12.037
Wang Z, Li R (2018) Transverse vibration of rotating tapered cantilever beam with hollow circular cross-section. Shock Vibrat https://doi.org/10.1155/2018/1056397
Dong S, Li L, Zhang D (2019) Vibration analysis of rotating functionally graded tapered beams with hollow circular cross-section. Aerospace Sci Technol https://doi.org/10.1016/j.ast.2019.105476
Feyzollahzadeh M, Bamdad M (2019) Vibration analysis of rotating beam with variable cross section using Riccati transfer matrix method. Str Eng Mech 70(2):199–207. https://doi.org/10.12989/sem.2019.70.2.199
Gao F, Wu Z, Li F, Zhang C (2019) Numerical and experimental analysis of the vibration and band-gap properties of elastic beams with periodically variable cross sections. Waves Random Complex Media 29(2):299–316. https://doi.org/10.1080/17455030.2018.1430918
Song M, Deng Z, Hu W (2021) Coupling dynamic behavior of space flexible hollow beam. Int J Appl Mech https://doi.org/10.1142/s1758825121500824
Hu W, Ye J, Deng Z (2020) Internal resonance of a flexible beam in a spatial tethered system. J Sound Vibrat https://doi.org/10.1016/j.jsv.2020.115286
Hu W, Yu L, Deng Z (2020) Minimum control energy of spatial beam with assumed attitude adjustment target. Acta Mech Solida Sin 33(1):51–60. https://doi.org/10.1007/s10338-019-00132-4
Hu W, Zhang C, Deng Z (2020) Vibration and elastic wave propagation in spatial flexible damping panel attached to four special springs. Commun Nonlinear Sci Numer Simul https://doi.org/10.1016/j.cnsns.2020.105199
Hu W, Xi X, Zhai Z, Cui P, Zhang F, Deng Z (2022) Symplectic analysis on coupling behaviors of spatial flexible damping beam. Acta Mech Solida Sin 35(4):541–551. https://doi.org/10.1007/s10338-021-00297-x
Choi S, Kim YY (2021) Higher-order beam bending theory for static, free vibration, and buckling analysis of thin-walled rectangular hollow section beams. Comput Str https://doi.org/10.1016/j.compstruc.2021.106494
Li Z, Xu Y, Huang D (2021) Analytical solution for vibration of functionally graded beams with variable cross-sections resting on Pasternak elastic foundations. Int J Mech Sci https://doi.org/10.1016/j.ijmecsci.2020.106084
Hu WP, Deng ZC, Han SM, Zhang WR (2013) Generalized multi-symplectic integrators for a class of Hamiltonian nonlinear wave PDEs. J Comput Phys 235:394–406. https://doi.org/10.1016/j.jcp.2012.10.032
Hu W, Wang Z, Zhao Y, Deng Z (2020) Symmetry breaking of infinite-dimensional dynamic system. Appl Math Lett https://doi.org/10.1016/j.aml.2019.106207
Huang YA, Deng ZC, Yao LX (2007) An improved symplectic precise integration method for analysis of the rotating rigid-flexible coupled system. J Sound Vib 299(1–2):229–246. https://doi.org/10.1016/j.jsv.2006.07.009
Hu W, Xi X, Song Z, Zhang C, Deng Z (2023) Coupling dynamic behaviors of axially moving cracked cantilevered beam subjected to transverse harmonic load. Mech Syst Signal Process 204:110757. https://doi.org/10.1016/j.ymssp.2023.110757
Huai Y, Hu W, Song W, Zheng Y, Deng Z (2023) Magnetic-field-responsive property of Fe3O4/polyaniline solvent-free nanofluid. Phys Fluids https://doi.org/10.1063/5.0130588
Bridges TJ (1997) Multi-symplectic structures and wave propagation. Math Proc Cambridge Philos Soc 121(1):147–190. https://doi.org/10.1017/s0305004196001429
Hu W, Han Z, Bridges TJ, Qiao Z (2023) Multi-symplectic simulations of W/M-shape-peaks solitons and cuspons for FORQ equation. Appl Math Lett https://doi.org/10.1016/j.aml.2023.108772
Feng K (1984) On difference schemes and symplectic geometry. In: Proceeding of the 1984 Beijing Symposium on Differential Geometry and Differential Equations, Beijing 1984, pp. 42–58. Science Press
Meiss JD (1992) Symplectic maps, variational-principles, and transport. Rev Mod Phys 64(3):795–848. https://doi.org/10.1103/RevModPhys.64.795
Yoshida H (1990) Construction of higher-order symplectic integrators. Phys Lett A 150(5–7):262–268. https://doi.org/10.1016/0375-9601(90)90092-3
Lim CW, Xu XS (2010) Symplectic elasticity: theory and applications. Appl Mech Rev 63(5):050802. https://doi.org/10.1115/1.4003700
Zhong WX (2004) On precise integration method. J Comput Appl Math 163(1):59–78. https://doi.org/10.1016/j.cam.2003.08.053
Zhong WX, Williams FW (1994) A precise time-step integration method. Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science 208(6):427–430. https://doi.org/10.1243/pime_proc_1994_208_148_02
Zhang Y, Deng Z, Hu W (2017) Generalized multi-symplectic integrator for vibration of a damping string with the driving force. Int J Appl Mech https://doi.org/10.1142/s1758825117500041
Zhao PF, Qin MZ (2000) Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation. J Phys A-Math Gener 33(18):3613–3626. https://doi.org/10.1088/0305-4470/33/18/308
Preissmann A (1961) Propagation des intumescences dans les canaux et rivieres. In: First Congress French Association for Computation, Grenoble, pp. 433–442
Acknowledgements
The research is supported by the National Natural Science Foundation of China (12172281, 11972284), Fund for Distinguished Young Scholars of Shaanxi Province (2019JC-29), Foundation Strengthening Programme Technical Area Fund (2021-JCJQ-JJ-0565), the Fund of the Science and Technology Innovation Team of Shaanxi (2022TD-61) and the Fund of the Youth Innovation Team of Shaanxi Universities. The authors declare no competing financial or non-financial interests.
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Hu, W., Xi, X., Han, Z. et al. Structure-Preserving Analysis on Flexible Hub-Beam with Hollow Tapered Cross Section. J. Vib. Eng. Technol. 12, 5229–5239 (2024). https://doi.org/10.1007/s42417-023-01194-y
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DOI: https://doi.org/10.1007/s42417-023-01194-y