This paper proposes an improved variable-length beam element based on absolute nodal coordinate formulation and arbitrary Lagrangian–Eulerian description to build dynamic model of a one-dimensional medium with mass transportation and a non-ignorable torsion effect. The rotational angle of the presented element is interpolated using the same Hermite polynomials as the position vector such that the change rate of the rotational angles of the two nodes are also introduced into generalized coordinates of the element, which ensures the continuity of the nodal torque. Numerical examples demonstrate that the proposed element can precisely describe the dynamic behaviour of a one-dimensional medium. Furthermore, its ability to describe the torsion effect is significantly enhanced compared to earlier element in the literature. In engineering applications, the proposed element can be used in the dynamic analysis of drill stems in the drilling process, slender workpieces of cylinder shafts in turning processes and leading screws in ball screw mechanisms.
Shabana AA. An absolute nodal coordinates formulation for the large rotation and deformation analysis of flexible bodies. Report, Report no. MBS96-1-UIC, University of Illinois at Chicago, USA, 1996.
2.
BonetJWoodRD. Nonlinear continuum mechanics for finite element analysis, Cambridge, UK: Cambridge University Press, 1997, pp. 165–165.
3.
ShabanaAA. Computational continuum mechanics, 2nd ed. New York: Cambridge University Press, 2012, pp. 211–211.
4.
ShabanaAA. Definition of the slopes and the finite element absolute nodal coordinate formulation. Multibody Syst Dyn1997; 1: 339–348.
5.
SugiyamaHSudaY. A curved beam element in the analysis of flexible multi-body systems using the absolute nodal coordinates. Proc IMechE, Part K: J Multi-body Dynamics2007; 221: 219–231.
6.
DmitrochenkoONPogorelovDY. Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody Syst Dyn2003; 10: 17–43.
7.
DufvaKShabanaAA. Analysis of thin plate structures using the absolute nodal coordinate formulation. Proc IMechE, Part K: J Multi-body Dynamics2005; 219: 345–355.
8.
HyldahlPMikkolaABallingO. A thin plate element based on the combined arbitrary Lagrange-Euler and absolute nodal coordinate formulations. Proc IMechE, Part K: J Multi-body Dynamics2013; 227: 211–219.
9.
MikkolaAMShabanaAA. A Non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications. Multibody Syst Dyn2003; 9: 283–309.
10.
KüblerLEberhardPGeislerJ. Flexible multibody systems with large deformations and nonlinear structural damping using absolute nodal coordinates. Nonlinear Dyn2003; 34: 31–52.
11.
OmarMAShabanaAA. A two-dimensional shear deformable beam for large rotation and deformation problems. J Sound Vib2001; 243: 565–576.
12.
ShabanaAAYakoubRY. Three dimensional absolute nodal coordinate formulation for beam elements: theory. J Mech Des2001; 123: 606–613.
13.
YakoubRYShabanaAA. Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. J Mech Des2001; 123: 614–621.
14.
DombrowskiSV. Analysis of large flexible body deformation in multibody systems using absolute coordinates. Multibody Syst Dyn2002; 8: 409–432.
15.
GerstmayrJShabanaAA. Analysis of thin beams and cables using the absolute nodal co-ordinate formulation. Nonlinear Dyn2006; 45: 109–130.
16.
Lu YJ. Positioning and orientating control study on the feed support system of a large radio telescope. PhD Thesis, Tsinghua University, China, 2007.
17.
TangJLRenGXZhuWDet al.Dynamics of variable-length tethers with application to tethered satellite deployment. Commun Nonlinear Sci Numer Simul2011; 16: 3411–3424.
18.
HongDFRenGX. A modeling of sliding joint on one-dimensional flexible medium. Multibody Syst Dyn2011; 26: 91–106.
19.
HongDFTangJLRenGX. Dynamic modeling of mass-flowing linear medium with large amplitude displacement and rotation. J Fluids Struct2011; 27: 1137–1148.
20.
DuJLCuiCZBaoHet al.Dynamic analysis of cable-driven parallel manipulators using a variable length finite element. J Comput Nonlinear Dyn2015; 10: 011013:1–011013:7.
21.
BaruhTH. Dynamics and control of a translating flexible beam with a prismatic joint. Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME1992; 114: 422–427.
22.
Al-BedoorBOKhuliefYA. An approximate analytical solution of beam vibrations during axial motion. J Sound Vib1996; 192: 159–171.
23.
YukselSGurgozeM. On the flexural vibrations of elastic manipulators with prismatic joints. Comput Struct1997; 62: 897–908.
24.
FungRFLuPYTsengCC. Non-linearly dynamic modeling of an axially moving beam with a tip mass. J Sound Vib1998; 218: 559–571.
25.
GurgozeMYukselS. Transverse vibrations of a flexible beam sliding through a prismatic joint. J Sound Vib1999; 223: 467–482.
26.
ZhuWDNiJHuangJ. Active control of translating media with arbitrarily varying length. J Vib Acoust Trans ASME2001; 123: 347–358.
27.
LiSHYangJBHuangQHet al.Independent model space vibration control of an axially moving cantilever beam, part I: theoretical analysis of approximation. Chin J Appl Mech2002; 19: 35–38.
28.
WangLChenHHHeXDet al.Vibration control of an axially moving cantilever beam with varying length. J Vib Eng2009; 22: 565–570.
29.
Sandilo SH. On boundary damping for an axially moving beam and on the variable length induced vibrations of an elevator cable. In: European nonlinear dynamics conference, Rome, Italy, 24–29 July 2011.
30.
Wang L. Study on the dynamics and control of axially moving beams. PhD Thesis, Nanjing University of Aeronautics and Astronautics, China, 2011.
31.
MaGLXuMLChenLQet al.Vibration characteristics of an axially moving variable length beam with a tip mass. Appl Math Mech2015; 36: 897–904.
32.
Zhao Y, Deng ZQ, Tian H, et al. Research on variable-length element of one-dimensional medium with torsion. In: Proceedings of the 4th joint international conference on multibody system dynamics, Montréal, Canada, 29 May–2 June 2016, paper no. a234.
33.
TianYDengZQTangDWet al.Structure parameters optimization and simulation experiment of auger in lunar soil drill-sampling device. J Mech Eng2012; 48: 10–15.
34.
Deng ZQ, Yang S, Sun J, et al. Dynamic modeling and analysis of rotating mechanism in planetary soil drilling sampler. In: 2014 IEEE international conference on mechatronics and automation, Tianjin, China, 3–6 August 2014, pp.663–668. New York: IEEE.
35.
Yang S, Deng ZQ, Sun J, et al. Dynamic analysis of feeding drive mechanism in planetary soil automatic drilling sampler. In: 2014 IEEE international conference on information and automation, Hailar, China, 28–30 July 2014, pp.763–768. New York: IEEE.
36.
LvBLLiWYOuyangHJ. Moving force-induced vibration of a rotating beam with elastic boundary conditions. Int J Struct Stab Dyn2015; 15: 1450035:1–1450035:24.
37.
HanXGWangMJOuyangHJ. Establishment of vibration model and experimental analyses of workpiece with variable mass and diameter in turning process. J Dalian Univ Technol2012; 52: 514–521.
38.
KatzR. The dynamic response of a rotating shaft subject to an axially moving and rotating load. J Sound Vib2001; 246: 757–775.
39.
HuangLLWangKS. Research on reliability of dynamic performance and precision of screw drive system. J Beijing Inform Sci Technol Univ2014; 29: 75–79.
40.
LiuYZChenLQChenWL. Mechanics of vibration, 2nd ed. Beijing: Higher Education Press, 2011, pp. 200–200.
41.
LiuYZ. Exact dynamical model of axially moving beam with large deformation. Chin J Theor Appl Mech2012; 44: 832–838.
42.
WickertJAMoteCD. Classical vibration analysis of axially moving continua. J Appl Mech Trans ASME1990; 57: 738–744.
43.
GattiPLFerrariV. Applied structural and mechanical vibrations-theory, methods and measuring instrumentation, New York: Taylor & Francis Group, 2003, pp. 360–360.
44.
KatzRLeeCWUlsoyAGet al.The dynamic response of a rotating shaft subject to a moving load. J Sound Vib2001; 122: 131–148.
