Abstract
In this paper a computational methodology on impact dynamics of the flexible multibody system is presented. First, the floating frame of reference approach and nodal coordinates on the basis of finite element formulation are used to describe the kinematics of planar deformable bodies. According to the kinematic description of contact conditions, the contact constraint equations of planar flexible bodies are derived. Based on the varying topology technique the impact dynamic equations for a planar multibody system are established. Then the initial conditions of the equations in each contact stage are determined according to the discontinuity theory in continuum mechanics. The experiments between the aluminum rods are performed to check the correctness of the proposed method. Through the comparison between the numerical and experimental results the proposed method is validated. Experimental results also show that the impulse momentum method cannot accurately predict the complex impact dynamic phenomena and the continuous model may lead to a serious error when used to simulate the impact problems with significant wave propagation effects.
Similar content being viewed by others
References
Chen M., Chen L.P., Zhang X.F. et al.: Research and dynamic simulation of docking locks with contact-impact. Aerosp. Sci. Technol. 7, 364–372 (2003)
Liu J.Y., Hong J.Z.: Impact with multiple contact points of the flexible multibody system and closed loops. China Mech. Eng. 11(6), 618–624 (2000) (in Chinese)
Pfeiffer F., Glocker C.: Contacts in multibody systems. J. Appl. Math. Mech. 64(5), 773–782 (2000)
Flores P., Ambrosio J.: Revolute joints with clearance in multibody system. Comput. Struct. 82, 1359–1369 (2004)
Huag E., Wu S.C., Yang S.M.: Dynamics of mechanical systems with Coulomb, friction, stiction, impact and constraint addition-deletion-I. Mech. Mach. Theory 21(5), 401–406 (1986)
Liu Y.Z.: Three-dimensional impact of a rigid ellipsoid on fixed surface with friction. Acta Mech. Sin. 29(6), 726–732 (1997) (in Chinese)
Zhang D.G.: A standard solution for the dynamics of multi-point collision. Acta Mech. Sin. 30(2), 252–256 (1998) (in Chinese)
Wang D., Conti C., Beale D.: Interface impact analysis of multibody system. ASME J. Mech. Des. 121, 128–135 (1999)
Chang C.C., Houston R.: Collisions of multibody systems. Comput. Mech. 27, 436–444 (2001)
Stoianovici D., Hurmuzlu Y.: A critical study of the applicability of rigid body collision theory. ASME J. Appl. Mech. 63(2), 307–316 (1996)
Khulief Y.A., Shabana A.A.: A continuous force model for the impact analysis of flexible multibody system. Mech. Mach. Theory 22(3), 213–224 (1987)
Lankarani H.M., Nikravesh P.E.: Continuous contact force models for impact analysis in multibody system. Nonlinear Dyn. 5, 193–207 (1994)
Liu C.S., Chen B.: The oblique impact dynamic study for a flexible beam undergoing large overall motion. Acta Mech. Sin. 32(4), 457–465 (2000) (in Chinese)
Yigit A.S.: On the use of an elastic–plastic contact law for the impact of a single flexible link. J. Dyn. Syst. Meas. Control 117(4), 527–533 (1995)
Diolaiti N., Melchioorri C., Stramigioli S.: Contact impedance estimation for robotic system. IEEE Trans. Robotics 21(5), 925–935 (2005)
Hong J.Z., Ni C.S.: Global dynamics simulation of multibody system with variable topology. Acta Mech. Sin. 28(5), 633–637 (1996) (in Chinese)
Hong J.Z.: Computational Dynamics of Multibody System, pp. 348–357. Higher Education Press, Beijing (1999) (in Chinese)
Shabana A.A.: Dynamics of Multibody Systems, pp. 191–269. Cambridge University Press, Cambridge (1998)
Klisch T.: Contact mechanics in multibody system. Multibody Syst. Dyn. 2, 335–354 (1998)
Oden J.T., Reddy J.N.: Variational Methods in Theoretical Mechanics, pp. 73–83. Springer, Berlin (1983)
Hughes T.J.R., Taylor R.L., Sackman J.L. et al.: A finite method for a class of contact-impact problems. Comput. Methods Appl. Eng. 8, 249–276 (1976)
Hu B., Eberhard P.: Simulation of longitudinal impact waves using time delay. ASME J. Dyn. Syst. Meas. Control 126, 644–649 (2004)
Seifried R., Schiehlen W., Eberhard P.: Numerical and experimental evaluation of the coefficient of restitution for repeated impacts. Int. J. Impact Eng. 32, 508–524 (2005)
Shen L.J., Guo Q.W., Liu J.Y.: Dynamic modeling and experimental technique for a flexible beam with cylindrical contact. J. Dyn. Control 5(2), 148–152 (2007) (in Chinese)
Sheng L.W., Liu J.Y., Yu Z.Y.: Dynamic modeling of flexible multibody system with elastic impact. J. Shanghai Jiaotong Univ. 40(10), 1790–1797 (2006) (in Chinese)
Hunt K.H., Crossley F.R.E.: Coefficient of restitution interpreted as damping in vibroimpact. ASME J. Appl. Mech. 42, 440–445 (1975)
Johnson K.L.: Contact Mechanics, pp. 96–122. Cambridge University Press, Cambridge (1985)
Lankarani H.M., Nikravesh P.E.: A contact force model with hysteresis damping for impact analysis of multi-body systems. ASME J. Mech. Des. 112, 369–376 (1990)
Goldsmith W.: Impact-Theory and Physical Behavior of the Colliding Solids, pp. 22–50. Arnold and Publishers, London (1960)
Author information
Authors and Affiliations
Corresponding author
Additional information
The project was supported by the National Natural Science Foundation of China (10772113).
Rights and permissions
About this article
Cite this article
Dong, FX., Hong, JZ., Zhu, K. et al. Numerical and experimental studies on impact dynamics of a planar flexible multibody system. Acta Mech Sin 26, 635–642 (2010). https://doi.org/10.1007/s10409-010-0359-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-010-0359-y