Nonlinear Dynamics

, Volume 51, Issue 1–2, pp 217–230 | Cite as

Enhanced nonlinear 3D Euler–Bernoulli beam with flying support

Original Paper

Abstract

Using Hamilton’s principle the coupled nonlinear partial differential motion equations of a flying 3D Euler–Bernoulli beam are derived. Stress is treated three dimensionally regardless of in-plane and out-of-plane warpings of cross-section. Tension, compression, twisting, and spatial deflections are nonlinearly coupled to each other. The flying support of the beam has three translational and three rotational degrees of freedom. The beam is made of a linearly elastic isotropic material and is dynamically modeled much more accurately than a nonlinear 3D Euler–Bernoulli beam. The accuracy is caused by two new elastic terms that are lost in the conventional nonlinear 3D Euler–Bernoulli beam theory by differentiation from the approximated strain field regarding negligible elastic orientation of cross-sectional frame. In this paper, the exact strain field concerning considerable elastic orientation of cross-sectional frame is used as a source in differentiations although the orientation of cross-section is negligible.

Keywords

3D Euler–Bernoulli beam theory 

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References

  1. 1.
    Karray, F., Modi, V.J., Chan, J.K.: Path planning with obstacle avoidance as applied to a class of space based flexible manipulators. Acta Astronaut. 37, 69–86 (1995)CrossRefGoogle Scholar
  2. 2.
    Hiller, M.: Modelling, simulation and control design for large and heavy manipulators. Robot. Auton. Syst. 19, 167–177 (1996)CrossRefGoogle Scholar
  3. 3.
    Shi, Z.X., Fung, E.H.K., Li, Y.C.: Dynamic modelling of a rigid-flexible manipulator for constrained motion task control. Appl. Math. Model. 23, 509–525 (1999)MATHCrossRefGoogle Scholar
  4. 4.
    Chen, W.: Dynamic modeling of multi-link flexible robotic manipulators. Comput. Struct. 79, 183–195 (2001)CrossRefGoogle Scholar
  5. 5.
    Siciliano, B., Villani, L.: An inverse kinematics algorithm for interaction control of a flexible arm with a compliant surface. Control Eng. Pract. 9, 191–198 (2001)CrossRefGoogle Scholar
  6. 6.
    Jen, C.W., Johnson, D.A., Gorez, R.: A reduced-order dynamic model for end-effector position control of a flexible robot arm. Math. Comput. Simul. 41, 539–558 (1996)CrossRefGoogle Scholar
  7. 7.
    Zohoor, H., Khorsandijou, S.M.: Dynamic model of a mobile robot with long spatially flexible links, submitted to J. Scientia Iranica (2007)Google Scholar
  8. 8.
    Nayfeh, A.H., Pai, P.F.: Linear and Nonlinear Structural Mechanics, Wiley Series in Nonlinear Science. Wiley, New York (2004)Google Scholar
  9. 9.
    D’ Souza, A.F., Garg, V.K.: Advanced Dynamics, Modeling and Analysis. Prentice-Hall, Englewood Cliffs, NJ (1984)Google Scholar
  10. 10.
    Thomson, W.T.: Theory of Vibration with Applications, 3rd edn. Prentice-Hall, Englewood Cliffs, NJ (1988)Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Center of Excellence in Design, Robotics, and Automation, School of Mechanical EngineeringSharif University of TechnologyTehranIran
  2. 2.School of Mechanical EngineeringSharif University of TechnologyTehranIran

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