On the dynamics of flexible beams under large overall motions-the plane case: Part I

Journal of Applied Mechanics, Transactions ASME

Volumn 53, Issue 4, 1986, Pages 849-854

  Simo, J C ^a,b   Vu Quoc, L ^b  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; ROBOTICS; STRUCTURAL ANALYSIS - DYNAMIC RESPONSE;

FLEXIBLE BEAM DYNAMIC RESPONSE; GALERKIN METHOD; TIME-STEPPING SCHEME;

BEAMS AND GIRDERS;

EID: 0022896771     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.3171870     Document Type: Article

References (26)

1. Antman, S. S., 1972, “The Theory of Rod,” Handbuch der Physics, Vol. VIa/2, Springer, Berlin.
2. Antman, S. S., 1974, “Kirchhoff’s Problem for Nonlinearly Elastic Rods,” Quart. J. ofAppl. Math., Vol. 32, pp. 221-240.
3. Ashley, H., 1967, “Observation of the Dynamic Behavior of Flexible Bodies in Orbit,” AIAA J., Vol. 5, No. 3, pp. 460-469.
4. Baghat, B. M., and Willmert, K. D., 1973, “Finite Element Vibrational Analysis of Planar Mechanism,” Mechanisms and Machine Theory, Vol. 8, pp. 497-516.
5. Belytschko, T., and Hughes, T. J. R., 1983, Computational Methods For Transient Analysis, Elsevier Science Publishers.
6. Canavin, J. R., and Likins, P. W., 1977, “Floating Reference Frames for Flexible Spacecrafts,” J. of Spacecraft, Vol. 14, No. 12, pp. 724-732.
7. de Veubeke, B. J., 1976, “The Dynamics of Flexible Bodies,” Int. J. of Engineering Sciences, Vol. 14, pp. 895-913.
8. Erdman, A. G., and Sandor, G. N., 1972, “Kineto-Elastodynamics-A Review of the State of the Art and Trends,” Mechanisms and Machine Theory, Vol. 7, pp. 19-33.
9. Fung, Y. C, 1965, Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, NJ.
10. Goldstein, H., 1980, Classical Mechanics, Second Ed., Addison Wesley, Reading, Massachusetts.
11. Grotte, P. B., McMunn, J. C, and Gluck, R., 1971, “Equations of Motion of Flexible Spacecraft,” J. of Spacecraft and Rockets, Vol. 8, No. 6, pp. 561-567.
12. Kane, T. R., and Levinson, D. A., 1981, “Simulation of Large Motions of Nonuniform Beams in Orbit: Part II-The Unrestrained Beam,” The J. of the Astronautical Sciences, Vol. 29, No. 3, pp. 213-244.
13. Kane, T. R., Likins, P. W., and Levinson, D. A., 1983, Spacecraft Dynamics, McGraw-Hill, New York.
14. Kumar, V. K., and Bainum, P. M., 1980, “Dynamics of a Flexible Body in Orbit,” J. of Guidance and Control, Vol. 3, No. 1, pp. 90-91.
15. Laskin, R. A., Likins, P. W., and Longman, R. W., 1983, “Dynamical Equations of a Free-Free Beam Subject to Large Overall Motions,” The J. of the Astronautical Sciences, Vol. 31, No. 4, pp. 507-528.
16. Levinson, D. A., and Kane, T. R., 1981, “Simulation of Large Motions of Nonuniform Beams in Orbit: Part I-The Cantilever Beam,” The J. of the Astronautical Sciences, Vol. 29, No. 3, pp. 245-276.
17. Likins, P. W., 1974, “Analytical Dynamics and Nonrigid Spacecraft Simulation,” Jet Propulsion Laboratory, Technical Report 32-1593, California Institute of Technology.
18. Petzold, L. R., 1982, “Differential/Algebraic Equations are Not ODE’s,” SIAMJ. Sci. Stat. Comput., Vol. 3, No. 3, pp. 367-384.
19. Reissner, E., 1972, “On a One Dimensional Finite Strain Beam: The Plane Problem,” J. Appl. Math. Phys., Vol. 23, pp. 795-804.
20. Reissner, E., 1973, “On a One-Dimensional Large-Displacement, Finite-Strain Beam Theory,” Studies in Applied Math, Vol. 52, pp. 87-95.
21. Reissner, E., 1981, “On Finite Deformations of Space-Curved Beams,” ZAMP, Vol. 32, pp. 734-744.
22. Simo, J. C, 1985, “A Finite Strain Beam Formulation. The Three Dimensional Dynamic Problem. Part I, “ Comp. Meth. Appl. Mech. Engrg., Vol. 49, pp. 55-70.
23. Simo, J. C, and Vu-Quoc, L., 1985, “Three Dimensional Finite Strain Rod Model. Part II: Computational Aspects,” Electronics Research Laboratory Memorandum No. UCB/ERL M85/31, University of California, Berkeley,-April. (Submitted for publication.)
24. Simo, J. C, and Vu-Quoc, L., 1986, The Role of Nonlinear Theories in the Dynamics Analysis of Rotating Structures, Electronics Research Laboratory Memorandum UCB/ERL M86/10, University of California, Berkeley, January.
25. Song, J. O., and Huag, E. J., 1980, “Dynamic Analysis of Planar Flexible Mechanism,” Comp. Meth. Appl. Mech. Engrg., Vol. 24, pp. 359-381.
26. Winfrey, R. C, 1971, “Elastic Link Mechanism Dynamics,” ASME J. of Engineering for Industry, Vol. 93, No. 1, pp. 268-272.