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Technical Brief

A Detailed Derivation of the Velocity-Dependent Inertia Forces in the Floating Frame of Reference Formulation

[+] Author and Article Information
Karim Sherif

Johannes Kepler University of Linz,
Altenbergerstr. 69,
Linz 4040, Austria
e-mail: karim.sherif@jku.at

Karin Nachbagauer

Faculty of Engineering and Environmental Sciences,
University of Applied Sciences Upper Austria,
Stelzhamerstr. 23,
Wels 4600, Austria
e-mail: karin.nachbagauer@fh-wels.at

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received June 24, 2013; final manuscript received November 21, 2013; published online July 11, 2014. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 9(4), 044501 (Jul 11, 2014) (8 pages) Paper No: CND-13-1155; doi: 10.1115/1.4026083 History: Received June 24, 2013; Revised November 21, 2013

In the case of complex multibody systems, an efficient and time-saving computation of the equations of motion is essential; in particular, concerning the inertia forces. When using the floating frame of reference formulation for modeling a multibody system, the inertia forces, which include velocity-dependent forces, depend nonlinearly on the system state and, therefore, have to be updated in each time step of the dynamic simulation. Since the emphasis of the present investigation is on the efficient computation of the velocity-dependent inertia forces as along with a fast simulation of multibody systems, a detailed derivation of the latter forces for the case of a general rotational parameterization is given. It has to be emphasized that the present investigations revealed a simpler representation of the velocity-dependent inertia forces compared to results presented in the literature. In contrast to the formulas presented in the literature, the presented formulas do not depend on the type of utilized rotational parameterization or on any associated assumptions.

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References

Shabana, A., 1997, “Flexible Multibody Dynamics: Review of Past and Recent Developments,” Multibody Syst, Dyn., 1, pp. 189–222. [CrossRef]
Wasfy, T., and Noor, A., 2003, “Computational Strategies for Flexible Multibody Systems,” Appl. Mech. Rev., 56(6), pp. 553–613. [CrossRef]
Shabana, A., 1997, “Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation,” Multibody Syst. Dyn., 1(3), pp. 339–348. [CrossRef]
Géradin, M., Robert, G., and Bernardin, C., 1984, “Dynamic Modelling of Manipulators With Flexible Members,” Advanced Software in Robotics, A. D. M.Géradin, ed., Elsevier, New York.
Shabana, A., 2005, Dynamics of Multibody Systems, 3rd ed., Cambridge University Press, New York.
Veubeke, B., 1972, “A New Variational Principle for Finite Elastic Displacements,” Int. J. Eng. Sci., 10, pp. 745–763. [CrossRef]
Simo, J., 1985, “A Finite Strain Beam Formulation. The Three-Dimensional Dynamic Problem. Part I,” Comput. Methods Appl. Mech. Eng., 49, pp. 55–70. [CrossRef]
Ibrahimbegović, A., 1995, “On Finite Element Implementation of Geometrically Nonlinear Reissner's Beam Theory: Three-Dimensional Curved Beam Elements,” Comput. Methods Appl. Mech. Eng., 122, pp. 11–26. [CrossRef]
Shabana, A., 2014, Dynamics of Multibody Systems, (4th ed., Cambridge University Press, New York.
Schwertassek, R. and Wallrapp, O., 1999, Dynamik flexibler Mehrkörpersysteme, Vieweg, Braunschweig/Wiesbaden.
Lugris, U., Naya, M., Luaces, A., and Cuadrado, J., 2009, “Efficient Calculation of the Inertia Terms in Floating Frame of Reference Formulations for Flexible Multibody Dynamics,” Proc. Inst. Mech. Eng., Part K: J. Multibody Dyn., 223, pp. 147–157.
Pfister, J., 2006, “Elastic Multibody Systems With Frictional Contacts,” Ph.D. dissertation, Universität Stuttgart, Stuttgart, Germany.
Yoo, W. S., and Haug, E. J., 1986, “Dynamics of Articulated Structures. Part I. Theory,” J. Struct. Mech., 14(1), pp. 105–126. [CrossRef]
Diebel, J., 2006, “Representing Attitude: Euler Angles, Quaternions, and Rotation Vectors,” Ph.D. dissertation, Stanford University, Palo Alto, CA.
Schwab, A., and Meijaard, J., 2006, “How to Draw Euler Angles and Utilize Euler Parameters,” Proceedings of the IDETC/CIE 2006, ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Philadelphia, PA, Sept. 10–13, Paper No. DETC2006-99307, pp. 1–7.
Serban, R., and Haug, E., 1998, “Analytical Derivatives for Multibody System Analyses,” Mech. Struct. Mach., 26(2), pp. 145–173. [CrossRef]
Schaffer, A., 2005, “On the Adjoint Formulation of Design Sensitivity Analysis of Multibody Dynamics,” Ph.D. dissertation, University of Iowa, Iowa City, IA.
Roberson, R., 1985, “On the Practical Use of Euler-Rodriguez Parameters in Multibody System Dynamic Simulation,” Ingenieur-Archiv, Springer-Verlag, 55(2), pp. 114–123. [CrossRef]
Shoemake, K., 1985, “Animating Rotation With Quaternion Curves,” Proceedings of SIGGRAPH 85, New York, NY, pp. 245–254.
Soo Kim, M., and Won Nam, K., 1995, “Interpolating Solid Orientations With Circular Blending Quaternion Curves,” Comput.-Aided Des., 27, pp. 385–398. [CrossRef]
Betsch, P., and Steinmann, P., 2002, “Frame-Indifferent Beam Finite Elements Based Upon the Geometrically Exact Beam Theory,” Int. J. Numer. Methods Eng., 54, pp. 1775–1788. [CrossRef]
Likins, P., 1976, “Modal Method for Analysis of Free Rotations of Spacecraft,” AIAA J., 5(7), pp. 1304–1308. [CrossRef]
Shabana, A., 1985, “Automated Analysis of Constrained Inertia-Variant Flexible Systems,” ASME J. Vib., Acoust., Stress, Reliab. Des., 107(4), pp. 431–440. [CrossRef]
Amirouche, F., 2006, Fundamentals of Multibody Dynamics: Theory and Applications, Birkhäuser, Boston, MA.
Pfeiffer, F., 2008, Mechanical System Dynamics (Lecture Notes in Applied and Computational Mechanics), Vol. 40, Springer-Verlag, Berlin/Heidelberg, Germany.
Ziegler, F., 1998, Mechanics of Solids and Fluids, 2nd ed., Springer, New York.
Parkus, H., 1995, Mechanik der festen Körper, 2nd ed., Springer, Vienna, Austria.
Pfeiffer, F., 1992, Einführung in die Dynamik, 2nd ed., Teubner, Stuttgart, Germany.

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Vector definitions of a flexible body in the FFRF

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