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Research Papers

A Generalized Component Mode Synthesis Approach for Flexible Multibody Systems With a Constant Mass Matrix

[+] Author and Article Information
Astrid Pechstein

Institute of Technical Mechanics,
Johannes Kepler University Linz,
Altenbergerstraße 69,
4040 Linz, Austria
e-mail: astrid.pechstein@jku.at

Daniel Reischl

e-mail: daniel.reischl@lcm.at

Johannes Gerstmayr

e-mail: johannes.gerstmayr@lcm.at
Linz Center of Mechatronics GmbH,
Altenbergerstraße 69,
4040 Linz, Austria

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 5, 2012; final manuscript received June 4, 2012; published online August 31, 2012. Assoc. Editor: Arend L. Schwab.

J. Comput. Nonlinear Dynam 8(1), 011019 (Aug 31, 2012) (10 pages) Paper No: CND-12-1025; doi: 10.1115/1.4007191 History: Received February 05, 2012; Revised June 04, 2012

A standard technique to reduce the system size of flexible multibody systems is the component mode synthesis. Selected mode shapes are used to approximate the flexible deformation of each single body numerically. Conventionally, the (small) flexible deformation is added relatively to a body-local reference frame which results in the floating frame of reference formulation (FFRF). The coupling between large rigid body motion and small relative deformation is nonlinear, which leads to computationally expensive nonconstant mass matrices and quadratic velocity vectors. In the present work, the total (absolute) displacements are directly approximated by means of global (inertial) mode shapes, without a splitting into rigid body motion and superimposed flexible deformation. As the main advantage of the proposed method, the mass matrix is constant, the quadratic velocity vector vanishes, and the stiffness matrix is a co-rotated constant matrix. Numerical experiments show the equivalence of the proposed method to the FFRF approach.

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References

Hurty, W. C., 1965, “Dynamic Analysis of Structural Systems Using Component Modes,” AIAA J., 3(4), pp. 678–685. [CrossRef]
Craig, R. R., Jr., and Bampton, M. C. C., 1968, “Coupling of Substructures for Dynamic Analyses,” AIAA J., 6(7), pp. 1313–1319. [CrossRef]
Lehner, M., and Eberhard, P., 2007, “A Two-Step Approach for Model Reduction in Flexible Multibody Dynamics,” Multibody Syst. Dyn., 17(2–3), pp. 157–176. [CrossRef]
Fehr, J., and Eberhard, P., 2010, “Error-Controlled Model Reduction in Flexible Multibody Dynamics,” ASME J. Comput. Nonlinear Dyn., 5(3), p. 031005. [CrossRef]
Shabana, A. A., 2005, Dynamics of Multibody Systems, 3rd ed., Cambridge University Press, New York.
Zienkiewicz, O. Z., and Taylor, R. L., 2000, The Finite Element Method. Volume 1: The Basis, 5th ed., Butterworth-Heinemann, Oxford, UK.
Gerstmayr, J., and Schoeberl, J., 2006, “A 3D Finite Element Method for Flexible Multibody Systems,” Multibody Syst. Dyn., 15(4), pp. 309–324. [CrossRef]
Wempner, G. A., 1969, “Finite Elements, Finite Rotations and Small Strains of Flexible Shells,” Int. J. Solids Struct., 5, pp. 117–153. [CrossRef]
Belytschko, T., and Hsieh, B. J., 1973, “Non-Linear Transient Finite Element Analysis With Convected Coordinates,” Int. J. Numer. Eng., 7, pp. 255–271. [CrossRef]
Gerstmayr, J., 2003, “Strain Tensors in the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation,” Int. J. Nonlinear Dyn., 34, pp. 133–145. [CrossRef]
Gerstmayr, J., and Ambrósio, J. A. C., 2008, “Component Mode Synthesis With Constant Mass and Stiffness Matrices Applied to Flexible Multibody Systems,” Int. J. Numer. Eng., 73, pp. 1518–1546. [CrossRef]
de Jalón, J. G., and Bayo, E., 1994, Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge, Springer-Verlag, New York.
Gerstmayr, J., and Pechstein, A., 2011, “A Generalized Component Mode Synthesis Approach for Multibody System Dynamics Leading to Constant Mass and stiffness Matrices,” Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2011.
Pechstein, A., Reischl, D., and Gerstmayr, J., 2011, “A Generalized Component Mode Synthesis Approach Leading to Constant Mass and Stiffness Matrices,” Proceedings of the Multibody Dynamics 2011, ECCOMAS Thematic Conference.
Humer, A., Reischl, D., and Gerstmayr, J., 2012, “Investigations on the Application of Energy-Momentum Schemes to Modally-Reduced Multibody Systems,” Proceedings of the 2nd Joint International Conference on Multibody System Dynamics.
Nikravesh, P. E., 1988, Computer-Aided Analysis of Mechanical Systems, Prentice-Hall, Englewood Cliffs, NJ.
Gerstmayr, J., 2007, “Nonlinear Constraints in the Absolute Coordinate Formulation,” Acta Mech., 192(1), pp. 191–211. [CrossRef]
Betsch, P., 2005, “The Discrete Null Space Method for the Energy Consistent Integration of Constrained Mechanical Systems. Part I: Holonomic Constraints,” Comput. Methods Appl. Mech. Eng., 194(50–52), pp. 5159–5190. [CrossRef]
Eberhard, P., Fehr, J., and Mathuni, S., 2009, “Influence of Model Reduction Techniques on the Impact Force Calculation of Two Flexible Bodies,” PAMM, Proc. Appl. Math. Mech., 9, pp. 111–112. [CrossRef]
Pechstein, A., Reischl, D., and Gerstmayr, J., 2011, “The Applicability of the Floating-Frame Based Component Mode Synthesis to High-Speed Rotors,” Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE 2011.

Figures

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Fig. 1

Representation of the total deformation in the floating frame

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Fig. 2

Finite element discretization of piston engine

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Fig. 3

Bearing of the crankshaft with 12 nodes and average center position

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Fig. 4

Speeding-up rotor: angular velocity ω of crankshaft and vertical position of piston

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Fig. 5

Initial angular velocity: angular velocity ω of crankshaft and vertical position of piston

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Fig. 6

Speeding-up rotor: midspan deflection of the connecting rod

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Fig. 7

Initial angular velocity: midspan deflection of the connecting rod

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