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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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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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