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RESEARCH PAPERS

A Practical Approach for the Linearization of the Constrained Multibody Dynamics Equations

[+] Author and Article Information
Dan Negrut1

Department of Mechanical Engineering, The University of Wisconsin, Madison, WI-53706negrut@wisc.edu

Jose L. Ortiz

 MSC.Software, Ann Arbor, Michigan 48105jose.ortiz@mscsoftware.com

1

Address all correspondence to this author.

J. Comput. Nonlinear Dynam 1(3), 230-239 (Feb 25, 2006) (10 pages) doi:10.1115/1.2198876 History: Received November 08, 2005; Revised February 25, 2006

The paper presents an approach to linearize the set of index 3 nonlinear differential algebraic equations that govern the dynamics of constrained mechanical systems. The proposed method handles heterogeneous systems that might contain flexible bodies, friction, control elements (user-defined differential equations), and nonholonomic constraints. Analytically equivalent to a state-space formulation of the system dynamics in Lagrangian coordinates, the proposed method augments the governing equations and then computes a set of sensitivities that provide the linearization of interest. The attributes associated with the method are the ability to handle large heterogeneous systems, ability to linearize the system in terms of arbitrary user-defined coordinates, and straightforward implementation. The proposed approach has been released in the 2005 version of the MSC.ADAMS/Solver(C++) and compares favorably with a reference method previously available. The approach was also validated against MSC.NASTRAN and experimental results.

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Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A nonuniform helicopter blade

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Figure 2

MSC.ADAMS model of the nonuniform helicopter blade

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Figure 3

Second flapping mode for 0rpm

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Figure 4

A washing machine example

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Figure 5

All terrain vehicle (ATV)

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Figure 6

A Rotor-stator model

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Figure 7

Eigenvalues for speeds 0to1Hz. Global (a) and local (b) reference frames.

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Figure 8

Rotor-stator model setup for numerical experiment

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Figure 9

FFT plots of signals (a) DX(2,4), (b) AY(4,1), and (c) DX(4,1,1)

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