Stability Analysis of Complex Multibody Systems

[+] Author and Article Information
Olivier A. Bauchau, Jielong Wang

Daniel Guggenheim School of Aerospace Engineering,  Georgia Institute of Technology, 270 Ferst Dr., Atlanta, GA 30332

J. Comput. Nonlinear Dynam 1(1), 71-80 (May 01, 2005) (10 pages) doi:10.1115/1.1944733 History: Revised May 01, 2005

The linearized stability analysis of dynamical systems modeled using finite element-based multibody formulations is addressed in this paper. The use of classical methods for stability analysis of these systems, such as the characteristic exponent method or Floquet theory, results in computationally prohibitive costs. Since comprehensive multibody models are “virtual prototypes” of actual systems, the applicability to numerical models of the stability analysis tools that are used in experimental settings is investigated in this work. Various experimental tools for stability analysis are reviewed. It is proved that Prony’s method, generally regarded as a curve-fitting method, is equivalent, and sometimes identical, to Floquet theory and to the partial Floquet method. This observation gives Prony’s method a sound theoretical footing, and considerably improves the robustness of its predictions when applied to comprehensive models of complex multibody systems. Numerical and experimental applications are presented to demonstrate the efficiency of the proposed procedure.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Sampling the output of a periodic system

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Figure 2

Frequencies and damping of the cantilevered wing: Case 1: dashed line (◇); Case 2: solid line (◻)

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Figure 3

Normalized singular values of matrix H0 for far field velocity U=500ft∕s. Case 1: (◇); Case 2: (◻). The horizontal lines represent the user-defined tolerances: εrank=10−3 and εnoise=10−5.

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Figure 4

Schematic of the wind turbine problem

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Figure 5

Damping in the wind turbine problem as a function of rotor angular speed: Analytical solution (◻); all three dampers active (▿); two dampers active only (◇); single damper active (▵)

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Figure 6

Multibody model of the soft in-plane tilt rotor system

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Figure 7

Multibody model of the soft in-plane tilt rotor system: detail of the hub

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Figure 8

Wing beamwise damping as a function of rotor collective angle; off-downstop configuration, 550rpm rotor angular speed, 25kn airspeed. Experimental measurements: solid line; case 1: dotted line; case 2: dashed-dotted line; case 3: dashed line.




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