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RESEARCH PAPERS

Dynamics of Large Scale Mechanical Models Using Multilevel Substructuring

[+] Author and Article Information
C. Papalukopoulos

Department of Mechanical Engineering, Aristotle University, 54 124 Thessaloniki, Greece

S. Natsiavas

Department of Mechanical Engineering, Aristotle University, 54 124 Thessaloniki, Greecenatsiava@auth.gr

J. Comput. Nonlinear Dynam 2(1), 40-51 (Jul 04, 2006) (12 pages) doi:10.1115/1.2389043 History: Received February 01, 2006; Revised July 04, 2006

An appropriate substructuring methodology is applied in order to study the dynamic response of very large scale mechanical systems. The emphasis is put on enabling a systematic study of dynamical systems with nonlinear characteristics, but the method is equally applicable to systems possessing linear properties. The accuracy and effectiveness of the methodology are illustrated by numerical results obtained for example vehicle models, having a total number of degrees of freedom lying in the order of a million or even bigger. First, the equations of motion of each component are set up by applying the finite element method. The order of the resulting models is so high that the classical substructuring methodologies become numerically ineffective or practically impossible to apply. However, the method developed overcomes these difficulties by imposing a further, multilevel substructuring of each component, based on the sparsity pattern of the stiffness matrix. In this way, the number of the equations of motion of the complete system is substantially reduced. Consequently, the numerical results presented demonstrate that besides the direct computational savings, this reduction in the dimensions enables the application of numerical codes, which capture response characteristics of dynamical systems sufficiently accurate up to a prespecified level of forcing frequencies. The study concludes by investigating biodynamic response of passenger-seat subsystem models coupled with complex mechanical models of ground vehicles resulting from deterministic or random road excitation.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Finite element model of the vehicle body

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Figure 2

A five degree of freedom passenger-seat model

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Figure 3

Distribution of nonzero elements in the stiffness matrix of the vehicle body after reordering

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Figure 4

Tree topology graph of the vehicle body stiffness matrix after reordering

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Figure 5

(a) Building block of tree structure and (b) corresponding structural components

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Figure 6

(a) Natural frequencies of car model A up to 500Hz. (b) Error in the natural frequencies obtained by ACMS and the method developed relative to the natural frequencies obtained by the Lanczos method.

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Figure 7

Accuracy comparison of method developed with MSC.Nastran methods ACMS and Lanczos: (a) point inertance and (b) transfer inertance function of car model A

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Figure 8

(a) Point and (b) transfer inertance function of car model A by requiring response accuracy up to 100, 500, and 900Hz

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Figure 9

Frequency-response diagrams for linearized models: (a) vertical acceleration at selected points of the vehicle body and the driver; (b) acceleration transmissibility function with respect to the ground; (c) acceleration transmissibility function with respect to the base of the driver seat; and (d) transmissibility ratios for the acceleration at the passengers’ heads

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Figure 10

Vertical acceleration: (a) at the front left wheel and (b) at the driver’s pelvis position, during passage over a half-sine road bump or pothole

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Figure 11

Vertical acceleration: (a) at the front left wheel and (b) at the driver’s pelvis position, during passage over a half-sine road bump of a nonlinear and a linearized vehicle model

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Figure 12

Reduced ride comfort boundaries recommended by ISO 2631

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Figure 13

Power spectral density for the acceleration of (a) the front left wheel and (b) the driver’s pelvis position

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Figure 14

Cumulative root-mean-square value of the acceleration of (a) the front left wheel and (b) the driver’s pelvis position

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