Numerical Stability Analysis of a Forced Two-D.O.F. Oscillator With Bilinear Damping

[+] Author and Article Information
Zsolt Szabó

Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, H-1521, Hungaryszazs@mm.bme.hu

Attila Lukács

Department of Mechatronics, Optics, and Instrumentation Technology, Budapest University of Technology and Economics, Budapest, H-1521, Hungarylukacs@mom.bme.hu

J. Comput. Nonlinear Dynam 2(3), 211-217 (Mar 09, 2007) (7 pages) doi:10.1115/1.2727487 History: Received October 13, 2005; Revised March 09, 2007

The current paper investigates the nonlinear stationary oscillations of a quarter vehicle model with two degrees of freedom subjected to a vertical road excitation. The damping of the wheel suspension has a bilinear characteristic, so that the damping strength is larger during compression than during restitution of the damper. For the optimization of the damping behavior the peak-to-peak swings have to be as small as possible. The unevenness of the road was approximated by filtered white noise which was modelled numerically using pseudorandom sequences. The first order form of the governing equations was transformed to hyperspherical representation. The stability was determined according to the largest Liapunov exponents obtained from the numerical simulation. For a chosen parameter range stability charts were constructed both in the stochastic and harmonic case (for comparison).

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Mechanical model

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Figure 2

Damping characteristic

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Figure 4

Spectrum of white noise

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Figure 5

Time plot of Zτ at μ=1

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Figure 6

Spectral density of Zτ at μ=1

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Figure 7

Contours of the largest Liapunov exponent at λ=0(a) for harmonic excitation and (b) for stochastic excitation

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Figure 8

Distribution of Rn (103 iterations)

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Figure 9

Distribution of Rn (106 iterations)

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Figure 10

Distribution of Un (105 iterations)

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Figure 11

Distribution of Vn (105 iterations)



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