Varying the Stiffness of a Beam-Like Neutralizer Under Fuzzy Logic Control

[+] Author and Article Information
M. R. F. Kidner, M. J. Brennan

Institute of Sound and Vibration Research, University of Southampton, Southampton, Hampshire, UK, SO17 1BJ

J. Vib. Acoust 124(1), 90-99 (Jul 01, 2001) (10 pages) doi:10.1115/1.1423634 History: Received May 01, 2000; Revised July 01, 2001
Copyright © 2002 by ASME
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Co-ordinates for the separation of the half beams: (a) pinned (b) clamped. (b) also shows a comparison of the exact (dotted line) and approximate (solid line) mode shape of 1st natural frequency of a clamped-sliding beam. This is equivalent to half the clamped-clamped beam.
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Possible tunable beam-like neutralizer mechanisms. (a) parallel (b) triangular (c) pinned (d) clamped
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The four beam-like neutralizers used for experiments (a) parallel (b) triangular (c) pinned (d) clamped
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Experimental set-up used to measure the variation of tuned frequency with beam separation
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(a) Typical accelerance of the beam like neutralizer. The dip indicates the tuned frequency, the variance of which with beam separation is shown in Fig. 5(b). Comparison of dynamic stiffness model results, (solid line), linear approximations, (dotted line) and experimental results, (crosses) for the variation in tuned frequency ωupperωlower as a function of the ratio of separation, h0 to the thickness d of the beams
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The tunable beam-like neutralizer
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Experimental results showing the host structure velocity with and without control (a) response of the host structure with a passive neutralizer attached (b) structure response with an active neutralizer under fuzzy logic control attached (c) structure response with an active neutralizer under proportional control attached. All responses are normalized to the level of the host structure with a tuned neutralizer attached.
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Block diagram of experimental set-up used to measure the tunable neutralizers response. The section enclosed in the dotted line indicates the objects that are directly connected.
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(a) Equivalent lumped parameter model used for the numerical simulations (b) corresponding beam-like neutralizer. Varying h0 is equivalent to varying k.
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The normalized dot product of the neutralizer and host structure velocity plotted against the normalized tuning frequency of the neutralizer. ξ=0.001: dash-dot line, ξ=0.01: dotted line, ξ=0.1: dashed line.
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The fuzzy sets which map a dot product estimate, equivalent to the cosine of the phase between the structure and neutralizer mass, to a number of stepper motor steps and hence a change in neutralizer stiffness
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Equivalent linear output fuzzy sets for tuning control. 19 sets are required to have the same resolution for small errors as the 7 nonlinear sets shown in Fig. 9.
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Frequency of excitation signal
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Flow chart of the control algorithm
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Simulation results for tuning control. Host structure velocity response to the excitation shown in Fig. 11 (a) velocity of the host structure with a passive neutralizer tuned to 142 Hz attached (b) structure velocity with an active neutralizer under fuzzy logic control attached (c) structure response with an active neutralizer under proportional control attached. All responses are normalized to the level of the host structure with a tuned neutralizer attached.



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