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Research Papers

Optimization of a Two Degree of Freedom System Acting as a Dynamic Vibration Absorber

[+] Author and Article Information
M. Febbo

Institute of Applied Mechanics (IMA), Department of Physics, Universidad Nacional del Sur, Avenida Alem 1253, 8000 Bahía Blanca, Argentina

S. A. Vera1

Institute of Applied Mechanics (IMA), Department of Physics, Universidad Nacional del Sur, Avenida Alem 1253, 8000 Bahía Blanca, Argentinasvera@uns.edu.ar

1

Corresponding author.

J. Vib. Acoust 130(1), 011013 (Jan 23, 2008) (11 pages) doi:10.1115/1.2827368 History: Received October 04, 2006; Revised November 09, 2007; Published January 23, 2008

This paper deals with the problem of finding the optimal stiffnesses and damping coefficients of a two degree of freedom (2DOF) system acting as a dynamic vibration absorber (DVA) on a beam structure. In this sense, a heuristic criterion for the optimization problem will be developed to contemplate this particular type of DVA. Accordingly, it is planned to minimize the amplitude of vibration in predetermined points of the main structure. Two optimizations will be proposed for two DVAs of 1DOF to compare their performances with the optimized 2DOF system. A simulated annealing algorithm is used to obtain the DVA’s optimal parameters for minimum amplitude in a given point of the beam. The best configuration depends on the location of the absorbers on the beam and, for a fixed location, on the distribution of the stiffness constants.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 4

Syntonization procedure. The Points A and B do posseses equal amplitude when c1=c2=0 with the situation c1=c2→∞.

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Figure 5

Results of the first optimization stage (f1) for a 2DOF DVA on a beam

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Figure 6

Frequency response of an undamped beam with a 1DOF DVA; the amplitude is shown for frequencies near the first resonance of the beam

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Figure 7

Displacement amplitude of a beam with two 1DOF DVAs and a 2DOF DVA for frequencies near its first resonance. DVA location: x1=0.75L, x2=0.55L, observation point xa=0.55L.

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Figure 8

Same as Fig. 7 for frequencies near the second resonance of the beam

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Figure 3

Flow diagram for the implementation of the simulated annealing algorithm

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Figure 2

(a) Uncoupled 2DOF DVA (two 1DOF DVAs) and (b) coupled 2DOF DVA

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Figure 9

Displacement amplitude, which shows a comparison between different configurations adopted by interchanging the location of the elastic constants of a 2DOF DVA

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Figure 10

Same as Fig. 9 for frequencies near the second resonance of the beam

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Figure 11

Displacement amplitude of a simply supported beam with two 1DOF DVAs and a 2DOF DVA for frequencies near the first resonance. DVA location: x1=0.1L, x2=0.3L, observation point xa=0.3L.

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Figure 1

Schematic representation of the MDOF DVA attached to a beam

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Figure 12

Same as Fig. 1 for frequencies near the second resonance of the beam

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Figure 13

Effect of the location on the effectiveness of a 2DOF DVA to reduce the vibration amplitude at xa=0.3L. Optimization results near the first resonant frequency of the bare beam.

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Figure 14

Effect of the location on the effectiveness of a 2DOF DVA to reduce the vibration amplitude at xa=0.3L. Optimization results near the second resonant frequency.

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Figure 15

Comparison between a 2DOF DVA and two 1DOF DVAs in the reduction of the displacement amplitude of a beam near its first resonance. The two 1DOFs were optimized using the traditional (Den Hartog) and SM optimization scheme.

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Figure 16

Same as Fig. 1 for frequencies near the second resonance of the beam

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