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Research Papers

Optimal Parameters and Characteristics of a Three Degree of Freedom Dynamic Vibration Absorber

[+] Author and Article Information
Mariano Febbo

Instituto de Física del Sur (IFISUR) and CONICET Departmento de Física,  Universidad Nacional del Sur, Bahía Blanca 8000, Argentinamfebbo@uns.edu.ar

J. Vib. Acoust 134(2), 021010 (Jan 18, 2012) (11 pages) doi:10.1115/1.4004667 History: Received April 05, 2010; Revised April 13, 2011; Published January 18, 2012; Online January 18, 2012

The present study is devoted to the determination of the optimal parameters and characteristics of a three degree of freedom dynamic vibration absorber (3 DOF DVA) for the vibration reduction of a plate at a given point. The optimization scheme uses simulated annealing and constrained simulated annealing, which is capable of optimizing systems with a set of constraints. Comparisons between a 3 DOF DVA and multiple (5) 1 DOF DVAs show a better performance of the former for vibration reduction. Regarding the characteristics of the optimal 3 DOF DVA, numerical tests reveal that the absorber is robust under variations of the observation point and for 10% variations of its mass, stiffness and damping. From the analysis of parameter changes of the plate, it is found that the optimal 3 DOF DVA is almost insensitive to a mass change, and sensitive to a change of Young’s modulus for low frequencies. In this case, a decrease in Young’s modulus causes a decrease in its effectiveness, and an increase improves it. The study of the effect of the 3 DOF DVA location on its effectiveness reveals that the requirements of closeness of the absorber to an antinode of the bare primary structure and to the observation point improve its performance. Additionally, for a rotational mode of the 3-DOF DVA about some axis, the effectiveness of the absorber at a given frequency can be notably increased if it is located at a position of the primary system with an in-phase or out-of- phase motion of the attachment points according to the rotational-mode characteristics of the 3-DOF DVA at this frequency.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 2

Flow diagram for the implementation of the constrained simulated annealing algorithm CSA (see text for initial values of parameters)

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Figure 3

Localization of five 1 DOF systems acting as DVAs for comparison with a 3 DOF DVA attached to the plate for vibration reduction

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Figure 4

First (a), second (b) and third (c) normal mode amplitudes of a totally simply supported (SSSS) rectangular plate; the four different selected locations [1-4] of the 3 DOF DVA mounted on the plate are also shown (see numerical values in text)

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Figure 1

(a) Plate with a 3 DOF system attached to it. (b) Nomenclature for the coordinates selected to describe the motion of the 3 DOF system

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Figure 5

(a) Amplitude of the displacement versus excitation frequency of a bare plate (dotted line), a plate with an undamped 3-DOF system attached to it (solid line), and a plate with a heavily-damped 3-DOF system attached to it (dashed dotted line). (b) Phase of the displacement of the compound system at the attachment points of the optimal 3 DOF DVA to the plate versus excitation frequency for case 1 (see text)

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Figure 6

(a) Amplitude of the displacement versus excitation frequency of a simply supported rectangular plate with five 1 DOF DVAs and one 3 DOF DVA. The five 1-DOF DVAs are located as shown in Fig. 4, and they change their positions in the same manner as the 3-DOF DVA. The center of mass of the 3 DOF DVA is located in (a): (xe , ye ) = (1.0, 0.5); (b) (xe , ye ) = (0.5, 0.5); (c) (xe , ye ) = (0.5, 0.75) and (d) (xe , ye ) = (1.0, 0.75). In the inset, “bare” indicates for the amplitude of the plate without attached systems.

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Figure 7

Frequency response for a variation of the observation point for an optimal 3 DOF DVA attached to a SSSS rectangular plate. Frequencies near the first (a), second (b) and third (c) resonance of the plate. The curves are all normalized with respect to the amplitude at resonance (of the bare plate) for each frequency and observation point (see text for constants).

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Figure 8

(a) Robustness of the optimal 3 DOF DVA attached to a SSSS rectangular plate when the mass or Young’s modulus (E) of the plate is decreased or increased by 10% compared with the original situation (original). The curves are all normalized with respect to the maximum amplitude of the first mode of the bare plate for each different case. (b) idem (a) for 10% variations of the mass, stiffness and damping constants of the optimal 3-DOF absorber.

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Figure 9

Amplitude of the displacement versus excitation frequency of a SSSS rectangular plate with different optimal 3 DOF DVAs to compare their effectiveness under variations of their locations. The DVA is located in (a) three different positions on the middle line parallel to the x axis, (b) three different positions on the main diagonal and (c) other three different positions on the middle line parallel to the y axis (see text for numerical values).

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Figure 10

Phase of the displacement of the compound system at the attachment points of the optimal 3 DOF DVA to the plate versus excitation frequency. The DVA is located in (a) 1x), in (b) 2x) and in (c) 3x) (see text). Dashed dotted lines indicates the resonant frequencies of the compound system in each case.

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