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TECHNICAL PAPERS

Pre-tensioned Layer Damping as a New Approach for Vibration Control of Elastic Beams

[+] Author and Article Information
Mostafa Abd-Elwahab

Department of Modelling and Simulation in Mechanics, German University in Cairo, Cairo, Egyptmostafa96@yahoo.com

Hany A. Sherif

Department of Mechanical Engineering, Military Technical College, Cairo, Egypthasherif@lycos.com

J. Vib. Acoust 128(3), 338-346 (Jul 25, 2005) (9 pages) doi:10.1115/1.2166855 History: Received July 25, 2004; Revised July 25, 2005

A new approach for suppression and control of mechanical vibration in elastic beams undergoing cyclic motion is presented. The proposed model is based on the idea of generating axial uniform damping forces on the surface of the vibrating structure. Equation of motion and expression for system damping of the new model are derived, where the effectiveness of this model for reducing lateral vibration of a base excited beam is theoretically determined at different force levels. The analysis included the first five mode shapes, and the performance at different boundary conditions is also discussed. The theoretical model is verified experimentally, and the technique used to generate the superficial forces is explained. A comparison between theoretical and experimental results is shown. It is found that the higher the generated superficial force value, the higher the attenuation percentage. The new model is characterized by its simplicity, which enhances its reliability and reduces its cost, as it provides the desired results with higher reliability and reasonable cost, compared with other approaches of active and intelligent structural designs.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Plain beam undergoing flexural vibration. (b) Forces and moments acting on element of the beam. (c) The beam under the application of the surface forces. (d) The beam sandwiched between two thin layers of a material with a loss factor ηd. (e) The beam sandwiched between two thin layers that are stretched to certain elastic extent generating a surface force F0.

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Figure 2

Frequency response function of a fixed-free beam/PTLD system against strain and exciting frequency at the 1st mode

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Figure 3

(a) Damping loss factor of a fixed-free beam/PTLD system at 1st resonance. (b) Damping loss factor of a fixed-free beam/PTLD system at 2nd resonance. (c) Damping loss factor of a fixed-free beam/PTLD system at 3rd resonance. (d) Damping loss factor of a fixed-free beam/PTLD system at 4th resonance. (e) Damping loss factor of a fixed-free beam/PTLD system at 5th resonance. (f) Damping loss factor of a fixed-free beam/PTLD system for the first five vibration modes at Ed∕E=0.01.

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Figure 4

Frequency response function of a fixed-free beam/PTLD system against strain and exciting frequency at the 2nd mode

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Figure 5

Construction of a fixed-free beam/PTLD system

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Figure 6

(a) Attenuation percentage of a fixed-free beam/PTLD system at 1st resonance (ε0=2000με). (b) Attenuation percentage of a fixed-free beam/PTLD system at 1st resonance (ε0=8000με). (c) Attenuation percentage of a fixed-free beam/PTLD system at 1st resonance (ε0=16000με).

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Figure 7

Dimensions of the plain beam used in the experiments in millimeters

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Figure 8

Sample plain beam fixed into the push rod of the shaker via a metallic base

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Figure 9

Schematic drawing of test setup and instrumentation

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Figure 10

The transfer function of the sample cantilevered plain beam

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Figure 11

The first two modes of vibration of the sample cantilevered plain beam

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Figure 12

(a) Comparison between the transfer functions of the beam/PTLD system at different superficial forces (ε0=0με). (b) Comparison between the transfer functions of the beam/PTLD system at different superficial forces (ε0=2000με). (c) Comparison between the transfer functions of the beam/PTLD system at different superficial forces (ε0=8000με). (d) Comparison between the transfer functions of the beam/PTLD system at different superficial forces (ε0=16000με).

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