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Research Papers

Optimal Vibration Suppression of Timoshenko Beam With Tuned-Mass-Damper Using Finite Element Method

[+] Author and Article Information
Fan Yang, Ramin Sedaghati

Department of Mechanical and Industrial Engineering, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, QC, H3G 1M8, Canada

Ebrahim Esmailzadeh1

Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1H 7K4, Canadaezadeh@uoit.ca

1

Corresponding author.

J. Vib. Acoust 131(3), 031006 (Apr 22, 2009) (8 pages) doi:10.1115/1.3085890 History: Received April 13, 2008; Revised October 16, 2008; Published April 22, 2009

In this study, the structural vibration analysis and design of a Timoshenko beam with the attached tuned-mass-damper (TMD) under the harmonic and random excitations are presented using the finite element technique. A design optimization methodology has been developed in which the derived finite element formulation of a Timoshenko beam with the attached TMD has been combined with the sequential quadratic programming optimization algorithm to find the optimal design variables of TMD in order to suppress the vibration effectively. The validity of the developed optimal TMD system design strategy has been verified through illustrative examples, in which the structural response comparisons and the sensitivity analysis of the design parameters have been presented. The results were compared with those available in literatures and very close agreement was achieved.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 8

Magnitude (transfer function) of the beam midspan transverse frequency response with respect to the optimal TMD parameters’ off-tuning listed in Table 4 under harmonic excitation. Solid line: optimal TMD, dashed and dotted lines: TMD with −20% and +20% deviations from optimal damping factor, and dashed-dotted and solid (light) lines TMD with −20% and +20% deviations from optimal frequency ratio.

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Figure 9

Sensitivity analyses for optimal TMD’s parameters’ off-tunings under harmonic loading. Solid and dotted lines represent the sensitivity for damping factor and frequency ratio, respectively.

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Figure 5

Sensitivity analyses for optimal TMD’s parameters’ off-tunings under random excitation (Case (2)). Solid and dotted lines represent the sensitivity for damping factor and frequency ratio, respectively.

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Figure 4

PSD of beam midspan transverse frequency response with respect to the optimal TMD parameters’ off-tuning listed in Table 3 for Case (2). Solid line: optimal TMD, dashed and dotted lines: TMD with −20% and +20% deviations from optimal damping factor, and dashed-dotted and solid (light) lines TMD with −20% and +20% deviations from optimal frequency ratio.

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Figure 3

PSD of the beam’s midspan transverse frequency response. Solid, dashed, and dotted lines represent the uncontrolled structure, structure with optimal TMD Case (1), and structure with optimal TMD Case (2) listed in Table 3, respectively.

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Figure 2

Optimal TMD parameters and value of objective function versus input mass ratio (μ): (a) optimal frequency ratio (fTMD), (b) optimal damping factor (ξTMD), and (c) value of objective function. Solid, dashed, and dotted lines represent Cases (1), (2), and (3), respectively. Note that the dotted line coincides with that of Eq. 19.

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Figure 1

Timoshenko beam with attached TMD system

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Figure 6

Optimal TMD parameters and value of objective function versus input mass ratio (μ): (a) optimal frequency ratio (fTMD), (b) optimal damping factor (ξTMD), and (c) value of objective function. Solid, dashed, and dotted lines represent Cases (1), (2), and (3), respectively. Note that in (a) and (b) the solid and dashed lines coincide with each other and dotted line coincides with that of Eq. 21.

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Figure 7

Magnitude (transfer function) of the beam’s midspan transverse frequency response (w) under harmonic excitation. Solid and dashed lines represent the response for uncontrolled structure and structure with optimal TMD (Case (2)), respectively.

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