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Research Papers

Vibration Suppression in Structures Using Cable Actuators

[+] Author and Article Information
Jimmy Issa

Department of Industrial and Mechanical Engineering, Lebanese American University, P.O. Box 36, ByBlos, Lebanon

Ranjan Mukherjee2

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226mukherji@egr.msu.edu

Steven W. Shaw

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226

The critical buckling load is Tc=mini{Ti}, where Ti>0 and det[ΩkgTi]=0 for all values of i.

It should be noted that the first natural frequency of the cable is approximately fc=574.3rad/s for T=10N and fc=679.5rad/s for T=14N. These are much higher than the natural frequencies of the modes being controlled.

2

Corresponding author.

J. Vib. Acoust 132(3), 031006 (Apr 22, 2010) (8 pages) doi:10.1115/1.4000783 History: Received March 07, 2009; Revised November 02, 2009; Published April 22, 2010; Online April 22, 2010

We investigate the use of cable tension for active vibration control in frame structures. A general formulation for this class of systems is developed using finite elements, which includes the dynamics of the structure and the effects of cable-structure interactions. It is found that the cable tension has two distinct effects on the structure. The first is a parametric effect in which the cable tension changes the stiffness of the structure, and the second is a direct effect that provides an external force on the structure. Based on this model, a general control scheme is developed that uses cable actuation to take advantage of these effects, both separately and together. The control scheme for all cases is based on modal amplitudes, and it applies and releases tension in such a manner that vibration energy is removed from the modes of the structure over a prescribed frequency range that depends on the bandwidth(s) of the actuator(s). The stability of the controlled systems is proven using nonlinear control theory. In addition, a method is developed for determining the optimal placement of cables for parametric stiffness control, which is verified via simulations. Finally, an experimental realization of the direct force control is tested on a frame structure and compared with simulations, demonstrating its effectiveness.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 12

Experimental results: plot of modal amplitudes a1 and a2, and control effort u for the frame structure in Fig. 1

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Figure 11

Experimental setup

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Figure 10

Plot of modal amplitudes q1=(a1,a2)T for the frames in Fig. 9 with the control strategy in Corollary 1

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Figure 9

The frame structure with three sample cable locations

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Figure 8

Plot of modal amplitudes q1=(a1,a2)T and control effort for simulation in Sec. 4

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Figure 7

A frame structure

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Figure 6

Feedback control design for frame structures

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Figure 5

A cable element in space and its projections on the xy and xz planes

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Figure 4

A six-DOF frame element with an axial load

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Figure 3

Vibration amplitudes for the first mode of the beam in Fig. 1

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Figure 2

Control system for the beam in Fig. 1

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Figure 1

A cantilever beam with a cable-supplied end force

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