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Research Papers

Wave Vibration Control of L-Shaped and Portal Planar Frames

[+] Author and Article Information
C. Mei

Department of Mechanical Engineering,
The University of Michigan–Dearborn,
4901 Evergreen Road, Dearborn, MI 48128
e-mail: cmei@umich.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 27, 2012; final manuscript received November 28, 2012; published online June 18, 2013. Assoc. Editor: Paul C.-P. Chao.

J. Vib. Acoust 135(5), 051022 (Jun 18, 2013) (16 pages) Paper No: VIB-12-1162; doi: 10.1115/1.4023831 History: Received May 27, 2012; Revised November 28, 2012

This paper discusses the control of coupled bending and axial vibrations in L-shaped and portal planar frame structures. The controller is designed based on a wave standpoint, in which vibrations are described as waves traveling along uniform structural waveguides, and being reflected and transmitted at structural discontinuities. Active discontinuities are created using active control forces/moments both along structural elements and at structural joints to control vibration waves. The classical Euler–Bernoulli as well as the advanced Timoshenko bending theories are applied in modeling and controlling the flexural vibrations in planar frames. The axial vibrations are modeled using the elementary theory as it is typically valid for frequencies up to twice the cutoff frequency of Timoshenko bending waves. Results are compared between the two bending vibration theories. It is concluded that for relatively higher frequencies, typically when the transverse dimensions are not negligible with respect to the wavelength, the effects of rotary inertia and shear distortion must be taken into account for both vibration analysis and control design.

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References

Figures

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Fig. 1

(a) Feedback control system. (b) Wave scattering at a point support.

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Fig. 2

Free body diagram of an L joint in planar motion

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Fig. 3

Waves generated by externally applied point forces and moments

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Fig. 4

Structural element control of an L-beam

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Fig. 5

Joint control of an L-beam

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Fig. 6

Receptance frequency responses of the L-beam subject to point transverse force excitation: Timoshenko (___) and Euler–Bernoulli (...) bending theories

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Fig. 7

Receptance frequency responses of the L-beam subject to point axial force excitation: Timoshenko (___) and Euler–Bernoulli (...) bending theories

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Fig. 8

Receptance frequency responses of the L-beam subject to bending moment excitation: Timoshenko (___) and Euler–Bernoulli (...) bending theories

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Fig. 9

Receptance frequency responses of the L-beam subject to point transverse force excitation: before and after structural element control

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Fig. 10

Receptance frequency responses of the L-beam subject to point longitudinal force excitation: before and after structural element control

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Fig. 11

Receptance frequency responses of the L-beam subject to bending moment excitation: before and after structural element control

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Fig. 12

Receptance frequency responses of the L-beam subject to point transverse force excitation: before and after joint control

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Fig. 13

Receptance frequency responses of the L-beam subject to point longitudinal force excitation: before and after joint control

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Fig. 14

Receptance frequency responses of the L-beam subject to bending moment excitation: before and after joint control

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Fig. 15

Structural element control of a portal frame

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Fig. 16

Joint control of a portal frame

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Fig. 17

Receptance frequency responses of the portal frame subject to point transverse force excitation: Timoshenko (___) and Euler–Bernoulli (...) bending theories

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Fig. 18

Receptance frequency responses of the portal frame subject to point axial force excitation: Timoshenko (___) and Euler–Bernoulli (...) bending theories

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Fig. 19

Receptance frequency responses of the portal frame subject to bending moment excitation: Timoshenko (___) and Euler–Bernoulli (...) bending theories

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Fig. 20

Receptance frequency responses of the portal frame subject to point transverse force excitation: before and after structural element control

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Fig. 21

Receptance frequency responses of the portal frame subject to point longitudinal force excitation: before and after structural element control

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Fig. 22

Receptance frequency responses of the portal frame subject to bending moment excitation: before and after structural element control

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Fig. 23

Receptance frequency responses of the portal frame subject to point transverse force excitation: before and after joint control

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Fig. 24

Receptance frequency responses of the portal frame subject to point longitudinal force excitation: before and after joint control

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Fig. 25

Receptance frequency responses of the portal frame subject to bending moment excitation: before and after joint control

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