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Research Papers

Wave Analysis of In-Plane Vibrations of L-Shaped and Portal Planar Frame Structures

[+] Author and Article Information
C. Mei

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

J. Vib. Acoust 134(2), 021011 (Jan 18, 2012) (12 pages) doi:10.1115/1.4005014 History: Received January 13, 2010; Accepted July 12, 2011; Published January 18, 2012; Online January 18, 2012

This paper concerns in-plane vibration analysis of coupled bending and longitudinal vibrations in L-shaped and portal planar frame structures. An exact analytical solution is obtained using wave vibration approach. The classical Euler-Bernoulli as well as the advanced Timoshenko bending theories are applied in modeling the flexural vibrations in planar frames. Reflection and transmission matrices corresponding to incident waves arriving at the “L” joint from various directions are obtained. A concise and systematic approach to both free and forced vibration analysis of coupled bending and longitudinal vibrations in L-shaped and portal planar frame structures is presented. Results are compared to the Euler-Bernoulli model results available in the literature. Good agreements have been reached.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Sign convention with positive parameters shown

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Figure 2

Free body diagram of an “L” joint

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Figure 3

Wave reflection and transmission at an “L” joint

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Figure 4

Waves generated by external forces and moments

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Figure 5

Wave analysis of an L-shaped frame

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Figure 6

Magnitudes of the characteristic polynomials of the L-shaped frames: Timoshenko model (___) and Euler-Bernoulli model (…)

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Figure 7

Modeshapes of the clamped-free L-shaped frame

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Figure 8

(a) Frequency responses of the L-shaped frame of Ref. [1]. (b) Frequency responses of the L-shaped frame of Ref. [2].

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Figure 9

Wave analysis of a portal frame

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Figure 10

Modeshapes of the clamped-clamped portal frame

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