Research Papers

Wave Analysis of In-Plane Vibrations of H- and T-shaped 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 130(6), 061004 (Oct 15, 2008) (10 pages) doi:10.1115/1.2980373 History: Received June 27, 2007; Revised April 01, 2008; Published October 15, 2008

This paper concerns in-plane vibration analysis of coupled bending and longitudinal vibrations in H- and T-shaped planar frame structures. An exact analytical solution is obtained using wave vibration approach. Timoshenko beam theory, which takes into account the effects of both rotary inertia and shear distortion, is applied in modeling the flexural vibrations in the planar frame. Reflection and transmission matrices corresponding to incident waves arriving at the “T” joint from various directions are obtained. Bending and longitudinal waves generated by a combination of point longitudinal forces, point bending forces, and bending moments are also obtained. Assembling these wave relations provides a concise and systematic approach to both free and forced vibration analyses of coupled bending and longitudinal vibrations in H- and T-shaped planar frame structures. Natural frequencies, modeshapes, and forced responses are obtained from wave vibration standpoint. The results are compared to results available in literature. Good agreement has been reached.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Free body diagram at a “T” joint

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Figure 2

Wave reflection and transmission at a “T” joint

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Figure 3

Waves generated by external forces and moments

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Figure 4

Wave analysis of an H-shaped beam

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Figure 5

Magnitudes of the characteristic polynomial of the H-shaped frame

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Figure 6

Modeshapes of the first three modes of the H-shaped beam: (a) the first modeshape, (b) the second modeshape, and (c) the third modeshape

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Figure 7

Frequency responses of the H-shaped frame subject to (a) point longitudinal force, (b) bending moment, and (c) point transverse force



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