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TECHNICAL PAPERS

Free and Forced Wave Vibration Analysis of Axially Loaded Materially Coupled Composite Timoshenko Beam 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 127(6), 519-529 (Apr 18, 2005) (11 pages) doi:10.1115/1.2128643 History: Received August 25, 2004; Revised April 18, 2005

In this paper, wave vibration analysis of axially loaded bending-torsion coupled composite beam structures is presented. It includes the effects of axial force, shear deformation, and rotary inertia; namely, it is for an axially loaded composite Timoshenko beam. The study also includes the material coupling between the bending and torsional modes of deformations that is usually present in laminated composite beam due to ply orientation. From a wave standpoint, vibrations propagate, reflect, and transmit in a structure. The transmission and reflection matrices for various discontinuities on an axially loaded materially coupled composite Timoshenko beam are derived. Such discontinuities include general point supports, boundaries, and changes in section. The matrix relations between the injected waves and externally applied forces and moments are also derived. These matrices can be combined to provide a concise and systematic approach to vibration analysis of axially loaded materially coupled composite Timoshenko beams or complex structures consisting of such beam components. The systematic approach is illustrated through numerical examples for which comparative results are available in the literature.

Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 9

Clamped free uniform beam subjected to external excitations

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Figure 10

Frequency responses of the uniform beam subjected to a point force: (___) without axial loading, (…) with 7.5N compressional loading and (-.-.-.) with 7.5N tensile loading; (a) torsional rotation and (b) flexural deflection

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Figure 13

Stepped cantilever beam subjected to external excitations

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Figure 14

Frequency responses of the stepped beam subjected to a point force excitation: (___) without axial loading, (…) with 7.5N compressional loading and (-.-.-.) with 7.5N tensile loading; (a) torsional rotation and (b) flexural deflection

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Figure 15

Frequency responses of the stepped beam due to a torque excitation: (___) without axial loading, (…) with 7.5N compressional loading and (-.-.-.) with 7.5N tensile loading; (a) torsional rotation and (b) flexural deflection

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Figure 1

Axially loaded uniform composite beam with unbalanced layup

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Figure 2

Definition of positive shear force, torque, and bending moment

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Figure 3

Wave propagation

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Figure 4

Wave reflection at a general boundary

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Figure 5

Wave reflection and transmission at a general discontinuity

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Figure 6

Wave reflection and transmission at change of section

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Figure 7

Waves generated by external excitations

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Figure 8

Uniform beam structure with boundaries A and B

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Figure 11

Frequency responses of the uniform beam subjected to a torque excitation: (___) without axial loading, (…) with 7.5N compressional loading and (-.-.-.) with 7.5N tensile loading; (a) torsional rotation and (b) flexural deflection

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Figure 12

Stepped cantilever beam

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