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Journal of Vibration and Acoustics | Volume 138 | Issue 2 | research-article
Research Papers

Experimental Validation of Wave Vibration Analysis of Complex Vibrations in a Two-Story Metallic Space Frame Based on the Timoshenko Bending Theory

[+] 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 Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 6, 2015; final manuscript received October 30, 2015; published online January 18, 2016. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 138(2), 021003 (Jan 18, 2016) (20 pages) Paper No: VIB-15-1306; doi: 10.1115/1.4032001 History: Received August 06, 2015; Revised October 30, 2015
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In a space frame, there exist in- and out-of-plane bending, axial, and torsional vibrations. The analysis of complex vibrations in such structures has relied mostly on numerical approaches. In this study, a wave-based analytical approach is applied to obtain solutions to vibrations in space frames. Both free and forced wave vibration responses are obtained, with bending vibrations modeled using the Timoshenko theory. A two-story steel space frame is built to validate the analytical results, and good agreements have been reached between the analytical and experimental studies. The effect of torsional rigidity adjustment on the accuracy of predicted vibrational responses in structures involving rotationally nonsymmetric cross sections is also examined.
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References

Figures

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Fig. 1

Definition of positive signs for shear forces, longitudinal force, bending moments, and torque

+Definition of positive signs for shear forces, longitudinal force, bending moments, and torque
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Definition of positive signs for shear forces, longitudinal force, bending moments, and torque
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Fig. 2

The Y joint—a joint with three uniform beams joined orthogonally

+The Y joint—a joint with three uniform beams joined orthogonally
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The Y joint—a joint with three uniform beams joined orthogonally
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Fig. 3

(a) Front view of FBD of the Y joint, (b) left view of FBD of the Y joint, and (c) top view of FBD of the Y joint

+(a) Front view of FBD of the Y joint, (b) left view of FBD of the Y joint, and (c) top view of FBD of the Y joint
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(a) Front view of FBD of the Y joint, (b) left view of FBD of the Y joint, and (c) top view of FBD of the Y joint
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Fig. 4

Wave transmission and reflection at the Y joint with incident waves from (a) beam 1, (b) beam 3, and (c) beam 2

+Wave transmission and reflection at the Y joint with incident waves from (a) beam 1, (b) beam 3, and (c) beam 2
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Wave transmission and reflection at the Y joint with incident waves from (a) beam 1, (b) beam 3, and (c) beam 2
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Fig. 5

The spatial K joint and the definition of coordinates

+The spatial K joint and the definition of coordinates
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The spatial K joint and the definition of coordinates
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Fig. 6

(a) Front view of FBD of the K joint, (b) left view of FBD of the K joint, and (c) top view of FBD of the K joint

+(a) Front view of FBD of the K joint, (b) left view of FBD of the K joint, and (c) top view of FBD of the K joint
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(a) Front view of FBD of the K joint, (b) left view of FBD of the K joint, and (c) top view of FBD of the K joint
Grahic Jump Location
Fig. 7

Wave transmission and reflection at the K joint with waves (a) incident from beam 1, (b) incident from beam 2, (c) incident from beam 3, and (d) incident from beam 4

+Wave transmission and reflection at the K joint with waves (a) incident from beam 1, (b) incident from beam 2, (c) incident from beam 3, and (d) incident from beam 4
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Wave transmission and reflection at the K joint with waves (a) incident from beam 1, (b) incident from beam 2, (c) incident from beam 3, and (d) incident from beam 4
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Fig. 8

Wave reflection at a boundary

+Wave reflection at a boundary
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Wave reflection at a boundary
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Fig. 9

Waves generated by externally applied forces and moments

+Waves generated by externally applied forces and moments
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Waves generated by externally applied forces and moments
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Fig. 10

The metal frame to be lifted by a hoister for free boundary conditions

+The metal frame to be lifted by a hoister for free boundary conditions
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The metal frame to be lifted by a hoister for free boundary conditions
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Fig. 11

Waves in the two-story space frame in the absence of external excitation

+Waves in the two-story space frame in the absence of external excitation
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Waves in the two-story space frame in the absence of external excitation
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Fig. 12

dB magnitude response of the characteristic polynomial of the two-story frame

+dB magnitude response of the characteristic polynomial of the two-story frame
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dB magnitude response of the characteristic polynomial of the two-story frame
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Fig. 13

Waves on Leg 1 due to external excitation and locations of impact hammer and accelerometers

+Waves on Leg 1 due to external excitation and locations of impact hammer and accelerometers
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Waves on Leg 1 due to external excitation and locations of impact hammer and accelerometers
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Fig. 14

Inertance frequency response with impact force in parallel to LH1 beam direction and responses measured by (a) accelerometer 1, (b) accelerometer 2, and (c) accelerometer 3

+Inertance frequency response with impact force in parallel to LH1 beam direction and responses measured by (a) accelerometer 1, (b) accelerometer 2, and (c) accelerometer 3
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Inertance frequency response with impact force in parallel to LH1 beam direction and responses measured by (a) accelerometer 1, (b) accelerometer 2, and (c) accelerometer 3
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Fig. 15

Inertance frequency response with impact force in parallel to LH2 beam direction and responses measured by (a) accelerometer 1, (b) accelerometer 2, and (c) accelerometer 3

+Inertance frequency response with impact force in parallel to LH2 beam direction and responses measured by (a) accelerometer 1, (b) accelerometer 2, and (c) accelerometer 3
View Large  |  Save Figure  |  Download Slide (.ppt)
Inertance frequency response with impact force in parallel to LH2 beam direction and responses measured by (a) accelerometer 1, (b) accelerometer 2, and (c) accelerometer 3

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