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

C. Mei

doi:10.1115/1.4032001

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

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

C. Mei

[+] 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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Abstract

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

Tu, T. H. , Yu, J. F. , Lien, H. C. , Tsai, G. L. , and Wang, B. P. , 2008, “ Free Vibration Analysis of Frames Using the Transfer Dynamic Stiffness Matrix Method,” ASME J. Vib. Acoust., 130(2), p. 024501. [CrossRef]

Petyt, M. , 2010, Introduction to Finite Element Vibration Analysis, Cambridge University Press, Cambridge, UK.

Graff, K. F. , 1975, Wave Motion in Elastic Solids, Ohio State University Press, Dover Publication, New York.

Cremer, L. , Heckl, M. , and Petersson, B. A. T. , 2014, Structure-Borne Sound, Springer-Verlag, Berlin.

Doyle, J. F. , 1989, Wave Propagation in Structures, Springer-Verlag, New York.

Mei, C. , and Mace, B. R. , 2005, “ Wave Reflection and Transmission in Timoshenko Beams and Wave Analysis of Timoshenko Beam Structures,” ASME J. Vib. Acoust., 127(4), pp. 382–394. [CrossRef]

Mei, C. , 2009, “ Hybrid Wave/Mode Active Vibration Control of Bending Vibrations in Beams Based on Advanced Timoshenko Theory,” J. Sound Vib., 322(1–2), pp. 29–38. [CrossRef]

Mei, C. , 2012, “ Studying the Effects of Lumped End Mass on Vibrations of a Timoshenko Beam Using a Wave-Based Approach,” J. Vib. Control, 18(5), pp. 733–742. [CrossRef]

Mei, C. , 2012, “ Wave Analysis of In-Plane Vibrations of L-Shaped and Portal Planar Frame Structures,” ASME J. Vib. Acoust., 134(2), p. 021011. [CrossRef]

Mei, C. , and Sha, H. , 2014, “ An Exact Analytical Approach for Free Vibration Analysis of Built-Up Space Frames,” ASME J. Vib. Acoust., 137(3), p. 031005. [CrossRef]

Meirovitch, L. , 2001, Fundamentals of Vibrations, McGraw-Hill, New York.

Cowper, G. R. , 1966, “ The Shear Coefficient in Timoshenko's Beam Theory,” ASME J. Appl. Mech., 33(2), pp. 335–340. [CrossRef]

Figures

Fig. 1

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

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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

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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

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Fig. 5

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

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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

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Fig. 8

Wave reflection at a boundary

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Fig. 9

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

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Fig. 11

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

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Fig. 13

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 L_H1 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 L_H2 beam direction and responses measured by (a) accelerometer 1, (b) accelerometer 2, and (c) accelerometer 3

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Mei CC. Experimental Validation of Wave Vibration Analysis of Complex Vibrations in a Two-Story Metallic Space Frame Based on the Timoshenko Bending Theory. ASME. J. Vib. Acoust. 2016;138(2):021003-021003-20. doi:10.1115/1.4032001.

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

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