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Dynamic Response and Wave Propagation in Three-Dimensional Framed Structures

Published online by Cambridge University Press:  20 December 2012

Y.-H. Pao ,
G.-H. Nie  and
D.-C. Keh
Y.-H. Pao*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10617, Taiwan
G.-H. Nie
Affiliation:
Institute of Applied Mechanics, Tongji University, Shanghai 200092, China
D.-C. Keh
Affiliation:
Development Engineer, Nassda Corporation, Taipei, Taiwan 10608, Taiwan
*
Corresponding author (yhpao.iam.ntu@gmail.com)
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Abstract

This paper extends the recently developed method of reverberation-ray matrix for planar structures to three-dimensional framed structures. The propagation of steady state axial, flexural and torsional waves, as well as the mode conversions through scattering of all three waves at connecting joints are evaluated in the frequency domain. The transient waves in all members are then determined by the Fourier synthesis. The transient responses of a two-storey framed building subject to a step time loading are calculated in detail. Numerical results are obtained for early time as well as moderately long time records. The results are shown to be accurate in arrival times of all three types of waves and in asymptotic values at times.

Keywords

3D framed structuresMethod of reverberation-ray matrix (MRRM)Dynamic responseWave propagation
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 1 , March 2013 , pp. 7 - 26
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

REFERENCES

1. Howard, S. M. and Pao, Y. H., “Analysis and Experiments on Stress Waves in Planar Trusses,” Journal of Engineering Mechanics, ASCE, 124, pp. 884–891 (1998).CrossRefGoogle Scholar
2. Pao, Y. H., Keh, D. C. and Howard, S. M., “Dynamic Response and Wave Propagation in Plane Trusses and Frames,” AIAA Journal, 37, pp. 594–603 (1999).Google Scholar
3. Chen, J. F. and Pao, Y. H., “Effects of Causality and Joint Conditions on Method of Reverberation-Ray Matrix,” AIAA Journal, 41, pp. 1138–1142 (2003).Google Scholar
4. Levine, H., Unidirectional Wave Motions, North-Holland, Amsterdam (1978).Google Scholar
5. Fellipa, C. A., “A Historical Outline of Matrix Structural Analysis: A Play in Three Acts,” Computers & Structures, 79, pp. 1313–1324 (2001).Google Scholar
6. Duncan, W. J. and Collar, A. R., “A Method of the Solution of Oscillations Problems by Matrices,” Philosophical Magazine, 17, p. 865 (1934).Google Scholar
7. Duncan, W. J. and Collar, A. R., “Matrices Applied to the Motions of Damped Systems,” Philosophical Magazine, 19, p. 197 (1935).Google Scholar
8. Frazer, R. A., Duncan, W. J. and Collar, A. R., Elementary Matrices and Some Applications to Dynamics and Differential Equations, Cambridge University Press, Cambridge (1938).Google Scholar
9. Argyris, J. J. and Kelsey, S., “Energy Theorems and Structural Analysis,” London: Butterworth. (Part I reprinted from Aircraft Engineering, 26 Oct-Nov, 1954 and 27 April-May, 1955) (1960).Google Scholar
10. Turner, M. J., The Direct Stiffness Method of Structural Analysis, Structural and Materials Panel Paper, AGARD Meeting, Aachen, Germany (1959).Google Scholar
11. Myklestad, N. O., “A New Method of Calculating Natural Modes of Uncoupled Bending Vibration,” Journal of the Aeronautical Sciences, 1, pp. 153–162 (1944).Google Scholar
12. Thomson, W. T., “Matrix Solution for the Vibration of Non-Uniform Beams,” Journal of Applied Mechanics, 17, pp. 337–339 (1950).Google Scholar
13. Thomson, W. T., “Transmission of Elastic Waves Through a Stratified Solid Medium,” Journal Applied Physics, 21, pp. 89–93 (1950).Google Scholar
14. Pestel, E. C. and Leckie, F. A., Matrix Method in Elastomechanics, McGraw-Hill, New York (1963).Google Scholar
15. Weaver, W. Jr. and Gere, J. M., Matrix Analysis of Framed Structures, Van Nonstrand Reinhold, New York (1965).Google Scholar
16. Clough, R. W. and Penzien, J., Dynamics of Structures, 3rd Edition, McGraw Hill, New York (1995).Google Scholar
17. Cooley, J. W. and Tukey, J. W., “An Algorithm for the Machine Calculation of Complex Fourier Series,” Mathematics and Computation, 19, pp. 297–301 (1965).CrossRefGoogle Scholar
18. Doyle, J. F., Wave Propagation in Structures, 2nd edition, Springer-Verlag, New York (1997).Google Scholar
19. Pao, Y. H., Chen, W. Q. and Su, X. Y, “The Reverberation-Ray Matrix and Transfer Matrix Analyses of Unidirectional Wave Motion,” Wave Motion, 44, pp. 419–438 (2007).Google Scholar
20. Pao, Y. H. and Chen, W. Q., “Elastodynamic Theory of Framed Structures and Reverberation-Ray Matrix Analysis,” Acta Mechanica, 204, pp. 61–79 (2009).CrossRefGoogle Scholar
21. Pao, Y. H., Su, X. Y. and Tian, J. Y., “Reverberation Matrix Method for Propagation of Sound in a Multilayered Liquid,” Journal of Sound and Vibration, 230, pp. 743–760 (2000).Google Scholar
22. Su, X. Y., Tian, J. Y. and Pao, Y. H., “Application of the Reverberation-Ray Matrix to the Propagation of Elastic Waves in a Layered Solid,” International Journal of Solids and Structures, 39, pp. 5447–5463 (2002).CrossRefGoogle Scholar
23. Timoshenko, S., Vibration Problems in Engineering, 3rd Edition, Van Nostrand Co., New York (1955).Google Scholar
24. Mindlin, R. D., Introduction to the Mathematical Theory of Vibrations of Elastic Plates, (Edition By Yang, Jiashi), Baker & Taylor Books (2006).Google Scholar
25. Howard, S. M., “Transient Stress Waves in Trusses and Frames,” Ph.D. Dissertation, Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, New York (1990).Google Scholar
26. Keh, D. C., “Analysis of Elastic Wave Propagation and Dynamic Stresses in Three-Dimensional Framed Structures,” Ph.D. Dissertation, National Taiwan University, Taiwan (1995).Google Scholar
27. Nagem, R. J. and Williams, J. H., “Dynamic Analysis of Large Space Structure Using Transfer Matrices and Joint Coupling Matrices,” Mechanical Structure and Machine, 17, pp. 349–371 (1989).CrossRefGoogle Scholar
28. Kennett, B. L. N., Seismic Wave Propagation in Stratified Media, Cambridge University Press (1983).Google Scholar
29. Miao, F. X., Sun, G. J. and Pao, Y. H., “Vibration Mode Analysis of Frames by the Method of Reverberation Ray Matrix,” Journal of Vibration and Acoustics, 131, 051005 (2009).Google Scholar
30. Guo, Y. Q., “Theory of Method of Reverberation Ray Matrix and its Applications,” Ph.D. Dissertation, Zhejiang University, China (2008).Google Scholar
31. Jiang, J. Q., “Reverberation Ray Analysis of Inhomogeneous Elastodynamic Equations and Nondestrucrive Inspection of Structures,” Ph.D. Dissertation, Zhejiang University, China (2008).Google Scholar
32. Timoshenko, S. and Young, D. H., Elements of Strength of Materials, 4th Edition, D. van Nostrand Company, Inc., (1962).Google Scholar