Abstract
This monograph reviews the properties and characteristics of modal vectors from both an analytic and experimental viewpoint. The commonly understood and well documented normal modes of undamped and proportionally damped models and structures are reviewed in detail. The less well documented and understood complex modes attributed to non-proportional damping are also explored in detail. New information relating to complex mode scaling, modal mass and associated frequency response functions is presented.
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References
Frazer, B.A., Duncan, W.J., Collar, A.R.: Elementary Matrices and Some Applications to Dynamics and Differential Equations, pp. 308–331. The University Press, Cambridge (1950)
Wylie Jr., C.R.: Advanced Engineering Mathematics, pp. 477–497. McGraw-Hill Book Company (1966)
Hurty, W.C., Rubinstein, M.F.: Dynamics of Structures, pp. 313–337. Prentice-Hall, Inc. (1964)
Allemang, R.J.: Vibrations: analytical and experimental modal analysis. UC-SDRL-CN-20-263-662 course notes, University of Cincinnati, August 2013
Flannelly, W.G., Lang, G.F.: Modal analysis for managers. Sound Vib. (1979)
Lang, G.F.: Modal testing principles. Technical Report Number 023/87, Schlumberger, 1987
Lang, G.F.: Demystifying complex modes. Sound Vib. (1989)
Lang, G.F.: Matrix madness and complex confusion. Sound Vib. (2012)
Acknowledgement
Dr. Randall J. Allemang, Contributing Editor of Sound & Vibration magazine, Professor of Mechanical Engineering at the University of Cincinnati and Director of its Structural Dynamics Research Laboratory gave generously of his time and specialized knowledge by reviewing and editing this monograph. Like a good flight instructor, he let this novice try to blaze his way through the haze, then brought me back to a more realistic mathematical flight before I could do serious damage. In dynamics and mathematics as in learning to fly, “Good judgment comes with experience; unfortunately, experience is usually gained through bad judgment.” Thank you for the experience!
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© 2017 The Society for Experimental Mechanics, Inc.
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Lang, G.F. (2017). Understanding Modal Vectors. In: Mains, M., Blough, J. (eds) Topics in Modal Analysis & Testing, Volume 10. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-54810-4_8
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DOI: https://doi.org/10.1007/978-3-319-54810-4_8
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54809-8
Online ISBN: 978-3-319-54810-4
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