Abstract
By taking infinite periodic beams as examples, the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propagation constant in the present paper, and the corresponding hierarchical finite element formulation is then derived. Thus, it provides the numerical analysis of that problem with a firm theoretical basis of variational principles, with which one may conveniently illustrate the mathematical and physical mechanisms of the wave propagation in periodic structures and the relationship with the natural vibration. The solution is discussed and examples are given.
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References
Brillouin L. Wave Propagation in Periodic Structures, New York: Dover Publication, 1953
Heckl M. A. Wave propagation in beam-plate systems.Journal of Acoustic Society of American, 1961, 33: 640
Mead D. J. Free Wave Propagation in Periodically Supported Infinite Beams.Journal of Sound and Vibration, 1970.11(2): 181–197
Mead D J, Zhu D C, Bardell N S. Free vibration of an orthogonally stiffened flat plate.Journal of Sound and Vibration, 1988,127(1): 19–48
Lanczos C. Linear Differential Operators. Chapter 4, D. Van Nostrand Company, Ltd 1961
Zhu D C. Natural vibration analysis of rotating beams with high-order finite elements.Chinese Journal of Aeronautics, 1988, 1(1): 12–18
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Supported by Doctorate Training Fund of National Education Commission of China
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Dechao, Z., Wei, C. The mutual variational principle of free wave propagation in periodic structures. Acta Mech Sinica 9, 149–155 (1993). https://doi.org/10.1007/BF02487494
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DOI: https://doi.org/10.1007/BF02487494