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Doppler Effects for Dispersive Waves in Beam and Plate with a Moving Edge

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Mechanics and Model-Based Control of Advanced Engineering Systems

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Abstract

Doppler effects for dispersive deflection waves are discussed for 1D beam and 2D plate with a moving edge. The frequency shift and reflection angle and amplitude are derived exactly. The Doppler effects for the dispersive wave are much different from those for non-dispersive elastic and electromagnetic waves. But their approximate frequency shifts are identical to each other in the case of slow edge motion. However the reflection angle for the non-dispersive wave can exceed π∕2, that for the dispersive wave cannot exceed and the reflected dispersive wave with the critical angle runs along the moving edge as if it were the evanescent wave.

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References

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Authors and Affiliations

  1. Yamagata University, Yonezawa, Yamagata, 992-8510, Japan

    Kazumi Watanabe

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  1. Kazumi Watanabe
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Correspondence to Kazumi Watanabe .

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Editors and Affiliations

  1. Inst. of Problems in Mech. Eng., Russian Academy of Sciences, St. Petersburg, Russia

    Alexander K. Belyaev

  2. Universität Linz, Linz, Austria

    Hans Irschik

  3. Universität Linz, Linz, Austria

    Michael Krommer

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© 2014 Springer-Verlag Wien

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Watanabe, K. (2014). Doppler Effects for Dispersive Waves in Beam and Plate with a Moving Edge. In: Belyaev, A., Irschik, H., Krommer, M. (eds) Mechanics and Model-Based Control of Advanced Engineering Systems. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1571-8_31

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  • DOI: https://doi.org/10.1007/978-3-7091-1571-8_31

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  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-1570-1

  • Online ISBN: 978-3-7091-1571-8

  • eBook Packages: EngineeringEngineering (R0)

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