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タイトル: 21. Propagation and Apparent Attenuation of Elastic Waves in a Heterogeneous Medium with Certain Periodic Structures
その他のタイトル: 21. ある周期構造を有する不均質媒質を伝わる弾性波
著者: ONDA, Isao
著者(別言語): 音田, 功
発行日: 1964年12月25日
出版者: 東京大学地震研究所
掲載誌情報: 東京大学地震研究所彙報. 第42冊第3号, 1964.12.25, pp. 427-447
抄録: The attenuation of seismic waves propagated in a heterogeneous medium is investigated. Heterogeneity of the medium is represented by the velocity distribution alone and the structure under consideration is expressed in Fourier cosine series. In this proplem the differential equation is of Hill's type, and conditions of instabilityare discussed. Since the unstable solutions obtained are of the standing waves, some modification and reformation for discussing the stability of the progressive waves are made. It is concluded that the wave amplitude with wave length λn isaffected by the structural component with wave length Ln=λn/2 and is independent, of the other components, and that the function of the apparent attenuation for the specified wave amplitude is of hyperbolic secant but not of exponential. On the other hand, the phase of this specific wave is shifted by every component of the structure. In addition, the phase shift of waves passing through the medium is negligibly small; the phase velocity is apparently fixed for all frequencies. A similar problem will arise in that of surface wave propagation along a rough surface. In the appendix, Hill's equation is solved in forms convenient in discussing the stability of its solution.
URI: http://hdl.handle.net/2261/12164
ISSN: 00408972


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