8. A Motion of Water Excited by an Earthquake[I]. : The Case of a Rectangular Basin(one-dimensional)
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It is well known that the water surface of a pond, reservior and lake is disturbed on the occasion of an earthquake. In the present purview, the problem of the water motion accompanied by an earthquake is treated theoretically. The used model is a onedimensional rectangular basin and the generator of water disturbance is given only at the bottom in a form of periodic, propagated waves. Then the following conclusions are obtained :- (1) When the period of the ground motion ≪ the period of the. n-th mode of the eigen oscillations, i.e. ω0 ≫ (ω0: the angular frequency of the ground motion; γn: the angular frequency of the n-th mode of the eigen oscillations), the generated water waves move with the period of the earthquake at the time of the duration of the ground motion and, after the termination of the earthquake, with a period of the eigen oscillation. (2) When ω0≪≪n, the water waves produced by the ground motion have, in the midst of the earthquake, two kinds of periods which are relevant to that of the earthquake and those of the eigen oscillations of the lake water, and, after the earthquake, the former disappears and the latter only remain. (3) When ω0■γn, the wave height of the n-th mode of the waves is in proportion to a time duration of the earthquake. (4) When kl→0(k: the wave number of the earthquake wave ; l: the length of the lake), the whole surface of the water oscillates uniformly with a period of an earthquake and no higher modes of the waves are generated. (5) When kl→nr, the modes of the waves with a difference of even numbers from the n-th one are not produced on the surface of water. At the beginning of the earthquake, the modes of the waves on the lower side of the resonant mode (the n-th one) are more excited by the ground motion than those on the upper side(n: positive integers). When the lake is very shallow, a similarphenomenon takes place, that is to say, the nearby modes of the waves on the lower side of the resonant one are more excited by the earthquake than those on the upper side. (6) When the ground motion lasts unlimitedly, even though the amplitude of the earthquake is so small, the produced water waves increase in height infinitely to the extent that the linear theory used in this paper cannot be applied. Then the period of the water waves is nearly equal to that of the earthquake. In the subsequent articles, other cases will be considered.大地震の際に,池,貯水地,湖などの水面がじよう乱を受けることは良く知られた現象である,併しこれに対する理論的な解析は未だおこなわれていない.そこで筆者は本報告および後の報告でこの問題を理論的に究明しようと考え,まず本報告では,一次元の矩形の湖の水底に周期的な伝播波を有限時間与えるモデルを用いて解析を試みた.そして次のような結論を得た.(1)(地震波の周期)≪(湖水の固有振動の第n番目のモードの周期)のとき,発生した水波は地震波継続中は地震波の周期で動き,地震波通過後は湖水の固有振動周期で動く.
- 1965-07-15
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