Abstract

The problem of wave generation on the surface of a liquid layer lying on an elastic half-space is considered. The generation source is located in an elastic medium. The joint system of equations of the theory of elasticity in a half-space and the theory of waves in a liquid is solved. On the basis of the previously obtained simplified solution of the dispersion equation for the water mode, taking into account the influence of the elastic half-space and the integral representation of the displacement of the liquid surface caused by a source of a simple form, analytical formulas are constructed for solving the problem under the assumption of long waves. Comparison of results obtained by analytical formulas and integral representations is carried out.

中文翻译：

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弹性基础底部源在液体表面产生长波的线性问题的简单解

摘要

考虑在位于弹性半空间上的液体层的表面上产生波的问题。产生源位于弹性介质中。解决了半空间弹性理论和液体波动理论的联合方程组。在先前获得的水模式色散方程简化解的基础上，考虑到弹性半空间的影响以及由简单形式的源引起的液面位移的积分表示，解析建立了在长波假设下解决问题的公式。比较分析公式和积分表示法获得的结果。