Abstract We consider wave propagation processes generated by forces of various types in a two-component Biot medium. Based on the Fourier transform of generalized functions, we construct a Green tensor describing the process of propagation of waves in spaces of dimension $$N=1,2,3 $$ acted upon by pulsed sources of force that are lumped at the coordinate origin and given by the singular Dirac delta function. Based on this tensor, generalized solutions are constructed to these equations under various disturbance sources that are described by both regular and singular generalized functions. For the regular acting forces, we provide integral representations of the solutions that can be used to calculate the stress-strain state of a porous water-saturated medium.

中文翻译：

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双组分Biot介质运动方程的基本解和广义解及其性质

摘要 我们考虑在双组分 Biot 介质中由各种类型的力产生的波传播过程。基于广义函数的傅立叶变换，我们构建了一个绿色张量，描述了波在维度为 $$N=1,2,3 $$ 的空间中的传播过程，这些过程受到集中在坐标原点的脉冲力源的作用并由奇异的狄拉克 delta 函数给出。基于该张量，在由正则广义函数和奇异广义函数描述的各种扰动源下构建这些方程的广义解。对于规则作用力，我们提供了可用于计算多孔水饱和介质的应力应变状态的解的积分表示。