We established equilibrium and motion equations for media with internal structure, characterized by integral geometry parameters. These equations are linear differential equations of the infinite order. Besides usual elastic waves, there are many waves with sufficiently lower velocities without bottom limit. Corresponding dispersion equations have both real and imaginary roots. Complex roots represent parametric resonances (catastrophes). This model of structured continuum describes intermediate states between statics and dynamics. It means that the equilibrium equations are valid for large scales, while the dynamic equations are valid in small ones.

中文翻译：

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多孔和破裂介质的平衡和动力学

我们建立了具有内部结构的介质的平衡和运动方程，以积分几何参数为特征。这些方程是无限阶的线性微分方程。除了通常的弹性波之外，还有许多速度足够低且没有下限的波。相应的色散方程有实根和虚根。复根代表参数共振（灾难）。这种结构化连续体模型描述了静态和动态之间的中间状态。这意味着平衡方程适用于大尺度，而动力学方程适用于小尺度。