Abstract This paper is dedicated to propagation of waves with assigned length in a model describing the evolutionary behavior of materials with double porosity. Basic equations are considered for an isotropic and homogeneous material which occupies the entire three dimensional space. Wave solutions with assigned wavelength are sought. It is shown that there exist two shear waves that are undamped in time, non-dispersive and that are unaltered by the presence of pore system. There also exist other three longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave and two quasi-pore modes due to presence of pore system. The dispersion relation is explicitly established like a quartic equation and it is shown that it could allow negative real roots, thus explaining the existence of standing waves. A numerical analysis indicates that the speed of propagation of the longitudinal quasi-elastic wave is larger than the wave speed for its counterpart from the classical elasticity theory. The propagation of the Rayleigh surface waves is addressed and the corresponding secular equation is explicitly established.

中文翻译：

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双孔隙率材料中的波传播

摘要 本文致力于在描述双孔隙率材料演化行为的模型中具有指定长度的波的传播。对于占据整个三维空间的各向同性且均质的材料，考虑基本方程。寻找具有指定波长的波解决方案。结果表明，存在两种不随时间衰减、无色散且不受孔隙系统影响的剪切波。由于孔隙系统的存在，还存在其他三种随时间分散和衰减的纵波解：一种纵向准弹性波和两种准孔隙模式。色散关系像四次方程一样明确建立，并表明它可以允许负实根，从而解释了驻波的存在。数值分析表明，纵向准弹性波的传播速度大于经典弹性理论对应的波速。讨论了瑞利表面波的传播，并明确建立了相应的长期方程。