Nonlinearity must be considered with some porous granular media because of the large deformation under seismic waves. In this study, the propagation of nonlinear waves in porous media is studied based on the Biot theory and the governing equations are obtained by the Lagrangian formulation. Three new nonlinear parameters are introduced to consider the coupled nonlinearity between the solid and fluid components in porous media. It is shown that an additional nonlinear wave with a double frequency is generated by the coupling effect of linear fast and slow waves. When only a shear wave is applied at the source, no double-frequency nonlinear wave is predicted and three nonlinear longitudinal waves are generated. On the basis of the practical case studies, the effect of strong nonlinearity is computed under the influence of a one-dimensional single longitudinal wave source and a single shear wave source.

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To study the energy evolution and acoustic emission characteristics of layered sandstone under anchorage in the process of deformation and failure, the sandstone samples from Chuxiong Yi Autonomous Prefecture, Yunnan Province were selected for uniaxial compression testing. The energy evolution in the process of sandstone failure and the spatial fractal characteristics of acoustic emission events in the process of deformation and failure were investigated. Research results show that anchoring can make layered sandstone store more energy, the stored energy first increases, then decreases with the increase of bedding angle; the B value of sandstone under anchorage is generally higher than that of unanchored sandstone in the whole deformation and failure process, and the continuous decline in B value can be used to indicate a precursor to instability and failure; under the action of anchoring, the D value of sandstone (its fractal dimension) also increases, then decreases with the increase of bedding angle. The D value changes within [2, 3]. At a given bedding angle, the D value of anchored sandstone is greater than that of unanchored sandstone, the D value of 30° anchored sandstone increased the most (by 12.33%); the maximum D value occurred in 45° anchored sandstone (reaching 2.72) and the spatial distribution of acoustic emission events and damage of sandstone under anchorage is also more uniform; under increasing stress, the number of acoustic emission events is less widely distributed in the early stage and more densely distributed in the later stage. The growth rate of the D value varies across different peak stress ranges, which is more significant under the action of anchorage. The acoustic emission event counts grow evenly and slowly in the space, and the toughness of sandstone is improved to a certain extent under the action of anchorage.

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Membrane-type acoustic metamaterials (MAMs) are lightweight and flimsy materials with excellent low-frequency insulation performance, which breaks the limitations of the traditional mass law and provides a new idea for noise reduction in the low-frequency range. To further broaden the sound insulation bandwidth on the premise of lightweight design, a novel MAM with petal-like rings is proposed, and the parametric studies on the structural parameters of split rings are carried out in this paper. By combining the finite element model simulation and impedance tube test, the effectiveness of the proposed structure and the correctness of the numerical simulation are validated. Moreover, the sound transmission loss curves and modal shapes of four different structures are computed and analyzed to clarify the insulation mechanism of the novel structure. Finally, the width, the center angle, the centroid position, and the weight of the split rings in the novel structure are parametrically analyzed to figure out the regulation rules of the sound insulation characteristics.