A new method of analysing pressure wave dependences is presented and tested against the published experimental data. Upon the results of examination of more than 90 rock samples, it was found that a significant portion of rocks (~ 45 %) exhibit negative Poisson ratios at lower pressures. Such a significant number of naturally auxetic rocks suggests that the occurrence of negative Poisson ratios is not as exotic as assumed previously.

The process of wave propagation in the discrete chain of bilinear oscillators subjected to several types of external harmonic excitation has been analysed. The phenomenon of sign inversion of the displacement is observed for tension–compression excitation. The solution for wave propagation in a continuous 1-D bimodular rod is developed and the numerical results are compared showing good agreement.

In order to assess energy loss during wave propagation in fragmented media, an impact model is proposed. The proposed model can be expressed by or used together with other linear damping models, which is important for the determination of mechanical characteristics of such media and mineral exploration.

The article aids the understanding of the propagation of vibration through complex media (e.g., soil). It presents various techniques to better interpret signals (recorded vibrations). The mathematical work done in the article can be utilized for various engineering applications such as oil or mineral exploration, designing materials for shock protection or energy-trapping. The conclusion of the article also mentions some of the ongoing as well as future work related to the research.

We concentrate on the stick-slip-like movement occurring under rate-independent friction due to the eigenoscillation of the fault faces and the associated wave propagation. Also, a simple mechanism of unusually high shear fracture or sliding zone propagation is considered. This is the P sonic propagation of sliding area over a fault based on the fact that the accumulation of elastic energy in the sliding plates can produce oscillations in the velocity of sliding (friction is constant).

The influence of fluid injection on tectonic fault sliding and generation of seismic events was studied in the paper by a multi-degree-of-freedom rate-and-state friction model with a two-parametric friction law. The considered system could exhibit different types of motion. The main seismic activity could appear directly after the start of fluid injection or in the post-injection phase (after some days or months). Such an influence of injection on seismicity is observed in the real cases.

Parametric excitation of edge waves with a frequency 2 times less than the frequency of surface waves propagating perpendicular to the inclined bottom are investigated in laboratory experiments. The domain of instability on the plane of surface wave parameters (amplitude–frequency) is found. The subcritical instability is observed in the system of parametrically excited edge waves. It is shown that breaking of surface waves initiates turbulent effects and can suppress the parametric generation.

Extreme water waves impacting ships and offshore structures can not only cause severe structural damage, but also threaten the safety of passengers and crew. Accordingly, the motivation for the present work is to better understand the dynamics of extreme waves in two cases: the case of "green water" and the case of "freak waves". Our methodology can simulate those two events in order to estimate the forces of such extreme waves and thus aid engineers in the design of safer maritime structures.

We have obtained new evidence of the existence of strain waves in the Earth based on a statistical analysis of the dynamics of seismicity along the northern boundary of the Amurian plate and the data derived from in situ GPS experimental observations. Our results (the periodicity of the seismic components, spatial cycles of the seismicity maxima and migration rate of earthquakes) allow us to identify the dynamics of seismicity along the northern boundary of the Amurian plate as a wave process.