G-type dispersion equation under suppressed rigid boundary:analytic approach

This paper studies dispersion of a G-type earthquake wave under the influence of a suppressed rigid boundary. Inside the Earth, the density and rigidity of the crustal layer and the mantle of the Earth vary exponentially and periodically along the depth. The displacements of the wave are found in the individual medium followed by a dispersion equation using a suitable analytic approach and a boundary condition. The prominent effect of inhomogeneity contained in the media, the rigid boundary plane, and the initial stress on the phase and group velocities is shown graphically.

Effect of rigid boundary on propagation of torsional surface waves inporous elastic layer

The paper presents the effect of a rigid boundary on the propagation of torsional surface waves in a porous elastic layer over a porous elastic half-space using the mechanics of the medium derived by Cowin and Nunziato （Cowin, S. C. and Nunziato, J. W. Linear elastic materials with voids. Journal of Elasticity, 13（2）, 125-147 （1983））. The velocity equation is derived, and the results are discussed. It is observed that there may be two torsional surface wave fronts in the medium whereas three wave fronts of torsional surface waves in the absence of the rigid boundary plane given by Dey et al. （Dey, S., Gupta, S., Gupta, A. K., Kar, S. K., and De, P. K. Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores. Tamkang Journal of Science and Engineering, 6（4）, 241-249 （2003））. The results also reveal that in the porous layer, the Love wave is also available along with the torsional surface waves. It is remarkable that the phase speed of the Love wave in a porous layer with a rigid surface is different from that in a porous layer with a free surface. The torsional waves are observed to be dispersive in nature, and the velocity decreases as the oscillation frequency increases.

INTERACTION OF A CAVITATION BUBBLE AND AN AIR BUBBLE WITH A RIGID BOUNDARY

The motion of a spark-induced cavitation bubble and an air bubble near a rigid boundary is experimentally studied by using high-speed photography.Several dimensionless parameters are used to describe the geometrical configuration of the bubble-bubble-boundary interaction.The bubble-bubble interaction can be considered in two different conditions.The cavitation bubble will collapse towards the air bubble if the air bubble is relatively small,and away from the air bubble if the air bubble is relatively large.The two zones are identified in the bubble-boundary interaction,and they are the danger zone and the safety zone.The relative position,the bubble-boundary distance and the bubble-bubble distance play important roles in the bubble-bubble-boundary interaction,which can be considered in several conditions according to the responses of the bubbles.Air jets are found to penetrate into the cavitation bubbles.The cavitation bubble and the air bubble（air jet） move in their own way without mixing.The motion of a cavitation bubble may be influenced by an air bubble and/or a rigid boundary.The influence of the air bubble and the influence of the boundary may be combined,like some thing of a vector.

Investigation of cavitation bubble collapse near rigid boundary by lattice Boltzmann method

The dynamics of the bubble collapse near a rigid boundary is a fundamental issue for the bubble collapse application and prevention. In this paper, the bubble collapse is modeled by adopting the lattice Boltzmann method （LBM） and is verified, and then the dynamic characteristics of the collapsing bubble with the second collapse is investigated. The widely used Shan-Chen model in the LBM multiphase community is modified by coupling with the Carnahan-Starling equation of state （C-S EOS） and the exact difference method （EDM） for the forcing term treatment. The simulation results of the bubble profile evolution by the LBM are in excellent agreements with the theoretical and experimental results. From the two-dimensional pressure field evolution, the dynamic characteristics of the different parts during the bubble collapse stage are studied. The role of the second collapse in the rigid boundary damage is discussed, and the impeding effect between two collapses is demonstrated.

On study of non-spherical bubble collapse near a rigid boundary

This paper applies numerical methods to investigate the non-spherical bubble collapse near a rigid boundary. A three-dimensional model, with the mass conservation equation reformulated for considering the compressibility effect, is built to deal with the coupling between the pressure and the flow velocity in the momentum and energy equations and to simulate the temporal evolution of the single bubble oscillation and its surrounding flow structure. The investigations focus on the global bubble patterns and its schlieren contours, as well as the high-speed jet accompanied when the bubble collapses and the counter jet is generated in the rebound stage. The results show that the robust pressure waves emitted due to the bubble collapse lead to substantial changes of the flow structures around the bubble, especially the formation of the counter jet generated in the rebound stage. Furthermore, compared with the high-speed jet when the bubble collapses, the counter jet in the rebound stage emits the momentum several times greater in the magnitude and in diametrically opposite direction at the monitoring point.

INFLUENCE OF RIGID BOUNDARY ON THE LOVE WAVE PROPAGATION IN ELASTIC LAYER WITH VOID PORES

In this paper, a mathematical model for Love wave propagation in a porous elastic layer under a rigid boundary resting over a poro-elastic half-space has been developed. The study shows that such a medium transmits two types of Love waves. The first front depends on the change in volume fraction of the pores whereas the second front depends upon the modulus of rigidity of the elastic matrix of the medium and is the same as the Love wave in an elastic layer over an elastic half-space. It is observed that the first front is many times faster than the shear wave in the medium with void pores due to the change in the volume fraction of the pores and is significant.

Effect of sample size on the response of DEM samples with a realistic grading

This paper shows that for DEM simulations of triaxial tests using samples with a grading that is repre- sentative of a real soil, the sample size significantly influences the observed material response. Four DEM samples with identical initial states were produced： three cylindrical samples bounded by rigid wails and one bounded by a cubical periodic cell, When subjected to triaxial loading, the samples with rigid boundaries were more dilative, stiffer and reached a higher peak stress ratio than the sample enclosed by periodic boundaries. For the rigid-wall samples, dilatancy increased and stiffness decreased with increasing sample size, The periodic sample was effectively homogeneous, The void ratio increased and the contact density decreased close to the rigid walls, This heterogeneity reduced with increasing sample size. The positions of the critical state lines （CSLs） of the overall response in e-log p＇ space were sensitive to the sample size, although no difference was observed between their slopes. The critical states of the interior regions of the rigid-wall-bounded samples approached that of the homogeneous periodic sample with increasing sample size. The ultimate strength of the material at the critical state is independent of sample size.