COUPLED 3D WAVE EQUATIONS WITH IRREGULAR FLUID-ELASTIC INTERFACE: THEORETICAL DEVELOPMENT

In marine seismic exploration, ocean-bottom cable techniques accurately record the multicomponent seismic wavefield; however, the seismic wave propagation in fluid–solid media cannot be simulated by a single wave equation. In addition, when the seabed interface is irregular, traditional finite-difference schemes cannot simulate the seismic wave propagation across the irregular seabed interface. Therefore, an acoustic–elastic forward modeling and vector-based P- and S-wave separation method is proposed. In this method, we divide the fluid–solid elastic media with irregular interface into orthogonal grids and map the irregular interface in the Cartesian coordinates system into a horizontal interface in the curvilinear coordinates system of the computational domain using coordinates transformation. The acoustic and elastic wave equations in the curvilinear coordinates system are applied to the fluid and solid medium, respectively. At the irregular interface, the two equations are combined into an acoustic–elastic equation in the curvilinear coordinates system. We next introduce a full staggered-grid scheme to improve the stability of the numerical simulation. Thus, separate P- and S-wave equations in the curvilinear coordinates system are derived to realize the P- and S-wave separation method.

Numerical study of the three-dimensional wave equation using the mesh-free kp-Ritz method

Percussive drilling, that uses rotary torque and axial impact simultaneously, is an established method of making holes in concrete. This paper deals with the development of a finite element model, based on three-dimensional wave propagation, which represents the impact process of percussive drilling in concrete. The solid model of the percussive drilling system consists of five separate components, viz. shank, fluted body, socket tip, carbide blade and concrete target. After integration and meshing, the finite element model is analysed using three-dimensional wave propagation techniques. The bias weight and the impact impulse were set up as inputs to the drilling system. A "surface to surface eroding" interface was selected for the drill tip-concrete contact surface while a "rigid wall" interface was chosen for the concrete-ground support contact surface. Simulation results showed the usefulness of the model in understanding how the three-dimensional wave, due to impact, propagates through the drilling system resulting in penetration of the drill bit into concrete. The accuracy of the model was successfully verified with prior-known one-dimensional analytical model and experimental penetration results. Finally, to illustrate the potential use of this model to design and analyse percussive drilling system, the effect of variation of rake angle, helix angle, point angle, and bias weight on the extent of penetration is presented. The results clearly showed the importance of simulating the impact process for designing new percussive drill bits.

A technique similar to inverting Abel's equation is used to invert the descent of dimensions method between three-dimensional, cylindrically-symmetric and two-dimensional wave propagation. The end result is a very simple relationship between the two types of wave propagation. Apart from its intrinsic interest, the large number of two-dimensional studies reported in the literature could now be related to their three-dimensional counterparts.

In order to better understand bone conduction sound propagation across the skull, three-dimensional (3D) wave propagation on the skull surface was studied, along with its dependence on stimulation direction and location of a bone conduction hearing aid (BCHA) actuator. Experiments were conducted on five Thiel embalmed whole head cadaver specimens. Stimulation, in the 0.1-10 kHz range, was sequentially applied at the forehead and mastoid via electromagnetic actuators from commercial BCHAs, supported by a 5-N steel band. The head response was quantified by sequentially measuring the 3D motion of ∼200 points (∼15-20 mm pitch) across the ipsilateral, top, and contralateral skull surface via a 3D laser Doppler vibrometer (LDV) system, guided by a robotic positioner. Low-frequency stimulation (<1 kHz) resulted in a spatially complex rigid-body-like motion of the skull that depended on both the stimulation condition and head support. The predominant motion direction was only 5-10 dB higher than other components below 1 kHz, with no predominance at higher frequencies. Sound propagation direction across the parietal plates did not coincide with stimulation location, potentially due to the head base and forehead remaining rigid-like at higher frequencies and acting as a large source for the deformation patterns across the parietal sections.

PurposeThe purpose of this paper is to show the applicability of a discrete Hodge operator in the context of the De Rham cohomology to bicomplex-valued electromagnetic wave propagation problems. It was applied in the finite element method (FEM) to get a higher accuracy through conformal discretization. Therewith, merely the primal mesh is needed to discretize the full system of Maxwell equations.Design/methodology/approachAt the beginning, the theoretical background is presented. The bicomplex number system is used as a geometrical algebra to describe three-dimensional electromagnetic problems. Because we treat rotational field problems, Whitney edge elements are chosen in the FEM to realize a conformal discretization. Next, numerical simulations regarding practical wave propagation problems are performed and compared with the common FEM approach using the Helmholtz equation.FindingsDifferent field problems of three-dimensional electromagnetic wave propagation are treated to present the merits and shortcomings of the method, which calculates the electric and magnetic field at the same spatial location on a primal mesh. A significant improvement in accuracy is achieved, whereas fewer essential boundary conditions are necessary. Furthermore, no numerical dispersion is observed.Originality/valueA novel Hodge operator, which acts on bicomplex-valued cotangential spaces, is constructed and discretized as an edge-based finite element matrix. The interpretation of the proposed geometrical algebra in the language of the De Rham cohomology leads to a more comprehensive viewpoint than the classical treatment in FEM. The presented paper may motivate researchers to interpret the form of number system as a degree of freedom when modeling physical effects. Several relationships between physical quantities might be inherently implemented in such an algebra.

A multiple point source model is developed in this research for studying both shear and compressional spherical wave propagation in a non-viscous fluid-saturated elastic porous medium. Relative displacement between the fluid and solid of the medium is quantified by the spherical wave governing equations, such that the waves described are more representative to that in engineering practices. The shear wave has shown significant influences on the characteristics of superposed shear and compressional waves generated by multiple point sources. Utilization of multiple point sources shows higher efficiency and effectiveness in generating desired waves, in comparing with that of single source. Specifically, the multiple sources model is more energy effective in comparing with the single source model by always producing larger magnitudes of relative displacement than a single source with the same energy, which becomes more significant when the distance between the source and the considered geological particles increases. Multiple point sources also show advantages on duration, direction control and magnitude adjustment for the waves generated. Numerical analyses are performed for comparing different shear, compressional and the superposed wave responses under single and multiple sources.

During the seismic damage investigation of Wenchuan earthquake, it is found that some of the entrance lining structures, such as that of the Longxi Tunnel, suffered significant pavement blowup, which can be attributed to the effect of Rayleigh wave. Unlike the conventional analysis under shear wave propagating upwards, numerical dynamic analysis under the effect of Rayleigh wave in time domain is much more complicated in practice. In this paper, a practical wave motion input method for three-dimensional Rayleigh wave propagation problems in time domain is proposed and consequently applied in a numerical model to analysis the dynamic response characteristics of tunnel entrance. Desirable simulation result and sufficient accuracy is accomplished with the proposed approach. The particular seismic damage of tunnel entrance that was observed in Longxi tunnel is reproduced successfully in the simulation.

Elastic metamaterials possess band gaps, or frequency ranges that are forbidden to wave propagation. Existing solutions for impeding three-dimensional (3D) wave propagation largely rest on high-volume fractions of mass inclusions that induce and tailor negative effective density-based local resonances. This study introduces a class of elastic metamaterials that achieve low-frequency band gaps with a volume fraction as low as 3% (mass density as low as $0.034\phantom{\rule{0.1em}{0ex}}\mathrm{g}/{\mathrm{cm}}^{3}$). The working of the proposed design hinges on a 3D trampolinelike mode behavior that gives rise to wide, omnidirectional, and low-frequency band gaps for elastic waves despite very low-mass densities. Such a 3D trampoline effect is derived from a network of overhanging nodal microarchitectures that act as locally resonating elements, which give rise to band gaps at low frequencies. The dynamic effective properties of the metamaterial are numerically examined, which reveal that the band gap associated with the trampoline effect is resulted from a negative effective modulus coupled with a near-zero yet positive effective density. The experimental characterization is then made possible by fabricating the metamaterial via a light-based printing system that is capable of realizing microarchitectures with overhanging microfeatures. This design strategy could be useful to applications where simultaneous light weight and vibration control is desired.

This study aims to systematically investigate the wave propagation behavior in curved sandwich nanoplates incorporating zirconia–Ti6Al4V cores and graphene-enhanced foam layers, subjected to combined thermal and magnetic fields. To achieve this, a high-order shear deformation plate theory coupled with nonlocal strain gradient elasticity theory is employed. Three distinct foam distribution patterns—U-foam, S1-foam, and S2-foam—are considered to assess their influence on wave characteristics. The results reveal that phase and group velocities decrease with increasing foam content, thermal softening effects, and reduced curvature radius, whereas the presence of a magnetic field contributes to increased wave velocities. Interestingly, the impact of foam distribution varies significantly among configurations, with U-foam showing the most pronounced effect (40%), followed by S1-foam (10%) and S2-foam (3%). These findings underscore the potential applicability of such nanostructures in advanced engineering systems, particularly in radar-absorbing materials; high-temperature nanoelectromechanical systems; and lightweight, thermally responsive sensors for wearable healthcare technologies.

In this paper, a class of radiation boundary conditions for two-and three-dimensional elastic wave propagation is developed. The boundary conditions are based on compositions of simple first-order operators. Some recent empirical investigations have suggested that certain earlier radiation boundary conditions may be unstable if the ratio of P-wave velocity to S-wave velocity is sufficiently large. The boundary conditions developed in the present paper are stable for all values of the velocity ratio. The boundary operators used here are defined by relatively simple formulas that apply without modification to problems in both two and three dimensions. Given an arbitrary angle of incidence, some parameters in the boundary conditions can be adjusted to make the conditions perfectly absorbing for P- waves and/or S-waves traveling at that angle of incidence to the boundary.

Wave propagation in glass fibre-reinforced polymer (GFRP) bars subjected to progressive damage—Experimental and numerical results

Shell type structures are used in a wide variety of industrial components, especially in automotive or aeronautic industries. A full understanding and predictive modeling of elastic waves propagation through those structures can be of great importance at their design stage for several reasons, such as the noise reduction in a vehicle or the control of high energy shock waves triggered by pyrotechnic cut in a space launcher. This paper deals with the theoretical and numerical modeling of elastic wave propagation in shells. The aim is to discuss the relevance of theoretical models and to develop appropriate and efficient numerical tools.

On the three-dimensional wave propagation through cascading screens having a periodic system of arbitrary openings

Large differences in the ultrasonic velocity of the solid and liquid phases of semiconductors have stimulated an interest in the use of laser ultrasonic methods for locating and characterizing solid–liquid interfaces during single crystal growth. A previously developed two-dimensional ray tracing analysis has been generalized and used to investigate three-dimensional ultrasonic propagation across solid–liquid interfaces in cylindrical bodies where the receiver is located at an arbitrary position relative to the source. Numerical simulations of ultrasonic ray paths, wavefronts, and time of flight have indicated that ultrasonic sensing in the diametral plane is a preferred sensing configuration since the transmitted, reflected, and refracted rays all propagate in this plane, significantly simplifying analysis of the results. While other sensing configurations can also provide information about solid–liquid interfaces, they require a more complicated analysis because the planes in which reflected and refracted rays propagate are not known a priori, and fewer ray paths are accessible for interface interrogation because of large refractions.