Converging spherical and cylindrical elastic–plastic waves of small amplitude

Converging spherical and cylindrical elastic-plastic waves in an isotropic work-hardening medium is investigated on the basis of a finite difference method. The small amplitude pressure is applied instantaneously and maintained on the outer surface of a spherical or a cylindrical medium. It is found that for undercritical loading, the induced wave structure is an elastic front followed in turn by an expanding plastic region and an expanding elastic region. For supercritical loading, the elastic front is followed in turn by an expanding plastic region, a narrowing elastic region and an expanding plastic region. After yielding is initiated, the strength of the elastic front is constant and equal to the critical loading pressure. The motion of the continuous elastic-plastic interface is discussed in detail. Spatial distributions of pressure near the axis show the strength of the converging wave is nearly doubled in the reflecting stage.

A note on the surface motion of a semi-cylindrical canyon for incident cylindrical SH waves radiated by a finite fault

The plane-wave assumption for incident SH waves can be a good approximation for cylindrical and spherical waves radiated from finite sources, even when the source is as close as twice the size of the inhomogeneity, and when the source and the inhomogeneity are described within the same coordinate system. However, in a more general setting, and when the fault＇s radiation pattern must be considered, the plane-wave approximation may not yield satisfactory answers for arbitrary orientation of the fault. Jalali et al. （2015） demonstrated this for a semi-cylindrical, sedimentary valley, and in this study we extend their results to a case in which the semi-circular, sedimentary valley is replaced by a canyon. We describe the effects of incident cylindrical waves on the amplitudes of surface motion in and near the semi-cylindrical canyon when the causative faults are at different distances and have different curvatures and orientations.

Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map

In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.

Acoustic field simulations of logging while drilling by cylindrical finite difference with variable grids

This study proposes an elastic finite difference(FD)time domain method with variable grids in three-dimensional cylindrical coordinates.The calculations will diverge and become less accurate by conventional cylindrical FD as the grid size gradually becomes more extensive with the increasing radius.To prevent grids from being too coarse in far fields,we compensate for the grid cell infl ation by refi ning the grid step in the azimuthal direction.The variable grid FD in the cylindrical coordinate systems has a higher effi ciency in solving acoustic logging while drilling(LWD)problems because the grid boundaries are consistent with those of the drill collar and the borehole.The proposed algorithm saves approximately 94%of the FD grids,80%of the computation time,and memory with a higher calculation accuracy than the FD on rectangular grids for the same models.We also calculate the acoustic LWD responses of the fl uid-fi lled borehole intersecting with fractures.Refl ections are generated at the fractures,which can be equivalent to an additional scattering source.The mode conversions between the collar and the Stoneley waves are revealed.The Stoneley spectra are more sensitive to the fracture.Finally,the logs in a heterogeneous formation with two refl ectors far from the borehole are modeled,and a means of estimating the azimuth of geological interfaces from refl ections is proposed.

An approach to viscoelastic c haracterization of dispersive media by inversion of a general wave propagation model

In the characterization of elastic properties of tissue using dynarmic optical coherence elasto-graphy,shear/surface waves are propagated and tracked in order to estimate speed and Y oung's modulus.However,for dispersive tssues,the displacement pulse is highly damped and distorted during propagation,diminishing the ffectiveness of peak tracking approaches,and leading to biased cstimates of wave speed.Further,plane wave propagation is sometimes assumed,which contributes to estimation erors.Therefore,we invert a wave propagation model that incorpo-rates propagation,decay,and distortion of pulses in a dispersive media in order to accurately estimate its elastic and viscous components.The model uses a general first-order approximation of dispersion,avoiding the use of any particular rheological model of tisue.Experiments are conducted in elastic and viscoelastic tissue mimicking phantoms by producing a Gaussian push using acoustic radiation force excitation and measuring the wave propagation using a Fourier domain optical coherence tomography system.Results confirmed the ffectiveness of the inversion method in est imat ing viscoelastic parameters in both the viscoelastic and elastic phantoms when compared to mechanical measurements.Finally,the viscoelastic characterization of a fresh porcine comea was conducted.Preliminary results validate this approach when compared to other methods.

Transmission characteristics of terahertz Bessel vortex beams through a multi-layered anisotropic magnetized plasma slab

The transmission of terahertz(THz)Bessel vortex beams through a multi-layered anisotropic magnetized plasma slab is investigated by using a hybrid method of cylindrical vector wave functions(CVWFs)and Fourier transform.On the basis of the electromagnetic boundary conditions on each interface,a cascade form of expansion coefficients of the reflected and transmitted fields is obtained.Taking a double Gaussian distribution of the plasma density as an example,the influences of the applied magnetic field,the incident angle and polarization mode of the incident beams on the magnitude,OAM mode and polarization of the transmitted beams are analyzed in detail.The results indicate that the applied magnetic field has a major effect upon the polarization state of the transmitted fields but not upon the transmitted OAM spectrum.The incident angle has a powerful influence upon both the amplitude profile and the OAM spectrum of the transmitted beam.Furthermore,for multiple coaxial vortex beams,an increase of the maximum value of the plasma density causes more remarkable distortion of both the profile and OAM spectrum of the transmitted beam.This research makes a stable foundation for the THz OAM multiplexing/demultiplexing technology in a magnetized plasma environment.

Theoretical analysis for sound wave scattering by parallel cylindrical tubes in boilers

Although the sonic soot cleaning techniques have been applied in boilers in power plants, petrochemical works and general industries world wide, most of the correlated basic problems have not been well solved yet. By using Helmholtz integral equation, sound wave scattered by heat-exchanger tubes is numerically calculated. Sound field distribution characteristics on the tube surfaces and around the tube group is obtained. The results can be applied to the development of sonic soot cleaning techniques in boilers.

Effects of Vortex Generator on Cylindrical Protrusion Aerodynamics

Experimental and numerical studies were carried out to evaluate the effect of vortex generator on a small cylindrical protrusion at Mach number 2.0. The experiments were performed using the supersonic blow down wind tunnel on different heights of cylindrical protrusion with vortex generator placed ahead of them. The upstream and downstream flow around the cylindrical protrusion is influenced by vortex generator as is observed using both visualization and pressure measurement techniques. Numerical studies using three dimensional steady implicit formulations with standard k-ω turbulence model was performed. Results obtained through the present computation are compared with the experimental results at Mach 2.0. Good agreements between computation and experimental results have been achieved. The results indicate that the aerodynamic drag acting on cylindrical protrusion can be reduced by adopting vortex generator.

Solitary Wave Solutions of KP equation,Cylindrical KP Equation and Spherical KP Equation

Three(2+1)-dimensional equations–KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the Kd V equation have been known already, substituting the solutions of the Kd V equation into the corresponding transformation of variables respectively, the single and 2-solitary wave solutions of the three(2+1)-dimensional equations can be obtained successfully.