A non-reflecting wave equation through directional wave-field suppression and its finite difference implementation

The acoustic wave equation describes wave propagation directly from basic physical laws, even in heterogeneous acoustic media. When numerically simulating waves with the wave equation, contrasts in the medium parameters automatically generate all scattering effects. For some applications - such as propagation analysis or certain wave-equation based imaging techniques - it is desirable to suppress these reflections, as we are only interested in the transmitted wave-field. To achieve this, a modification to the constitutive relations is proposed, yielding an extra term that suppresses waves with reference to a preferred direction. The scale-factor $$\alpha$$ α of this extra term can either be interpreted as a penetration depth or as a typical decay time. This modified theory is implemented using a staggered-grid, time-domain finite difference scheme, where the acoustic Poynting-vector is used to estimate the local propagation direction of the wave-field. The method was successfully used to suppress reflections in media with bone tissue (medical ultrasound) and geophysical subsurface structures, while introducing only minor perturbations to the transmitted wave-field and a small increase in computation time.

Least-Squares Reverse Time Migration Using the Gradient Preconditioning Based on Transmitted Wave Energy

A gradient preconditioning approach based on transmitted wave energy for least-squares reverse time migration (LSRTM) is proposed in this study. The gradient is preconditioned by using the energy of “approximate transmission wavefield,” which is calculated based on the non-reflecting acoustic equation. The proposed method can effectively avoid a huge amount of calculation and storage required by the Hessian matrix or approximated Hessian matrix and can overcome the influence of reflected waves, multiples, and other wavefields on the gradient in gradient preconditioning based on seismic wave energy (GPSWE). The numerical experiments, compared with that using GPSWE, show that LSRTM using the gradient preconditioning based on transmitted wave energy (GPTWE) can significantly improve the imaging accuracy of deep target and accelerate the convergence rate without trivial increased calculation.

Dynamic Behavior of Coal Pillar under Different Load Percentage by Numerical Simulation

The stability and dynamic response of coal pillar is of great importance in underground coal mining. In this paper, a series of uniaxial compressive experiments were first carried out to investigate the mechanical properties of coal. Subsequently, a statistical constitutive damage model for coal was proposed and applied to the numerical simulation. The proposed strain damage softening function showed almost the same goodness-of-fit on the experimental curve. According to this investigation, a numerical model FLAC3Dwas created to investigate the dynamic behavior of the coal pillar under different load percentage (LP). Modelling suggests that the incident and transmitted wave stress evolution observes similar rule and its process can be divided into three stages, namely, static preload, dynamic disturbance, and stabilized stages. The effects of dynamic disturbance intensity are also studied at 10 MPa, 20 MPa, and 30 MPa of peak stress, respectively. The results indicate that under the same load percentage, the peak incident and transmitted wave stress increase with the increase of dynamic disturbance intensity. On the contrary, the attenuation decreases. It is also observed that the failure zone interior the coal can be predicted by the wave propagation.

Representative Transmission Coefficient for Evaluating the Wave Attenuation Performance of 3D Floating Breakwaters in Regular and Irregular Waves

Wave attenuation performance is the prime consideration when designing any floating breakwater. For a 2D hydrodynamic analysis of a floating breakwater, the wave attenuation performance is evaluated by the transmission coefficient, which is defined as the ratio between the transmitted wave height and the incident wave height. For a 3D breakwater, some researchers still adopted this evaluation approach with the transmitted wave height taken at a surface point, while others used the mean transmission coefficient within a surface area. This paper aims to first examine the rationality of these two evaluation approaches via verified numerical simulations of 3D heave-only floating breakwaters in regular and irregular waves. A new index—a representative transmission coefficient—is then presented for one to easily compare the wave attenuation performances of different 3D floating breakwater designs.

Investigation of Contact Conditions During Stamping of a Thin Plate

Stamping is one of the most used manufacturing processes, where real-time monitoring is quite difficult due to high speed of the mechanical press, which leads to deterioration of the accuracy of the products In the present work, a method is developed to model elastic waves propagation in solids to measure contact conditions between die and workpiece during stamping. A two-dimensional model is developed that reduces the wave propagation equations to two-dimensional equations. To simulate the wave propagation inside the die-workpiece model, the finite difference time domain (FDTD) method and modified Yee algorithm has been employed. The numerical stability of the wave propagation model is achieved through courant stability condition, i.e., Courant-Friedrichs-Lewy (CFL) number. Two cases, i.e., flat die-workpiece interface and inclined die-workpiece interface, are investigated in the present work. The elastic wave propagation is simulated with a two-dimension (2D) model of the die and workpiece using reflecting boundary conditions for different material properties. The experimental and simulation-based results of reflected and transmitted wave characteristics are compared for different materials in terms of reflected and transmitted wave height ratio and material properties such as acoustic impedance. It is found that the numerical simulation results are in good agreement with the experimental results.

Dynamic Behavior of Coal Pillar Under Different Load Percentage by Numerical Simulation

The stability and dynamic response of coal pillar is of great importance in underground coal mining. In this paper, a series of uniaxial compressiveexperimentswerefirst carried out to investigate the mechanical properties of coal. Subsequently, a statistical constitutive damage model for coal was proposed and applied to the numerical simulation. The proposed strain damage softening function showed almostthe same goodness-of-fit on the experimental curve. A numericalmodel FLAC3Dwas created to investigate the dynamic behavior of the coal pillar under different load percentage(LD). Modelling suggests that the incident and transmitted wave stress evolution observesa similar rule and its process can be divided into three stages, namely, static preload, dynamic disturbance and stabilized stages.Under the same load percentage, the peak incident and transmitted wave stress increase with the increase of dynamic disturbance intensity. On the contrary, the attenuation decrease. It is also observed that the failure zone interior the coal can be predicted by the wave propagation.