Application of transparent boundary conditions to high-order finite-difference schemes for the wave equation in waveguides

We propose a method for generating finite-difference approximations of transparent boundary conditions (TBCs) with the fourth and sixth order in space. It is based on the wave equation solution continuation extra two or three layers of grid points outside the computational domain to use them in central-difference operators on approaching the boundary. We present the theoretical background of the method, give estimates of computational resources, and discuss accuracy and stability results of numerical tests in 1D and 2D cases.     

A Gautschi time-stepping approach to optimal control of the wave equation

A Gautschi time-stepping scheme for optimal control of linear second order systems is proposed and analyzed. Convergence rates are proved and shown to be valid in numerical experiments. The temporal discretization is combined with finite element and spectral based spatial discretizations, which are compared among themselves.     

非均匀部分相干光束在自由空间中的传输

本文介绍了非均匀部分相干光束的概念, 并用数值模拟的方法详细研究了其在自由空间传输后的变化. 研究结果表明, 经过自由空间传输后非均匀部分相干光束会发生不同于传统相干模型光束的显著变化. 这种变化和光束传输距离、光源空间相干度分布、光源光强分布密切相关. 经过传输后, 源平面自相干附近点的空间相干度发生突变, 在短距离传输过程中源平面高相干区域的空间相干度会降低, 接收面各点的空间相干曲线不再相同, 随着传输距离增加, 非均匀空间相干度会逐渐趋于均匀.     

S波段微波热致超声成像系统研究

微波热致超声成像技术通过向物体发射微波脉冲, 导致物体吸收电磁波温度迅速升高, 产生瞬时压力波, 从而激发产生超声波信号, 通过传感器对产生的超声波信号进行采集并成像, 最终还原了反映物体吸收电磁波能量特性的图像, 由于此方法兼具了微波成像的高对比性和超声成像的高分辨率特点, 理论上验证了热声成像技术对早期乳腺肿瘤检测的可行性. 本实验兼顾系统成像深度和分辨率, 采用S波段的微波脉冲信号源对物体进行辐射, 利用圆形扫描方式对待测物体进行检测, 同时为了更好的验证成像性能, 本实验同时使用了肿瘤仿体及实际生物组织进行成像实验. 通过实验分析, 验证了该系统对肿瘤仿体和生物组织检测的有效性, 以及系统的高分辨率和高对比度特性, 为早期乳房肿瘤检测提供了进一步的理论支撑.     

A finite element method based comparative fracture assessment of carbon black and silica filled elastomers: Reinforcing efficacy of carbonaceous fillers in flexible composites

This study is focused on numerical investigation on fracture behaviors of carbon black (CB) and silica filled elastomeric composites. Finite element analysis (FEA) in compliance with multi-specimen method is used to calculate J-integral and geometry factor of the rubber composites up to a displacement of 20 mm for single edge notch in tension (SENT) and double edge notch in tension (DENT) specimens. An empirical relationship between crack tip opening displacement (CTOD) and crack advancement is established depending on notch to width ratio (NWR). The stress contours across the notches for SENT and DENT specimens is discussed briefly. It is found that fracture propagation resistance of CB filled elastomer is 125% more than that of silica filled elastomer. Although, Silica filled elastomer have good tensile strength and crosslink density but it fails to replace carbon black in terms of fracture properties. The critical J-integral for CB filled elastomer is 18.7% and 32.2% more than silica filled elastomer for SENT and DENT specimens respectively. The effect of specimen type on various fracture properties is also explored. The factor of safety is found to be significantly more in case of CB filled elastomers making them less vulnerable to crack propagation and catastrophic failure.     

On the use of some numerical damping methods of spurious oscillations in the case of elastic wave propagation

The use of finite element and finite difference methods of spatial and temporal discretization for solving structural dynamics problems gives rise to purely numerical errors. Among the many numerical methods used to damp out the spurious oscillations occurring in the high frequency domain, it is proposed here to analyse and compare the well-known Bulk Viscosity method, which modifies the stresses calculations and a method recently presented by Tchamwa and Wielgosz, which is based on a modification of an explicit time integration algorithm. The efficiency of both methods is evaluated in a 2-D axisymmetric compressive test.     

The wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges

In this paper,wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach.The dynamic responses,active and reactive power flow in the finite plate are calculated by the Mindlin plate theory (MPT) and classic plate theory (CPT).To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate,the near-field and far-field waves are entirely contained in the wave approach.The in-plane longitudinal and shear waves are also considered.The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies.The influence of the plate thickness on the vibrational power flow is investigated.From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies.Furthermore,the effects of structural damping on the active and reactive power flow at the junction are also analyzed.     

On a wave equation with supercritical interior and boundary sources and damping terms

This article addresses nonlinear wave equations with supercritical interior and boundary sources, and subject to interior and boundary damping. The presence of a nonlinear boundary source alone is known to pose a significant difficulty since the linear Neumann problem for the wave equation is not, in general, well‐posed in the finite‐energy space H¹(Ω) × L₂(?Ω) with boundary data in L₂ due to the failure of the uniform Lopatinskii condition. Further challenges stem from the fact that both sources are non‐dissipative and are not locally Lipschitz operators from H¹(Ω) into L₂(Ω), or L₂(?Ω). With some restrictions on the parameters in the model and with careful analysis involving the Nehari Manifold, we obtain global existence of a unique weak solution, and establish exponential and algebraic uniform decay rates of the finite energy (depending on the behavior of the dissipation terms). Moreover, we prove a blow up result for weak solutions with nonnegative initial energy.