A NOVEL METHOD OF SOLVING THE EXACT EQUATIONS FOR CAPILLARY-GRAVITY WAVES

A new method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The nonlinear surface is expressed by Fourier series with finite number of terms, after the computational domain is transformed into a unit circle. The dynamic boundary equation is used in its exact nonlinear form and the coefficients of Fourier series are found by the Newton-Raphson method successively. This is a neat method, Yielding high prescision with little computational effort.

3D elastic waveform modeling with an optimized equivalent staggered-grid finite-difference method

Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.

Numerical solutions to regularized long wave equation based on mixed covolume method

The mixed covolume method for the regularized long wave equation is devel- oped and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.

Signal processing method for shear wave velocity measurement

Soil shear wave velocity （SWV） is an important parameter in geotechnical engineering. To measure the soil SWV, three methods are generally used in China, including the single-hole method, cross-hole method and the surface-wave technique. An optimized approach based on a correlation function for single-hole SWV measurement is presented in this paper. In this approach, inherent inconsistencies of the artificial methods such as negative velocities, and too-large and too-small velocities, are eliminated from the single-hole method, and the efficiency of data processing is improved. In addition, verification using the cross-hole method of upper measuring points shows that the proposed optimized approach yields high precision in signal processing.

Optimum fifth order Stokes wave theory

This Paper improves the existing fifth order Stokes wave theory by using least Square method, and givesthe optimum result in the meaning of minimum error Squares to satisfy the free surface boundary conditions, and thewave profile can be adjusted according to the measured data. This paper also gives a simplified method for derivingthe parameters of the existing fifth order Stokes wave.

Nonlinear Capillary-Gravity Waves Produced by a Vertically Oscillating Plate

The nonlinear capillary-gravity wave produced by a vertically oscillating plate, in which the contact-angle model is considered, is studied by use of the Boundary Integral Equation Method (BIEM). The present numerical experiment shows that the code is robust and efficient for modeling the generation and propagation of capillary-gravity waves. It is found that the wave heights of stationary periodic nonlinear waves radiated away from the plate are dependent on the parameters involved in the contact-angle model. The effect of the contact-angle hysteresis and the nonlinearity of capillary-gravity waves on the wave profile is discussed in the paper.

Error Estimates of H^1-Galerkin Mixed Methods for the Viscoelasticity Wave Equation

H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.

Lie Symmetry Analysis, Optimal Systems and Explicit Solutions of the Dispersive Long Wave Equations

In this paper, the dispersive long wave equation is studied by Lie symmetry group theory. Firstly, the Lie symmetries of this system are calculated. Secondly, one dimensional optimal systems of Lie algebra and all the symmetry reductions are obtained. Finally, based on the power series method and the extended Tanh function method, some new explicit solutions of this system are constructed.

An Optimization Method in Inverse Elastic Scattering for One-Dimensional Grating Profiles

Consider the inverse diffraction problem to determine a two-dimensional periodic structure from scattered elastic waves measured above the structure.We formulate the inverse problem as a least squares optimization problem,following the two-step algorithm by G.Bruckner and J.Elschner[Inverse Probl.,19(2003),315–329]for electromagnetic diffraction gratings.Such a method is based on the Kirsch-Kress optimization scheme and consists of two parts:a linear severely ill-posed problem and a nonlinear well-posed one.We apply this method to both smooth(C2)and piecewise linear gratings for the Dirichlet boundary value problem of the Navier equation.Numerical reconstructions from exact and noisy data illustrate the feasibility of the method.

New Developments in Structural Health Monitoring Based on Diagnostic Lamb Wave

Structure health monitoring based on diagnostic Lamb waves has been found to be one of the most promising techniques recently. This paper has a brief review of the new developments on this method including the basic novel of the method, fundamentals and mathematics of Lamb wave propagation, narrowband and wideband Lamb wave excitation methods, optimization of excitation factors and diagnostic Lamb wave interpretation methods.

Multi-objective Optimization of Non-uniform Beam for Minimum Weight and Sound Radiation

A multi-objective optimization of non-uniform beams is presented for minimum radiated sound power and weight. The transfer matrix method is used to compute the structural and acoustic responses of a non-uniform beam accurately and efficiently. The multi-objective particle swarm optimization technique is applied to search the Pareto optimal solutions that represent various compromises between weight and sound radiation. Several constraints are imposed, which substantially reduce the volume fraction of feasible solutions in the design space. Two non-uniform beams with different boundary conditions are studied to demonstrate the multi-objective optimal designs of the structure. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.

THE OPTIMIZATION OF THE HULL FORM WITH THE MINIMUM WAVE MAKING RESISTANCE BASED ON RANKINE SOURCE METHOD

The hull form optimization concerns one of the most important applications of wave making resistance theories. In order to obtain a hull form with the minimum wave making resistance, an optimization design method based on the CFD is proposed, which combines the Rankine source method with the nonlinear programming （NLP）. The bow-body shape is optimized with the minimum wave making resistance as the objective function. A hull form modification function is introduced to represent an improved hull surface, which can be used to generate a new smooth hull surface by multiplying it by the offset data of the original hull surface. The parameters of the hull form modification function are taken as the design variables. Other constraint conditions can also be considered, for example, in optimizing the lines of the bow, appropriate displacements can be taken as the basic constraints. S60 hull form is selected as the original hull. Three improved hulls are obtained by optimal design. Rankine source method proves to be an effective method in ship form optimization based on analysis of the resistance performance and lines of the improved hull.

Ship hull optimization based on wave resistance using wavelet method

The ship hull surface optimization based on the wave resistance is an important issue in the ship engineering industry. The wavelet method may provide a convenient tool for the surface hull optimization. As a preliminary study, we use the wavelet method to optimize the hull surface based on the Michel wave resistance for a Wigley model in this paper. Firstly, we express the model＇s surface by the wavelet decomposition expressions and obtain a reconstructed surface and then validate its accuracy. Secondly, we rewrite the Michel wave resistance formula in the wavelet bases, resulting in a simple formula containing only the ship hull surface＇s wavelet coefficients. Thirdly, we take these wavelet coefficients as optimization variables, and analyze the main wave resistance distribution in terms of scales and locations, to reduce the number of optimization variables. Finally, we obtain the optimal hull surface of the Wigley model through genetic algorithms, reducing the wave resistance almost by a half. It is shown that the wavelet method may provide a new approach for the hull optimization.

Shape Optimization of Bow Bulbs with Minimum Wave-Making Resistance Based on Rankine Source Method

The hull form optimization concerns one of the most important applications of wave-making resistance theories.In recent years,scholars can determine the hull form by using the optimization method based on the computational fluid dynamics(CFD)and other mathematical techniques.In this paper,the hull form optimization method based on the Rankine source method and nonlinear programming(NLP)is discussed;in the optimization process,a hull form modification function is introduced to represent an improved hull surface and to generate a new smooth hull surface by changing its frame lines and bow stem profiles under the prescribed design constraints. Numerical example is given for a practical container hull form.Finally,shape optimization of bow bulls is shown for non-protruding and protruding bow bulls.This study presents a simplified and practical design method to the select frame lines of bow bulls.

Shape optimization design of a heaving buoy of wave energy converter based on fully parametric modeling and CFD method

The hydrodynamic shape of the heaving buoy is an important factor of the motion response in waves and thus concerns the energy conversion efficiency for the point absorbers(PAs).The current experience-based designs are time consuming and not very efficient,hence,faster and smarter methods are desirable.An automated optimization method based on a fully parametric modeling method and computational fluid dynamics(CFD),is proposed in this paper.Using this method,a benchmark buoy is screen designed and then optimized by maximizing the heave motion response.The geometry is described parametrically and deformed by means of the free-form deformation(FFD)method.During the optimization process,the expansion factor of control points is the basis for the variations.A combination of the Sobol and the non-dominated sorting genetic algorithm II(NSGA-II)is used to search for the solutions.After several iterations,the heaving buoy shape with optimal heave motion response is obtained.The analyses show that the heave motion response has increased 55.3%after optimization.The developed methodology is valid and seems to be a promising way to design a novel buoy that can significantly improve the wave energy conversion efficiency of the PAs in future.

基于77 GHz毫米波角雷达的天线罩优化设计方法

77 GHz毫米波雷达因其体积小和分辨率高等特点在无人驾驶车辆领域具有广阔的应用前景。天线罩作为毫米波雷达系统的重要组成部分,能有效防御恶劣环境对雷达系统工作性能的影响,但天线罩在保护雷达系统的同时会在雷达电磁波传播路径上引入介质,从而造成天线辐射性能的衰减。为了改善天线罩对雷达天线辐射性能的影响,本文提出了一种基于77 GHz毫米波角雷达天线罩的优化设计方法。该优化方法以遗传算法(GA)作为优化算法,运用MATLAB将GA与高频仿真软件HFSS结合,通过优化拱形天线罩横截面圆弧的圆心角和天线罩与天线的垂直间距,使雷达天线在其工作频段内具有高增益和低旁瓣的同时,增大天线3 dB方位面波束宽度,提高毫米波角雷达视场角的宽度。仿真结果表明,优化天线罩后阵列天线的3 dB方位面波束宽度增大了37°,工作带宽增大了1.04 GHz,俯仰面最大旁瓣降低了1.02 dB。分析结果表明,基于优化方法设计的天线罩能够有效增大毫米波角雷达阵列天线的视场角,拓宽该雷达天线阵列的工作频带,并降低其俯仰面最大旁瓣。77 GHz毫米波角雷达天线罩数值算例验证了该优化方法的有效性。

基于ACBO-GM联合方法的高维变量结构模型修正

工程结构模型修正常面临变量维度高、非线性程度强等现实问题,其模型修正的精度和效率受到严重影响,为改善这一不足,提出基于改进物体碰撞算法(Advanced Colliding Bodies Optimization,ACBO)和高斯白噪声扰动(Gaussian-white-noise Mutation,GM)的联合修正方法。在联合方法中,ACBO实现从传统的“一对一”到“优对多”的碰撞模式的转变,GM则用于保证碰撞过程中种群的多样性,可有效提升结构模型修正效率。基于一系列测试函数,对比分析标准物体碰撞算法(Colliding Bodies Optimization,CBO)和联合优化方法的优化性能;给出基于ACBO-GM联合方法的修正流程,并将其应用于钢框架修正算例和悬臂梁修正实例,对比研究基于联合修正方法与基于遗传算法(Genetic Algorithm,GA)的修正精度和效率。研究表明,ACBO-GM联合优化方法在精度和效率方面都明显优于传统的CBO方法,该优化方法的可行性得到验证;基于ACBO-GM联合方法在钢框架和悬臂梁两个工程结构修正案例中的应用,其修正精度均与基于GA方法的精度一致,但修正效率显著优于基于GA的修正方法。

基于传递矩阵的管路-壳体耦合系统动力学建模

针对管路-支撑-壳体耦合系统的振动响应快速预报和传递特性分析,采用Riccati传递矩阵法建立直管-弯管-变径管-泵-阀门复杂组合管路的动力学模型,以获取考虑流固耦合效应时组合管路的频响特性;采用频响函数子结构综合方法建立组合管路-支撑-壳体耦合系统的动力学模型,以获得在管路系统泵源模拟激励下的振动传递特性。对耦合系统的位移频响、传递特性开展分析,得到如下结论:对组合管路利用Riccati变换可解决传递矩阵法多管段数值精度累积误差的问题,在垂向简谐力激励下壳体和管路受到的垂向力大于轴向力和横向力,在各个支撑处通过各个方向传递的功率流量级基本一致。

Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media

Weak Galerkin finite element method is introduced for solving wave equation with interface on weak Galerkin finite element space(Pk(K),P_(k−1)(∂K),[P_(k−1)(K)]^(2)).Optimal order a priori error estimates for both space-discrete scheme and implicit fully discrete scheme are derived in L1(L2)norm.This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes.Finite element algorithm presented here can contribute to a variety of hyperbolic problems where physical domain consists of heterogeneous media.

Optimization design of optical waveguide in mach-zehnder electro-optical polymer modulator

In order to reduce transmission loss of the optical waveguide in Mach-Zehnder (M-Z) electro-optical (EO) polymer modulator,the basic iterative formula of semi-vector finite-difference beam propagation method (FD-BPM) is obtained from the scalar wave equation. The transition waveguide is combined with S-type bend branch waveguide for the M-Z EO modulator in the branch waveguide. The effects of structure parameters such as ridge width,length of the branch waveguide and interferometer spacing on the transmission loss are systematically studied by using the semi-vector FD-BPM method. The structure is optimized as an S-sine bend branch waveguide,with rib width w=7μm,length of branch waveguide L=1200μm and interferometer spacing G=22 μm. The results show that the optimized structure can reduce transmission loss to 0.083 dB,which have a certain reference value to the design of optical waveguide in M-Z polymer modulator.