Uniform version of the modified theory of physical optics based boundary diffraction wave theory

The potential function of the modified theory of physical optics based boundary diffraction wave theory is made uniform by using the principles of the uniform theory of diffraction. The line integration of this new function along the edge contour gives the uniform diffracted fields which are finite for the transition regions of the diffraction geometry. The method is applied to the diffraction problem by the edge of a curved surface.     

A boundary diffraction wave in the Fresnel-Kirchhoff theory

A method for transformation of the Fresnel-Kirchhoff diffraction surface integral into an integral over the contour bounding this surface is proposed for an observation point in the Fresnel zone. An expression for the boundary wave field is obtained for a parametric representation of the contour. Examples of application of the obtained relations are given. Calculated dependences are compared to the experimental results.     

A new DRBEM model for wave refraction and diffraction

A numerical model using the dual reciprocity boundary element method (DRBEM) is developed to study the combined refraction and diffraction of water waves propagating around islands or solid offshore structures over a seabed with a variable depth. Based on the well-known mild-slope equation, the model has been validated by comparison with both analytical solutions and standard numerical solutions available in the literature. The results show that a considerable improvement in terms of numerical efficiency has been achieved with the adoption of the DRBEM and the model has a great potential to be used in engineering practice to solve wave refraction and diffraction problems.     

一种基于本征波匹配的EMD边界处理方法

希尔伯特-黄变换(Hilbert-Huang Transform,简称HHT)是上世纪末出现的一种处理非线性非平稳信号的新方法 ,EMD边界处理是其中的关键技术之一。着重介绍了一种基于本征波匹配的EMD边界处理方法——本证波匹配预测法,特别是介绍了将该方法和其他两种有代表性的EMD边界处理方法应用于仿真信号和和实测信号的算例对比,从而验证了本证波匹配预测法的先进性。本文工作使得相关研究得到较大程度地深化和完善。     

Uniform decay for wave equations with weakly dissipative boundary feedback

In this paper, we consider a wave equation with a nonlinear weakly dissipative boundary feedback localized on a part of the boundary. We establish an explicit and general decay rate result, using some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term.     

Analysis of diffracted fields with the extended theory of the boundary diffraction wave for impedance surfaces

Uniform diffracted fields from impedance surfaces are investigated by the extended theory of boundary diffraction wave (ETBDW). The new vector potential of the ETBDW is constructed by considering the pseudoimpedance boundary condition. The method is applied to the diffraction problem from an impedance half-plane. It is shown that the total fields from an impedance half-plane reduce to the case of a perfectly electric or magnetic conducting and opaque half-plane for special values of surface impedance. The total and diffracted fields are compared numerically with the exact solution for the impedance half-plane and modified theory of physical optics (MTPO) solution for an impedance wedge. The numerical results show that the field expressions are in very good agreement with the exact and MTPO solutions.     

A superposition method of reflected wave for moving string vibration with nonclassical boundary

A reflected wave superposition method is proposed for an axially traveling string with classical and nonclassical boundaries, based on the reflection of the propagating wave on both sides of the string, combining its initial conditions and the continuity conditions in order to obtain the expressions for the reflected wave. The reflection process, in three phases, is deduced and a determinate expression for the transverse vibration is obtained. The correctness and superiority of the proposed method is verified by comparison with the Newmark-β method for an axially moving string with a fixed and a spring-dashpot boundary.     

Quantum theory of light diffraction

At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the relativistic quantum theory approach. We find that the slit length, slit width, slit thickness and wavelength of light affect the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern cannot be explained by wave-optical approach, but it can be explained in quantum theory. We compare the theoretical results with single- and multiple-slits experimental data, and find the theoretical results are in accordance with the experimental data. In addition, we give some theory predictions. We think all new predictions will be tested by the light diffraction experiment.     

Finite element formulation of exact non‐reflecting boundary conditions for the time‐dependent wave equation

A modified version of an exact Non‐reflecting Boundary Condition (NRBC) first derived by Grote and Keller is implemented in a finite element formulation for the scalar wave equation. The NRBC annihilate the first N wave harmonics on a spherical truncation boundary, and may be viewed as an extension of the second‐order local boundary condition derived by Bayliss and Turkel. Two alternative finite element formulations are given. In the first, the boundary operator is implemented directly as a ‘natural’ boundary condition in the weak form of the initial–boundary value problem. In the second, the operator is implemented indirectly by introducing auxiliary variables on the truncation boundary. Several versions of implicit and explicit time‐integration schemes are presented for solution of the finite element semidiscrete equations concurrently with the first‐order differential equations associated with the NRBC and an auxiliary variable. Numerical studies are performed to assess the accuracy and convergence properties of the NRBC when implemented in the finite element method. The results demonstrate that the finite element formulation of the (modified) NRBC is remarkably robust, and highly accurate. Copyright © 1999 John Wiley & Sons, Ltd.     

Accurate H-shaped absorbing boundary condition in frequency domain for scalar wave propagation in layered half-space

An accurate absorbing boundary condition (ABC) is developed in frequency domain for finite element analysis of scalar wave propagation in unbounded layered half-space. The proposed ABC is H-shaped line that consists of two parts: a new ABC at horizontal bottom boundary of finite domain to replace semiinfinite strip below horizontal boundary and between two vertical boundaries, and a general consistent ABC at vertical lateral boundary to replace semiinfinite layered half-space outside vertical boundary. The key point for constructing the ABC is that a new continued fraction (CF) is presented to expand dynamic stiffness of underlying half-space, and the CF-based stress-displacement relationship is then transformed into an auxiliary variable system with square of horizontal wavenumber. The ABC has only one undetermined real parameter that is the CF-order independent of frequency and incidence angle of propagating outgoing waves. The parameter can be chosen relatively small value to achieve an accurate ABC. Moreover, the ABC can couple seamlessly with finite element method of finite domain. The finite domain can be chosen very small size due to high accuracy of the ABC. Numerical examples are finally given to demonstrate the effectiveness of the ABC.     

Accurate radiation boundary conditions for the time‐dependent wave equation on unbounded domains

Asymptotic and exact local radiation boundary conditions (RBC) for the scalar time‐dependent wave equation, first derived by Hagstrom and Hariharan, are reformulated as an auxiliary Cauchy problem for each radial harmonic on a spherical boundary. The reformulation is based on the hierarchy of local boundary operators used by Bayliss and Turkel which satisfy truncations of an asymptotic expansion for each radial harmonic. The residuals of the local operators are determined from the solution of parallel systems of linear first‐order temporal equations. A decomposition into orthogonal transverse modes on the spherical boundary is used so that the residual functions may be computed efficiently and concurrently without altering the local character of the finite element equations. Since the auxiliary functions are based on residuals of an asymptotic expansion, the proposed method has the ability to vary separately the radial and transverse modal orders of the RBC. With the number of equations in the auxiliary Cauchy problem equal to the transverse mode number, this reformulation is exact. In this form, the equivalence with the closely related non‐reflecting boundary condition of Grote and Keller is shown. If fewer equations are used, then the boundary conditions form high‐order accurate asymptotic approximations to the exact condition, with corresponding reduction in work and memory. Numerical studies are performed to assess the accuracy and convergence properties of the exact and asymptotic versions of the RBC. The results demonstrate that the asymptotic formulation has dramatically improved accuracy for time domain simulations compared to standard boundary treatments and improved efficiency over the exact condition. Copyright © 2000 John Wiley & Sons, Ltd.     

液体-压电晶片界面上电边界条件对兰姆波激发的影响

本文对液体-压电晶片结构中,不同电边界条件下叉指换能器所激发的兰姆波传播特性进行了分析研究,给出了不同电边界条件下兰姆波的相速度、叉指换能器激发兰姆波的机电耦合系数与压电晶片的归一化厚度、晶体切向之间的关系曲线,为实际设计中电边界条件的正确选择提供了理论基础。     

Modelling of short wave diffraction problems using approximating systems of plane waves

This paper describes a finite element model for the solution of Helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element. The approach is based on partition of unity isoparametric elements. At each finite element node the potential is expanded in a discrete series of planar waves, each propagating at a specified angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

A high‐order approach for modelling transient wave propagation problems using the scaled boundary finite element method

A high‐order time‐domain approach for wave propagation in bounded and unbounded domains is proposed. It is based on the scaled boundary FEM, which excels in modelling unbounded domains and singularities. The dynamic stiffness matrices of bounded and unbounded domains are expressed as continued‐fraction expansions, which leads to accurate results with only about three terms per wavelength. An improved continued‐fraction approach for bounded domains is proposed, which yields numerically more robust time‐domain formulations. The coefficient matrices of the corresponding continued‐fraction expansion are determined recursively. The resulting solution is suitable for systems with many DOFs as it converges over the whole frequency range, even for high orders of expansion. A scheme for coupling the proposed improved high‐order time‐domain formulation for bounded domains with a high‐order transmitting boundary suggested previously is also proposed. In the time‐domain, the coupled model corresponds to equations of motion with symmetric, banded and frequency‐independent coefficient matrices, which can be solved efficiently using standard time‐integration schemes. Numerical examples for modal and time‐domain analysis are presented to demonstrate the increased robustness, efficiency and accuracy of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Time‐dependent absorbing boundary conditions for elastic wave propagation

This paper develops a finite element scheme to generate the spatial‐ and time‐dependent absorbing boundary conditions for unbounded elastic‐wave problems. This scheme first calculates the spatial‐ and time‐dependent wave speed over the cosine of the direction angle using the Higdon's one‐way first‐order boundary operator, and then this operator is used again along the absorbing boundary in order to simulate the behaviour of unbounded problems. Different from other methods, the estimation of the wave speed and directions is not necessary in this method, since the wave speed over the cosine of the direction angle is calculated automatically. Two‐ and three‐dimensional numerical simulations indicate that the accuracy of this scheme is acceptable if the finite element analysis is appropriately arranged. Moreover, only the displacements along absorbing boundary nodes need to be set in this method, so the standard finite element method can still be used. Copyright © 2001 John Wiley & Sons, Ltd.     

Unified formulation of radiation conditions for the wave equation

A family of radiation boundary conditions for the wave equation is derived by truncating a rational function approximation of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second‐order wave equations on the radiating surface. Several well‐established radiation boundary conditions appear as special cases, corresponding to different choices of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms of selected directions with ideal transmission is presented. A mechanical interpretation of the fictitious surface densities enables identification of suitable conditions at corners and boundaries of the radiating surface. Numerical examples illustrate excellent results with one or two fictitious layers with suitable corner and boundary conditions. Copyright © 2001 John Wiley & Sons, Ltd.     

基于波传播方法的边界条件对圆柱壳振动特性的影响分析

在波传播分析方法基础上,采用一种改进傅立叶级数的方法建立了弹性约束边界条件下圆柱壳结构模态分析模型,结合模态叠加理论,给出了圆柱壳结构在任意径向点力激励下的振动响应.通过与商业分析软件ANSYS的结果比较验证了本文方法的高效性与精确性,随后详细分析了边界约束刚度对圆柱壳结构自由振动特性和结构振动响应的影响,并给出了刚度影响的一般性规律.     

A boundary condition in Padé series for frequency‐domain solution of wave propagation in unbounded domains

A boundary condition satisfying the radiation condition at infinity is frequently required in the numerical simulation of wave propagation in an unbounded domain. In a frequency domain analysis using finite elements, this boundary condition can be represented by the dynamic stiffness matrix of the unbounded domain defined on its boundary. A method for determining a Padé series of the dynamic stiffness matrix is proposed in this paper. This method starts from the scaled boundary finite‐element equation, which is a system of ordinary differential equations obtained by discretizing the boundary only. The coefficients of the Padé series are obtained directly from the ordinary differential equations, which are not actually solved for the dynamic stiffness matrix. The high rate of convergence of the Padé series with increasing order is demonstrated numerically. This technique is applicable to scalar waves and elastic vector waves propagating in anisotropic unbounded domains of irregular geometry. It can be combined seamlessly with standard finite elements. Copyright © 2006 John Wiley & Sons, Ltd.     

The solution of a mixed boundary value problem in the theory of diffraction

Summary An exact solution is obtained for the problem of the diffraction of a cylindrical sound wave by an absorbent semi-infinite plane. The two faces of the half-plane have different impedance boundary conditions. The problem which is solved is a mathematical model for a noise barrier whose surface is treated with two different acoustically absorbent materials.The usual Wiener-Hopf method (which is the standard technique for solving half-plane problems) has to be modified to give a solution to the present mixed boundary value problem.