Scattering by cavities of arbitrary shape in an infinite plate and associated vibration problems

This paper presents a solution for the displacement of a uniform elastic thin plate with an arbitrary cavity, modelled using the biharmonic plate equation. The problem is formulated as a system of boundary integral equations by factorizing the biharmonic equation, with the unknown boundary values expanded in terms of a Fourier series. At the edge of the cavity we consider free-edge, simply-supported and clamped boundary conditions. Methods to suppress ill-conditioning which occurs at certain frequencies are discussed, and the combined boundary integral equation method is implemented to control this problem. A connection is made between the problem of an infinite plate with an arbitrary cavity and the vibration problem of an arbitrarily shaped finite plate, using the jump discontinuity present in single-layer distributions at the boundary. The first few frequencies and modes of displacement are computed for circular and elliptic cavities, which provide a check on our numerics, and results for the displacement of an infinite plate are given for four specific cavity geometries and various boundary conditions.     

Propagation in an elastic wedge using the virtual source technique

The virtual source technique, which is based on the boundary integral method, provides the means to impose boundary conditions on arbitrarily shaped boundaries by replacing them by a collection of sources whose amplitudes are determined from the boundary conditions. In this paper the virtual source technique is used to model propagation of waves in a range-dependent ocean overlying an elastic bottom with arbitrarily shaped ocean-bottom interface. The method is applied to propagation in an elastic Pekeris waveguide, an acoustic wedge, and an elastic wedge. In the case of propagation in an elastic Pekeris waveguide, the results agree very well with those obtained from the wavenumber integral technique, as they do with the solution of the parabolic equation (PE) technique in the case of propagation in an acoustic wedge. The results for propagation in an elastic wedge qualitatively agree with those obtained from an elastic PE solution.     

Reconstruction of a complex-shaped defect from the known arrival time of the reflected ultrasonic wave

The problem of reconstructing the boundary of an arbitrarily shaped defect formed inside an elastic body from the measured time of arrival of the reflected ultrasonic wave in the echo method is considered. The characteristic size of the defect is assumed to be greater than the wavelength, and the defect is irradiated from the far-field zone, which means that the incident wave can be considered as plane. An algorithm is developed for reconstructing the convex envelope of a nonconvex defect from the arrival times of echo signals measured at different angles with the use of circular scanning.     

Boundary element method for bandgap computation of photonic crystals

A boundary element method for computing bandgap structures of two-dimensional photonic crystals is developed. For photonic crystals composed of a square or triangular lattice of parallel cylinders with arbitrarily shaped cross-sections, the boundary integral equations are formulated for a unit cell. Constant boundary elements are adopted to discretize the boundaries. Applying the periodic boundary conditions and the interface conditions, we obtain a linear eigenvalue equation with relatively small matrices. The solution of the eigenvalue equation yields the Bloch wave vectors for given frequencies. The convergence of the method for the desired accuracy and efficiency is examined by some typical numerical examples. It is shown that the present method is efficient and accurate and thus provides a flexible treatment of electromagnetic waves in periodic structures with inclusions of arbitrary shape.     

Scattering of Gaussian beam by arbitrarily shaped inhomogeneous particles

A hybrid finite element-boundary integral method is applied to characterize the scattering of an arbitrarily incident-focused Gaussian beam by arbitrarily shaped inhomogeneous particles. Specifically, the Davis–Barton fifth-order approximation in combination with rotation Euler angles is used to represent the arbitrarily incident Gaussian beams. The finite element method is employed to formulate the fields in the interior region of the inhomogeneous particle, while the boundary integral equation is applied to represent the fields in the exterior region. The interior and exterior fields are coupled by means of the field continuity conditions. To reduce the computational burden, the frontal method and the multilevel fast multipole algorithm are adopted to solve the resultant matrix equation. Numerical results for differential scattering cross sections of several selected inhomogeneous particles are presented and can be served as further study on this subject.     

Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries

An approach to express an incident shaped beam with respect to an arbitrarily oriented spheroidal particle having layers with non-confocal boundaries is presented. To overcome the difficulty of non-confocal boundary conditions connected with different spheroidal coordinate systems, a theoretical procedure is developed to deal with the non-confocal boundary conditions by virtue of a transformation for vector wave functions. The unknown coefficients of scattered and internal electromagnetic fields are determined by solving a system of linear equations derived from the boundary conditions and relations between the spheroidal vector wave functions and spherical ones. Numerical results of the normalized scattering cross section for a two-layered non-confocal prolate spheroid are evaluated. PACS 42.25.Fx; 42.25.Bs     

FREE VIBRATION ANALYSIS OF ARBITRARILY SHAPED PLATES WITH A MIXED BOUNDARY CONDITION USING NON-DIMENSIONAL DYNAMIC INFLUENCE FUNCTIONS

A new approach using the non-dimensional dynamic influence functions has been developed for free vibration analysis of arbitrarily shaped plates with a mixed boundary condition involving both simply supported edges and clamped ones. Since the proposed method is based on the collocation method using one-dimensional and wave-type functions, no integration procedure is needed on boundary edges of the plate of interest and numerical calculation schemes are relatively concise. In order to settle the incompleteness of the system matrix, which is due to the discarding of a complex natural boundary condition at simply supported edges, an additional simple equation is devised by means of using a geometric approximation on curved edges. Finally, verification examples show that a complete system matrix formed in this way successfully gives accurate eigenvalues compared with FEM (ANSYS) and other methods.     

Transverse vibrations of circular plates of varying thickness with non-uniform edge constraints

Free vibrations of circular plates varying in thickness and with flexible edge supports have been studied by several investigators for the restricted case when the supports are represented by uniformly distributed springs of constant stiffness.In the present study an approximate method is presented for dealing with supports possessing rotational flexibility which varies arbitrarily around the boundary.The method consists in representing the varying stiffness in terms of a Fourier expansion in the polar angle and approximately expressing the displacement function using a summation of polynomial co-ordinate functions which exactly satisfies only the essential boundary condition. The Ritz method is then applied in order to obtain the frequency determinant. The method can be easily extended to the forced vibrations case.     

Carpet Cloak Design for Rough Surfaces

Conventional carpet cloak structures have been utilized to conceal the objects located on a planar perfect electric conductor surface. We systematically investigate hiding arbitrarily shaped objects on a rough surface, as a more general and practical scenario. In addition, the required cloak is designed considering different boundary conditions for the surface beneath the object, despite the previous studies. To achieve an invisibility cloak, taking advantage of linear coordinate transformation, a simple homogeneous material is obtained to realize the cloak structure, facilitating the fabrication processes. Numerical simulations validate the performance of the proposed cloaking method. Therefore, the proposed structure is capable of cloaking in more general and complicated scenarios.     

ON THE ROLES OF COMPLEMENTARY AND ADMISSIBLE BOUNDARY CONSTRAINTS IN FOURIER SOLUTIONS TO THE BOUNDARY VALUE PROBLEMS OF COMPLETELY COUPLED r TH ORDER PDES

A heretofore unavailable double Fourier series based approach, for obtaining non-separable solution to a system of completely coupled linear r th order partial differential equations with constant coefficients and subjected to general (completely coupled) boundary conditions, has been presented. The method has been successfully implemented to solve a class of hitherto unsolved boundary-value problems, pertaining to free and forced vibrations of arbitrarily laminated anisotropic doubly curved thin panels of rectangular planform, with arbitrarily prescribed (both symmetric and asymmetric with respect to the panel centerlines) admissible boundary conditions and subjected to general transverse loading.Existing solutions such as those due to Navier or Levy are based on the well-known method of separation of variables. Such solutions represent particular solutions whenever the method of separation of variables work, and when these particular solution functions fortuitously satisfy the boundary conditions. For derivation of the complementary solution, the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives. Such discontinuities form sets of measure zero.Various cases of lamination, geometry and dynamic response (forced and free vibrations) of a class of thin anisotropic laminated shells (curved panels) have been shown to follow from the above. Six sets of boundary conditions are used to illustrate the present method for the derivation of complementary solutions. Navier-type solutions whenever available form special cases of the present general solution.     

Geometry and spectrum of Casimir forces

We present a new approach to the Helmholtz spectrum for arbitrarily shaped boundaries and general boundary conditions. We derive the boundary induced change of the density of states in terms of the free Green's function from which we obtain nonperturbative results for the Casimir interaction between rigid surfaces. As an example, we compute the lateral electrodynamic force between two corrugated surfaces over a wide parameter range. Universal behavior, fixed only by the largest wavelength component of the surface shape, is identified at large surface separations, complementing known short distance expansions which we also reproduce with high precision.     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

Free vibration of polar-orthotropic sector plates

The free vibration of ring-shaped polar-orthotropic sector plates is analyzed by the Ritz method using a spline function as an admissible function for the deflection of the plates. For this purpose, the transverse deflection of a sector plate is written in a series of the products of the deflection function of a sectorial beam and that of a circular beam satisfying the boundary conditions. The deflection function of the sectorial beam is approximately expressed by a quintic spline function, which satisfies the equation of flexural vibration of the beam at each point dividing the beam into small elements. The frequency equation of the plate is derived by the conditions for a stationary value of the Lagrangian. The present method is applied to ring-shaped polar-orthotropic sector plates with some combination of boundary conditions, and the natural frequencies and the mode shapes are calculated numerically up to higher modes. This method is very effective for the study of vibration problems of variously shaped anisotropic plates including these sector plates.     

A Simplified Algorithm for Impedance Calculation of Arbitrarily Shaped Radiators

It is well known that a computationally efficient model for calculation of radiation impedance of an arbitrarily shaped piston has been developed. We simplify the proposed algorithm by using geometric characteristics and intrinsic relationship between the analytic expressions. As an example, the method accuracy is illustrated and the radiation impedance of a right-angled triangular piston is calculated. The numerical results are in good agreement with that obtained directly by the quadruple integral method.     

Research on sound radiation from body in free field

I.IntroductionWhenastructurcvibratcs,itsvibratingsurfacewillmakesurroundingmediummovetogethcrwithit.Ifthernotionissofastthatthcmediumroundthestructureproduccaloca1contractionandcxpansionandthcypropagatefaraway,thesoundradiationisformed.Itispossiblctodcscribeanalytica11ytheradiationfic1dofsimplyandregularlyshapcdsourcessuchaspointsoundsourccs,spherica1soundsourccsandinflnite1engthllnearsoundsourccs,butitisa1mostimpossib1ctosolvetheradiationfiledbyanyanalyt-ica1methodforsourcesofvcrycomplicateds…     

任意复杂流-固边界的格子Boltzmann处理方法

本文提出了一种适用于流固耦合领域中任意复杂边界条件的lattice Boltzmann处理方法.该方法基于half-way反弹模型,在流固耦合处构建了一层虚拟边界,并结合有限差分的方法,获取虚拟边界上的变量值.改进后的方法确保了粒子反弹位置与宏观速度采集点的位置相同,计入了实际物理边界与网格线不重合时,偏移量对计算结果的准确影响,而且其适用范围被扩展到了任意静止或运动、平直或弯曲的复杂边界.文中研究了该方法在Poiseuille流、圆柱绕流和Couette流等经典条件下的边界处理能力,结果表明该方法与理论值符合良好,且当实际物理边界与网格线不重合时,与已发表文献中的结果相比,具有更高的精度.     

空间声场全息重建的波叠加方法研究

提出了基于波叠加法的近场声场全息技术，并将其用于任意形状物体的声辐射分析.在声辐射计算问题中，边界元法是通过离散边界面上的声学和位置变量来实现，而波叠加方法则通过叠加辐射体内部若干个简单源产生的声场来完成.因而，基于波叠加法的声全息就不存在边界面上的参数插值和奇异积分等问题，而这些问题是基于边界元法的声全息所固有的.与基于边界元法的声全息相比较，基于波叠加法的声全息在原理上更易于理解，在计算机上更容易实现.实验结果表明：该种全息技术在重建声场时，具有令人满意的重建精度. 关键词： 声全息 逆问题 波叠加方法 正则化方法     

截面为任意形状无限长螺线管的磁场

应用毕奥一萨伐尔定律计算了截面为任意形状无限长载流螺线管的磁场的磁感应强度,它与截面为圆形的无限长载流螺线管的磁场相同。     

On forced vibrations of composite circular membranes

The problem of the free vibrations of circular membranes consisting of any finite number of concentric parts from different materials has been solved quite generally in our former paper [1]. The present considerations are devoted to some new questions in the field of the forced vibrations of composite circular membranes.