Vibration characteristic analysis of buried pipes using the wave propagation approach

A theoretical analysis for the free vibration of simply supported buried pipes has been investigated using the wave propagation approach. The pipe modeled as a thin cylindrical shell of linear homogeneous isotropic elastic material buried in a linear isotropic homogeneous elastic medium of infinite extent. The vibrations of the pipe are examined by using Flüggle shell equation. The natural frequencies are obtained for the pipes surrounded by vacuo or elastic medium. The results are compared with those available in the literature and agreement is found with them. It is found that the free vibration frequency of the pipe does not appear for some of the axial or circular vibration modes and the real natural frequencies of the pipe are significantly dependent on the rigidity of the surrounding medium.     

Reverberation-ray matrix analysis for wave propagation in multiferroic plates with imperfect interfacial bonding

The dispersion behavior of waves in multiferroic plates with imperfect interfacial bonding has been investigated via the method of reverberation-ray matrix, which is directly established from the three-dimensional equations of magneto-electro-elasticity in the form of state space formalism. A generalized spring-layer model is employed to characterize the interfacial imperfection. By introducing a dual system of local coordinates for each single layer, the numerical instability usually encountered in the state space method can be avoided. Based on the proposed method, a typical sandwich plate made of piezoelectric and piezomagnetic phases is considered in numerical examples to calculate the dispersion curves and mode shapes. It is demonstrated that the results obtained by the present method is unconditionally stable as compared to the traditional state space method. The influence of different interfacial bonding conditions on the dispersion characteristics and corresponding mode shapes is investigated.     

Phenomenological approach on wave propagation in dielectric media with two relaxation times

In this paper dielectric phenomena with two relaxation times are discussed. By assuming a sinusoidal form for induction vector D a sinusoidal electric field is generated and it depends on unknown phenomenological coefficients whose expressions together to their numerical values as functions of frequency are obtained. Moreover, electromagnetic wave propagation is analysed obtaining wave vector as function of the aforementioned coefficients. The results are applied to a Vinylidene Chloride-Vinyl Chloride (VDC-VC) to test the applicability of the model.     

A variational approach for the classical anisotropic Heisenberg model in a crystal field

The variational approach based on the Bogoliubov inequality for the free energy is used to study the three-dimensional anisotropic Heisenberg XXZ model with a crystal field. The magnetization and the phase diagrams are obtained as a function of the parameters of the Hamiltonian. Limiting cases, such as isotropic Heisenberg, XY, and planar rotator models in two and three dimensions, are analyzed and compared to previous results obtained from analytical approximations as well as to those obtained from more reliable approaches such as series expansion and Monte Carlo simulations. A parametric procedure has been used in order to simplify the solutions of the self-consistent coupled equations.     

Pseudo-Hermiticity and electromagnetic wave propagation: The case of anisotropic and lossy media

Pseudo-Hermitian operators can be used in modeling electromagnetic wave propagation in stationary lossless media. We extend this method to a class of non-dispersive anisotropic media that may display loss or gain. We explore three concrete models to demonstrate the utility of our general results and reveal the physical meaning of pseudo-Hermiticity and quasi-Hermiticity of the relevant wave operator. In particular, we consider a uniaxial model where this operator is not diagonalizable. This implies left-handedness of the medium in the sense that only clockwise circularly polarized plane-wave solutions are bounded functions of time.     

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves.Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns.     

Light transmission along a slab waveguide with a core of anisotropic metamaterial

We investigated the dispersion property of a slab waveguide with an anisotropic metamaterial core whose permittivity tensor is partially negative. The subwavelength guidance characteristics are presented based on the boundary conditions. The results show that, at some specific frequencies, many high-order modes can exist in present waveguide even with the thickness of the guiding core 10 times smaller than the working wavelength. It is also found that different orientations of the optical axis of the anisotropic core will lead to different dispersion of the guided modes. If the orientation of the optical axis is properly chosen, the guided modes show a transition from backward wave to a forward wave as the frequency increases. During this transition, the group velocity of some guided modes can approach zero. Since the anisotropic metamaterial we discuss here can be fabricated in GHz, near- and mid-infra-red frequencies, our result may find some applications in wave trapper, integrated optical and nanophotonic devices.     

Slow propagation of plasmonic modes in a symmetrical waveguide containing anisotropic metamaterial

We study the slow propagation of plasmonic modes in a three-layer symmetric waveguide with anisotropic metamaterial claddings and a dielectric core. The dispersion equations for symmetric and anti-symmetric plasmonic modes are derived, and a graphic method is used to verify the zero-group-velocity point on the dispersion curves. Simulation results show the influences of signs of tensors and anisotropy of metamaterial on trapped plasmonic modes.     

Novel properties of wave propagation in biaxially anisotropic left‐handed materials

Some physically interesting properties and effects (including the quantum effects) of wave propagation in biaxially anisotropic left‐handed materials are investigated in this paper: (i) we show that in the biaxially gyrotropic left‐handed material, the left‐right coupling of circularly polarized light arises due to the negative indices in permittivity and permeability tensors of gyrotropic media; (ii) it is well known that the geometric phases of photons inside a curved fiber in previous experiments often depend on the cone angles of solid angles subtended by a curve traced by the direction of wave vector of light, at the center of photon momentum space. Here, however, for the light propagating inside certain anisotropic left‐handed media we will present a different geometric phase that is independent of the cone angles; (iii) the extra phases of electromagnetic wave resulting from the instantaneous helicity inversion at the interfaces between left‐ and right‐handed (LRH) media is also studied in detail by using the Lewis‐Riesenfeld invariant theory. Some interesting applications (e.g., controllable position‐dependent frequency shift, detection of quantum‐vacuum geometric phases and helicity reversals at the LRH interfaces etc.) of above effects and phenomena in left‐handed media is briefly discussed.     

AGSM光束在自由空间中的传输

 用矩阵方法研究了有扭曲的各向异性高斯-尔模型（AGSM）光束通过自由空间的传输。给出了光束参数的解析传输公式和详细数值计算结果，说明AGSM光束的传输特性以及扭曲因子和空间相关长度的影响。     

An alternative solution of the scattering from an anisotropic cylindrical dielectric shell

A method based on the approximate wave functions for anisotropic media and the mode-matching approach is developed to solve the problem of the electromagnetic scattering from an anisotropic cylindrical dielectric shell. The cylindrical shell is assumed to be infinite in length, and it is illuminated by a plane wave or a cylindrical wave from a line source. The problem is two-dimensional and the solutions to both types of polarization (TE and TM) are presented. The validity of this solution is verified by comparing the numerical results with those in literatures and the previous calculations based on the exact wave functions for anisotropic media. Numerical results show the higher computational efficiency of the present method for bounded anisotropic media.     

Appearance of extrema in the frequency shift produced by scattering from a rotational anisotropic particle

We investigate the analytical expression of the spectrum that is produced by scattering of a polychromatic plane light wave incident upon a rotational anisotropic particle. It is found that the appearance of extrema in the frequency shift of the scattered field can be exactly predicted by our derived equations of the rotation angle. Numerical examples are presented to illustrate the theoretical results and also to show the impact of the effective radius of the scattering potential on the frequency shift.     

基于波传播法的周期复合板振动带隙衰减特性研究

运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上, 分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程, 并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明: 周期板结构的振动带隙频率范围与激励方式和激励位置是相关的, 若周期复合板在宽度方向按某阶模态进行线激励, 则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的; 若周期板在点激励作用, 则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集. 此外, 还进一步研究了结构阻尼对振动衰减带隙的影响. 关键词： 周期复合板 带隙衰减特性 波传播法 结构阻尼     

An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems

Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numerical solution validates the discrete counterpart (DMP) of the maximum principle satisfied by the continuous solution. A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse. In this paper, a generalization of the condition, the so-called anisotropic non-obtuse angle condition, is developed for the finite element solution of heterogeneous anisotropic diffusion problems. The new condition is essentially the same as the existing one except that the dihedral angles are now measured in a metric depending on the diffusion matrix of the underlying problem. Several variants of the new condition are obtained. Based on one of them, two metric tensors for use in anisotropic mesh generation are developed to account for DMP satisfaction and the combination of DMP satisfaction and mesh adaptivity. Numerical examples are given to demonstrate the features of the linear finite element method for anisotropic meshes generated with the metric tensors.     

Alternative method for wave propagation within bounded linear media: Conceptual and practical implications

This paper uses an alternative approach to study the monochromatic plane wave propagation within dielectric and conductor linear media of plane-parallel faces. This approach introduces the time-averaged Poynting vector modulus as field variable. The conceptual implications of this formalism are that the nonequivalence between the time-averaged Poynting vector and the squared-field amplitude modulus is naturally manifested as a consequence of interface effects. Also, two practical implications are considered: first, the exact transmittance is compared with that given by Beer's Law, employed commonly in experiments. The departure among them can be significative for certain material parameter values. Second, when the exact reflectance is studied for negative permittivity slabs, it is shown that the high reflectance can be diminished if a small amount of absorption is present.     

An alternative method for plotting dispersion curves

Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves.     

Nonlinear propagation model for ultrasound hydrophones calibration in the frequency range up to 100 MHz

To facilitate the implementation and verification of the new ultrasound hydrophone calibration techniques described in the companion paper (somewhere in this issue) a nonlinear propagation model was developed. A brief outline of the theoretical considerations is presented and the model's advantages and disadvantages are discussed. The results of simulations yielding spatial and temporal acoustic pressure amplitude are also presented and compared with those obtained using KZK and Field II models. Excellent agreement between all models is evidenced. The applicability of the model in discrete wideband calibration of hydrophones is documented in the companion paper somewhere in this volume.     

Reprint of : Connection between wave transport through disordered 1D waveguides and energy density inside the sample: A maximum-entropy approach

We study the average energy – or particle – density of waves inside disordered 1D multiply-scattering media. We extend the transfer-matrix technique that was used in the past for the calculation of the intensity beyond the sample to study the intensity in the interior of the sample by considering the transfer matrices of the two segments that form the entire waveguide. The statistical properties of the two disordered segments are found using a maximum-entropy ansatz subject to appropriate constraints. The theoretical expressions are shown to be in excellent agreement with 1D transfer-matrix simulations.     

DGM-FD: A finite difference scheme based on the discontinuous Galerkin method applied to wave propagation

In this paper we formulate a numerical method that is high order with strong accuracy for numerical wave numbers, and is adaptive to non-uniform grids. Such a method is developed based on the discontinuous Galerkin method (DGM) applied to the hyperbolic equation, resulting in finite difference type schemes applicable to non-uniform grids. The schemes will be referred to as DGM-FD schemes. These schemes inherit naturally some features of the DGM, such as high-order approximations, applicability to non-uniform grids and super-accuracy for wave propagations. Stability of the schemes with boundary closures is investigated and validated. Proposed scheme is demonstrated by numerical examples including the linearized acoustic waves and solutions of non-linear Burger’s equation and the flat-plate boundary layer problem. For non-linear equations, proposed flux finite difference formula requires no explicit upwind and downwind split of the flux. This is in contrast to existing upwind finite difference schemes in the literature.