The Mode Spectrum of a Parallel-Plate Chirowaveguide

We study the complicated behavior of the dispersion curves of eigenmodes of a parallel-plate chirowaveguide with identical (electric) or mixed (nonidentical) conducting walls, which results from multiple crossovers of the curves corresponding to two sets of modes and undergoing a bifurcation at the cutoff frequency. We find the total number of crossover points in each modal pair, including both propagating and evanescent waves. The asymptotic behavior of the dispersion curves in the high-frequency domain is determined.     

Acoustics of shells

We discuss the physical phenomena that arise in the scattering of acoustic waves from fluid-immersed elastic (metal) shells which may be either evacuated or filled with the same or with a different fluid. The phenomena occurring here include the formation of circumferential (peripheral, or “surface”) waves that circumnavigate the shells, propagating either as elastic waves in the shell material or as fluid-borne waves of the Scholte-Stoneley type in the external or the internal fluid. By phase matching along a closed circuit, these waves may lead to prominent resonances in the acoustic scattering amplitude, and we demonstrate how the set of observed resonance frequencies is related to the dispersive phase velocities of the surface waves, so that one can be determined from the other. In addition, we discuss how the dispersion curves (phase velocity plotted vs. frequency) of the various types of surface waves show repulsion phenomena due to their coupling through the boundary conditions. The cases of spherical and cylindrical shells are investigated here as typical examples, and as an introductory topic we additionally mention surface waves on plates where related phenomena also occur. Both the theoretical and the experimental aspects of the present subject will be considered, including the experimental visualization of the surface waves.     

平行光子晶体波导的传输特性及应用

采用时域有限差分法研究两平行光子晶体波导的传输特性及模场分布,利用耦合模理论计算光子晶体波导的耦合系数。计算结果表明,在不同的频率范围内两平行光子晶体波导之间表现出不同的耦合特性:在高频段(0.32~0.44)(ωa/2πc)的范围内两直波导表现出相互的能量交换,实现光耦合,耦合系数随入射波 频率增加而减小;而在低频段(0.29~0.32)(ωa/2πc)的范围内,两波导的传输谱图几乎重合。最后,提出一种采用固定波导耦合长度同时实现光分束及光均分器的方案,当耦合长度取34a时,可将频率为0.333 (ωa/2πc)和 0.357(ωa/2πc)的两入射波分束传播,同时将低频段中的任意频率波进行能量均分。     

Coupled flexural,longitudinal and shear wave motion in two- and three-layered damped beams

The purpose of this paper is to show how a ceramic layer attached to a two-layered (elastic/viscoelastic) beam alters the wave propagation mechanism in the beam. The ceramic layer is assumed to possess mass but not longitudinal stiffness. Shear deformation, rotatory, longitudinal and transverse inertia forces are all included in the analysis. The equations of motion of the layered beam are derived by using the virtual work principle. Relevant dispersion curves for an infinite beam are presented and discussed, and are compared with dispersion curves obtained from a number of simplified theories. The influence of the inertia coupling between different wave types, caused by the ceramic layer, has been examined. The loss factors of the different waves are found to be critically dependent upon the inertia coupling and wave-number in particular wave-number regions. This occurs when uncoupled waves of different types have close wave-speeds. Under these circumstances a coupled wave can exist which has much less damping than any of its constituent uncoupled waves.     

压电网络复合板的波动特性与隔声性能分析

在压电网络复合板机电耦合波动方程基础上,首先对在其中传播的弯曲波的波动特性进行了分析,发现压电网络复合板中同时存在两种不同频散特性的弯曲波,电感电阻并联型压电网络复合板中存在的两种弯曲波的频散曲线具有频率转向现象;在频率转向区,弯曲波的衰减常数或达到最大或迅速增大这一结论为压电网络复合板的减振降噪设计提供了参考。对压电网络复合板中的能量分析给出了这一结论的机理:即在频率转向区板中的机械能与电能能够进行最大的能量交换;在波动分析的基础上对压电网络复合板的隔声特性进行了分析,发现压电网络复合板隔声曲线上的低谷随外界电感值的变化能够发生移动或者消失,最后结合压电网络复合板的波动频散特性对复合板的隔声机理进行了分析,为设计压电网络复合板的隔声性能提供了理论参考。      

Finite element analysis of guided waves in fluid-filled corrugated pipes

Free wave propagation in fluid-filled corrugated pipes is analyzed using finite element methods in combination with a wave-based approach. By combining discretized models with a wave-based approach, complex mechanism of wave motion in the three-dimensional waveguide is fully included. The pipes are treated as waveguides having periodic properties in the direction of wave propagation. The analysis of these guided waves leads to dispersion curves which show the strong frequency-dependency of the different wave modes. The method also allows the inclusion of coupling between fluid-borne and structure-borne wave modes which occur at the acoustic-structure interface. Phase and group velocities of the wave modes are derived in postprocessing steps. Additionally, the energy ratio of the fluid-domain and solid-domain vibrational energies is computed. Finally, linear damping models are included in order to explore wave mode attenuation.     

Hybridization of acoustic waves in piezoelectric plates

The interaction (hybridization) of different types of acoustic waves of zero and higher orders propagating in lithium niobate piezoelectric plates is theoretically investigated. Different crystallographic orientations of the plates and different directions of wave propagation in them are considered. It is shown that, for an electrically free plate with the propagation direction along any of the crystallographic axes, the dispersion curves have intersection points and hybridization is absent. However, when the propagation direction slightly changes or when one of the plate surfaces is short-circuited, the dispersion curves separate and the waves become coupled. A quantitative coefficient characterizing the degree of wave hybridization with allowance for both mechanical and electric coupling is introduced. It is shown that the dependence of this coefficient on the product of the plate thickness by the wave frequency determines the extent of separation of the dispersion curves of interacting waves. The phenomenon under study is of both fundamental and practical interest, for example, in connection with the problem of an efficient excitation of nonpiezoactive acoustic waves in piezoelectric plates.     

Optimum coupling and efficiency of dye lasers

Evanescent waves and fields play an important role in microwaves, quantum mechanics, optics and elastic waves. Because electromagnetic waves in waveguides have dispersion characteristics similar to those of a unidimensional de Broglie wave, there is a close analogy between quantum mechanical tunneling and the transition through an attenuating sector of a waveguide. Microwave “evanescent mode” filters, quantummechanical tunneling resonance and optical frustrated total internal reflection filters are compared in light of this analogy. The flowgraph technique and “unit real” function representation are shown to be effective in discussing the interdependence of incident and reflected waves in various locations in multilayered structures. In electrognetic and elastic waves, the role of evanescent waves is significant in the case of incident beams of limited extent. The role of equivalent circuits of transverse resonance is discussed in the context of oscillatory natural modes determining the character of propagating fields.     

Numerical investigation of dispersion relations for helical waveguides using the Scaled Boundary Finite Element method

In this paper, the dispersion properties of elastic waves in helical waveguides are investigated. The formulation is based on the Scaled Boundary Finite Element method (SBEFM). With a set of orthogonal unit basis introduced as the contravariant basis, the helical coordinate is firstly considered, where components of tensor retain the dimension of original quantity. Based on the strain–displacement relation, the eigenvalue matrix is obtained about wavenumbers and frequencies. The cross section of the waveguides is discretized by using high-order spectral elements. Moreover, the formulated linear matrix is utilized to design efficient and accurate algorithms to compute the eigenvalues of helical waveguides. Compared with the Pochhammer–Chree curves, the convergence and accuracy of the SBFEM are discussed. Finally, we give some dispersion curves for a wide range of lay angles and analyze in detail properties of cut-off frequency, mode separation and mode transition for elastic wave propagation in the helical waveguides.     

2维电感加载和电容加载传输线介质板中的隧道效应

 分析了平面电压波与一对2维电感加载传输线和电容加载传输线介质板的相互作用,在共轭匹配的条件下,推导出了传输线介质板内外的电压分布,并着重讨论了倏逝波和传播波波数的取值方法。仿真结果显示,这对介质板前面的电压幅度和相位与后面的电压幅度和相位是相同的,这说明了电压波的每一个空间傅里叶成分,包括电压传播波和电压倏逝波,能够完全通过这对共轭匹配板,表明在板中存在很强的隧道效应。     

Modulation instability of wave packets in the presence of linear and nonlinear mode coupling

Conditions for modulation instability of a wave packet consisting of two codirected linearly coupled waves propagating in a light guide with Kerr-type nonlinearity are formulated. The development of the instability with regard to light guide parameters, linear and nonlinear mode coupling, and input power is analyzed for symmetric and antisymmetric light guide excitations. Unlike in single-mode light guides, here modulation instability may arise in the frequency ranges of normal material dispersion and at the zero perturbation frequency.     

Harmonic Green's functions for flexural waves in semi-infinite plates with arbitrary boundary conditions and high-frequency approximation for convex polygonal plates

This paper provides a method for obtaining the harmonic Green's function for flexural waves in semi-infinite plates with arbitrary boundary conditions and a high frequency approximation of the Green's function in the case of convex polygonal plates, by using a generalised image source method. The classical image source method consists in describing the response of a point-driven polygonal plate as a superposition of contributions from the original source and virtual sources located outside of the plate, which represent successive reflections on the boundaries. The proposed approach extends the image source method to plates including boundaries that induce coupling between propagating and evanescent components of the field and on which reflection depends on the angle of incidence. This is achieved by writing the original source as a Fourier transform representing a continuous sum of propagating and evanescent plane waves incident on the boundaries. Thus, the image source contributions arise as continuous sums of reflected plane waves. For semi-infinite plates, the exact Green's function is obtained for an arbitrary set of boundary conditions. For polygonal plates, a high-frequency approximation of the Green's function is obtained by neglecting evanescent waves for the second and subsequent reflections on the edges. The method is compared to exact and finite element solutions and evaluated in terms of its frequency range of applicability.     

Guided wave dispersion curves for a bar with an arbitrary cross-section,a rod and rail example

Theoretical and experimental issues of acquiring dispersion curves for bars of arbitrary cross-section are discussed. Since a guided wave can propagate over long distances in a structure, guided waves have great potential for being applied to the rapid non-destructive evaluation of large structures such as rails in the railroad industry. Such fundamental data as phase velocity, group velocity, and wave structure for each guided wave mode is presented for structures with complicated cross-sectional geometries as rail. Phase velocity and group velocity dispersion curves are obtained for bars with an arbitrary cross-section using a semi-analytical finite element method. Since a large number of propagating modes with close phase velocities exist, dispersion curves consisting of only dominant modes are obtained by calculating the displacement at a received point for each mode. These theoretical dispersion curves agree in characteristic parts with the experimental dispersion curves obtained by a two-dimensional Fourier transform technique.     

Generalized thermoelastic waves in homogeneous isotropic plates

The propagation of thermoelastic waves in homogeneous isotropic plate subjected to stress-free and rigid insulated and isothermal conditions is investigated in the context of conventional coupled thermoelasticity (CT), Lord-Shulman (LS), Green-Lindsay (GL), and Green-Nagdhi (GN) theories of thermoelasticity. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms are derived. It is shown that the motion for SH modes gets decoupled from the rest of the motion and remains unaffected due to thermo-mechanical coupling and thermal relaxation effects. The phase velocities for SH modes have also been obtained. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases from the derived secular equations. At short wavelength limits the secular equations for symmetric and skew-symmetric waves in a stress-free insulated and isothermal plate reduce to Rayleigh surface waves frequency equations. Finally, the numerical solution is carried out for aluminum-epoxy composite material and the dispersion curves for symmetric and skew-symmetric wave modes are presented to illustrate and compare the theoretical results.     

Energy-momentum quanta in Fresnel's evanescent wave II

Four generalisations of results appearing in a previous paper, referred to as I, are here produced. (1) Formulas for the field strengths of the evanescent wave generated inside a vacuum sandwiched between two identical refracting media propagating symmetrical incident plane waves; the classical exponential damping factor being then replaced by hyperbolic cosines or sines (according to the field components), an extremely close approximation to a plane tachyon wave is thus obtained; (2) Compact formulas for the case where the evanescent wave is generated by a superposition of plane incident waves with propagation vectors k parallel to a common incidence plane; (3) Compact formulas for the other typical case where the dispersion on k is parallel to the reflecting plane; (4) Formulas for refraction and total reflection of a photon with a non-zero rest mass.We take the opportunity of this paper to review briefly various articles that had escaped us, where a transverse energy flux inside Fresnel's evanescent wave was discussed, and also some recent papers dealing with quantisation of the evanescent wave or related topics.     

Nonlinear waves and shocks in a rigid acoustical guide

A model is developed for the propagation of finite amplitude acoustical waves and weak shocks in a straight duct of arbitrary cross section. It generalizes the linear modal solution, assuming mode amplitudes slowly vary along the guide axis under the influence of nonlinearities. Using orthogonality properties, the model finally reduces to a set of ordinary differential equations for each mode at each of the harmonics of the input frequency. The theory is then applied to a two-dimensional waveguide. Dispersion relations indicate that there can be two types of nonlinear interactions either called "resonant" or "non-resonant." Resonant interactions occur dominantly for modes propagating at a rather large angle with respect to the axis and involve mostly modes propagating with the same phase velocity. In this case, guided propagation is similar to nonlinear plane wave propagation, with the progressive steepening up to shock formation of the two waves that constitute the mode and reflect onto the guide walls. Non-resonant interactions can be observed as the input modes propagate at a small angle, in which case, nonlinear interactions involve many adjacent modes having close phase velocities. Grazing propagation can also lead to more complex phenomena such as wavefront curvature and irregular reflection.     

Linear Analysis of Obliquely Propagating Longitudinal Waves in Partially Spin Polarized Degenerate Magnetized Plasma

Linear analysis of low frequency obliquely propagating electrostatic waves in a partially spin polarized degenerate magnetized plasma is presented. Using Fourier analysis, a general linear dispersion relation is derived for low frequency electrostatic lower hybrid(LH) wave, ion acoustic(IA) wave and ion cyclotron(IC) wave in the presence of electron spin polarization. It is found that the electron spin polarization gives birth to a new spin-dependent wave(spin electron acoustic wave) in the spectrum of these waves. Further, the electron spin polarization also causes drastic shifts in the frequency spectrum of these waves. These effects would have a strong bearing on wave phenomena in degenerate astrophysical plasmas.     

Full Wave Edge Accounting Analysis of Waves in Infinite Array of Stub-loaded Rectangular Waveguides

Eigenwave analysis is given to an infinite array of stub-loaded rectangular waveguides using the method of moments (Galerkin’s scheme), with the basis functions explicitly satisfying the rectangular-edge condition. The numerical data on propagation constants and field structure for different modes are presented as a function of geometrical parameters and frequency. The emphasis is on the groove dominant wave. In particular, its radiation loss is shown to be effectively controlled by adding some asymmetry to the groove geometry. Wave mode coupling effects have been revealed between the groove dominant wave and the planar waveguide section waves. The so-called Morse critical points of the dispersion equation are identified within the coupling domains.     

A coaxial 2D-periodic perforated directional coupler

We propose to couple two coaxial waveguides by 2D periodic perforation in the common wall in order to ensure selective coupling between two waves propagating in these waveguides. In the experiment at a frequency of 10 GHz, the H ₀₁ mode of the internal waveguide was converted to the rotating H ₅₁ mode of the external waveguide with a power loss of several percent.