Wave propagation in axially polarized piezoelectric hollow cylinders of sector cross section

In this paper, the problem of electroelastic waves propagating in piezoelectric hollow cylinders of sector cross section is studied for the case when the boundary surfaces of sector cut are covered by non-extensible membranes. The three-dimensional linear equations of motion for the piezoelectric cylinder are analytically integrated and different boundary conditions on the cylindrical surfaces yield frequency equations, which relate the frequencies of elastic waves to their wavenumbers. Numerical results for waveguides with various boundary conditions are presented to illustrate the approach. Analysis of the dispersion spectra is carried out, and cutoff frequencies are obtained and characterized; mode asymptotic behavior and amplitude distributions of wave characteristics are analyzed. The main effects of their transformation by variation of the angular measure and the ratio of inner and outer radii are discussed. The results obtained are in good agreement with the results for the special case of a hollow semicircular cylinder.     

Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section

We extend the design of radially symmetric invisibility cloaks through transformation optics as proposed by Pendry et al. [Science 312, 1780 (2006)] to coated cylinders of an arbitrary cross section. The validity of our Fourier-based approach is confirmed by both analytical and numerical results for a cloak displaying a non-convex cross section of varying thickness. In the former case, we evaluate the Green's function of a line source in the transformed coordinates. In the latter case, we implement a full-wave finite-element model for a cylindrical antenna radiating a p-polarized electric field in the presence of a F-shaped lossy object surrounded by the cloak.     

Three-dimensional vibration analysis of a torus with circular cross section

The free vibration characteristics of a torus with a circular cross section are studied by using the three-dimensional, small-strain, elasticity theory. A set of three-dimensional orthogonal coordinates system, comprising the polar coordinate (r, theta) at each circular cross section and the circumferential coordinate phi around the ring, is developed. Each of the displacement components u(r), v(theta), and w(phi) in the r, theta, and phi directions, respectively, is taken as a product of the Chebyshev polynomials in the r direction and the trigonometric functions in the theta and phi directions. Eigenfrequencies and vibration mode shapes have been obtained via a three-dimensional displacement-based extremum energy principle. Upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions. The eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross-sectional radius are investigated in detail. Very accurate eigenfrequencies and deformed mode shapes of the three-dimensional vibration are presented. All major modes such as flexural thickness-shear modes, in-plane stretching modes, and torsional modes are included in the analysis. The results may serve as a benchmark reference for validating other computational techniques for the problem.     

170 GHz缓变截面开放式谐振腔传播特性模拟

在数值计算方法的基础上,编程模拟了高次模式TE31,12模在传统及改进型开放式缓变截面谐振腔的传播特性,计算了开放式缓变截面谐振腔的绕射品质因数,研究了改进型缓变截面谐振腔连接段的曲率半径对绕射品质因数的影响。结果表明,连接段曲率半径越大,绕射品质因数值越小。为了证明结论的正确性,利用仿真软件HFSS对另一工作于低次模TE0,1模的改进型缓变截面谐振腔进行仿真计算,并和编程计算结果比较,也得到了同样的结论。     

Wave propagation in beams with anti-symmetric piezoelectric shunting arrays

Piezoelectric shunting arrays are employed to control the wave propagation in flexible beams. Contrary to conventional symmetric configuration, a substrate beam with anti-symmetric shunting arrays is investigated by adapted transfer matrix method. Compared with symmetric scheme, the anti-symmetric one demonstrates some distinctive characteristics.Primarily, the longitudinal and flexural waves are coupled, so they are correlated and must be considered simultaneously.Moreover, the attenuation of flexural wave is much stronger in anti-symmetric scenario, while the longitudinal wave demonstrates the converse side. As a result, the anti-symmetric scheme can be utilized to improve the vibration isolation capability of shunting arrays. Finally, the theoretical analyses are validated by finite element simulations.     

Spontaneously moving solitons in a cavity soliton laser with circular section

We show that in a cavity soliton laser based on a VCSEL with a saturable absorber the solitons can spontaneously move if the ratio of the carrier lifetimes in the amplifier and in the absorber takes appropriate values. The velocity is determined by the parameters of the system. In devices with a finite circular cross section the solitons move on circular trajectories along the boundary. This dynamical regime can be exploited to create trains of pulses with controlled intensity, frequency and wherein a determined delay can be applied.     

Radar cross section of the cavity with a loaded metal diaphragm

We propose a method for calculating the monostatic radar cross section of a two-dimensional cavity containing a plane-layered medium in the form of a loaded metal diaphragm which is located between two dielectric layers. The method is based on the modal technique and dyadic Green’s functions. The numerical results for the angular dependences of the radar cross section are presented for various parameters of the plane-layered medium. Limitations of the method and the possibilities of its further development are pointed out. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 320–327, April 2008.     

Radar cross section of a complex-shaped cavity with a loaded metal diaphragm

We propose a method for calculating the monostatic radar cross section of a two-dimensional complex-shaped cavity, which contains a plane-layered medium in the form of a loaded metal diaphragm placed on a dielectric layer. The method is based on the combined boundary-integral/modal method and the variational Galerkin method with the use of dyadic Green’s functions. The results of calculating the angular dependences of the radar cross section for various parameters of the plane-layered medium are presented. Restrictions of the applicability and potential for further development of the method are indicated.     

Differential cross section of inelastic electron scattering on a boson with arbitrary spin

A general formula is obtained for the differential cross section for the electrical generation of a boson at a boson of any spin. The case where the bosons in the initial and final states differ is considered. The boson electromagnetic peak is parametrized by physical form factors analogous to the Sachs form factors for nucleons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 76–79, December, 1977.     

Resistive MHD-equations for Tokamaks with arbitrary β and cross section

The complete set of hydromagnetic equations for the vector potential A and the momentum density a ≡ ?ν is transformed into a form appropriate for toroidal geometry. The toroidal components are represented by the usual poloidal flux functions Ψ and ψ, respectively, for which the equations of motion are derived. The poloidal components A_⊥ and a_⊥ are given by four potentials $\text{Φ}$, U, and φ, u for which we obtain Poisson equations in the poloidal plane. The corresponding source terms define the remaining variables, namely, $\text{Λ = ? · A, Ω = (? × A)}{}_{\mathrm{\zeta }}\text{/R, λ = ? · a, and ω = (? × a)}{}_{\mathrm{\zeta }}\text{/R}$, for which equations of motion are also derived. Finally, we find that in the limit of small toroidicity the scaling laws previously used are not applicable for toroidal geometry, and that the effort to obtain numerical solutions is not dramatically higher than without using any scaling law.     

Wave propagation in an infinite piezoelectric crystal under a thermal field

The paper deals with the propagation of vibrational waves in an infinite piezoelectric crystal plate belonging toC ₂ (monoclinic system) when some sort of heat flow is maintained. The dispersion equations have been determined under a thermal field and also in the case when the heat flow is absent, both for small and large values of the frequency.The authors express their sincere thanks for the helpful criticism of the referee in improving the paper.     

Stability and vibration of a helical rod with circular cross section in a viscous medium

The stability and vibration of a thin elastic helical rod with circular cross section in a viscous medium are discussed. The dynamical equations of the rod in the viscous medium are established in the Frenet coordinates of the centreline with the Euler angles describing the attitudes of the cross section as variables. We have proved that the Lyapunov and Euler conditions of stability of a helical rod in the space domain are the necessary conditions for the asymptotic stability of the rod in the time domain. The free frequencies and damping coefficients of torsional and flexural vibrations of the helical rod in the viscous medium are calculated.     

黏性介质中圆截面弹性细杆的平面振动

讨论圆截面弹性细杆在黏性介质中的平面振动. 基于Kirchhoff理论，以杆中心线的Frenet坐标系为参考系，建立其动力学方程，杆中心线为任意平面曲线时，其扭转振动与弯曲振动解耦. 讨论两端固定条件下任意形状杆的平面扭转振动，以及无扭转的轴向受压直杆和圆环杆的平面弯曲振动，导出其自由振动频率和阻尼系数. 证明空间域内压杆的Lyapunov稳定性和欧拉稳定性条件为时域内渐近稳定性的充分必要条件，或无阻尼压杆的稳定性必要条件. 圆环杆平衡恒满足渐近稳定性条件. 关键词： 弹性细杆 黏性介质 扭转振动 弯曲振动     

Analysis of dielectric waveguide structure of arbitrary cross section

A class of dielectric waveguide structures of arbitrary cross section in conjuction with one or more layer dielectrics is ana lysis with the Method of Lines(MOL). This leads to an eigenvalue problem where the nonphysical and spurious modes do not appear. Dispersion characteristic examples are calculated for structures suitable for mm waves and optical integrated circuits. Such as ridge guides, guide, and so on. The numerical examples are verified by results available from other methods.     

Analytic method of arbitrary cross section open groove guide

Groove guide is one of the waveguides that have been used at millimeter and submillimeter waveband. This paper analyzes arbitrary groove guides by means of the eigen-weighted boundary integral equation method that uses the eigenfunctions of a fictitious regular boundary as weighting functions. In comparison with the theoretical and experimental results published, the numerical results for rectangular, circular and V-groove guides using this method are exact enough with fast convergence and less calculation.The Project Supported by National Natural Science Foundation of P.R. China