Distribution of guided mode power flow between the layers of circular and elliptical multilayer optical fibers

An invariant expression in the form of a contour integral for guided mode power flow via an arbitrary area of the cross section of an optical fiber with constant permittivity is presented in polar and elliptical coordinates. Expressions for guided mode power flows via the cross sections of circular and elliptical multilayer optical fibers are obtained.     

Finite amplitude pressure field of elliptical and rhomboid transducers in three dimensions

Design of different type of transducers to enhance image quality by forming narrow beams at the principals of nonlinear acoustics is considered in the paper. Thus, the nonlinear pressure fields of elliptical and rhomboid transducers were simulated in three dimensions. The simulation method presented in this study is based on Aanonsen’s model for circular sources, and closely follows the model that recently explored for the nonlinear wave propagation due to square and rectangular sources in three dimensions [Kaya et al. “Pressure field of rectangular transducers at finite amplitude in three dimensions,” Ultrasound in Med. Biol., vol. 32, no. 2, pp. 271–280, 2006]. It is assumed that elliptical and rhomboid sources are plane sources, and driven at 2.25 MHz fundamental frequency. Typical results of nonlinear acoustical pressure field simulation are presented there in three dimensions for elliptical and rhomboid sources and compared with the results for rectangular source. The similarities and differences between the nonlinear pressure field of rectangular, elliptical and rhomboid sources are discussed. The numerical results show that diffraction effects and acoustical beam cross section depend on the source geometry a lot. It is noticeable that the nonlinear pressure field of a rectangular source has a broader beam profile than elliptical and rhomboid source.     

部分潜入水中任意形状等截面柱体的振动分析

本文研究部分潜入水中的任意形状等截面柱体的弯曲自由振动问题,应用Fourier级数匹配法,提供了一个精确计算这类柱水耦联系统振动特性的解析方法,结果可由计算机解出。本文最后取水中椭圆柱体为例,给出了一些具体的数值计算结果。     

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.     

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.     

Stress Concentration Near Stiff Cylindrical Inclusions under Anti-Plane Shear Loading

Doklady Physics - Analytical solutions for the problems of stress concentration near cylindrical inclusion with circular or elliptical cross section under the anti-plane shear loading are...     

One-dimensional longitudinal-torsional vibration converter with multiple diagonally slitted parts

For increasing the available vibration velocity of the one-dimensional longitudinal-torsional vibration converter, a new type of complex vibration converter with multiple slitted parts installed in the positions avoiding longitudinal nodal positions along the converter for decreasing the maximum vibration stress level at the vibration nodal part was studied. The free end of the converter vibrates in an elliptical or circular locus. Complex vibration systems with elliptical to circular or rectangular to square loci can be applied effectively for various high-power applications, including ultrasonic welding of metal or plastics, ultrasonic wire bonding of IC, LSI and electronic devices, and also ultrasonic motors. The converter with multiple slitted parts was improved in the vibration stress level and the quality factor compared with the converter with single slitted part.     

不同振动模式下颗粒分离行为的数值模拟

利用三维离散元法对垂直方向上的直线、圆和椭圆振动模式颗粒分离过程进行了数值模拟研究,对直线振动时上层大颗粒的波动及圆和椭圆振动时出现的聚集、循环等现象的形成机理进行了分析,并讨论了振动强度对各振动模式下颗粒分离形态的影响规律. 研究表明,综合运用空隙填充、侧面驱动的颗粒运动和能量非均匀分布三种机理,并结合颗粒群的速度矢量分布情况能够较好地解释各振动模式下的颗粒分离行为. 振动强度对圆和椭圆振动模式的分离形态具有显著的影响,并在振动强度约为3时,各种振动模式均具有良好的颗粒分离效果和稳定的颗粒运动状态.     

不同振动模式下颗粒分离行为的数值模拟

利用三维离散元法对垂直方向上的直线、圆和椭圆振动模式颗粒分离过程进行了数值模拟研究,对直线振动时上层大颗粒的波动及圆和椭圆振动时出现的聚集、循环等现象的形成机理进行了分析,并讨论了振动强度对各振动模式下颗粒分离形态的影响规律. 研究表明,综合运用空隙填充、侧面驱动的颗粒运动和能量非均匀分布三种机理,并结合颗粒群的速度矢量分布情况能够较好地解释各振动模式下的颗粒分离行为. 振动强度对圆和椭圆振动模式的分离形态具有显著的影响,并在振动强度约为3时,各种振动模式均具有良好的颗粒分离效果和稳定的颗粒运动状态. 关键词： 振动模式 颗粒分离 离散元法 数值模拟     

Free vibrations of elastic circular toroidal shells

In this paper, the free vibrations of elastic in vacuo circular toroidal shells under different boundary conditions are studied using the linear Sanders thin shell theory. Beam functions are used to describe the motion along the meridional direction whilst trigonometric functions are used to represent the deformation of the cross section. It is shown that both the natural frequencies and the mode shapes can be accurately predicted as long as the employed beam functions satisfy the boundary conditions at the ends of the shells. The dependence of the free vibration characteristics of an elastic toroidal shell upon boundary conditions and toroidal to cross-sectional radius ratio is also illustrated and explained in this paper.     

Propagation properties of anomalous hollow beams in a turbulent atmosphere

Propagation of circular and elliptical anomalous hollow beams in a turbulent atmosphere is investigated in detail. Based on the extended Huygens–Fresnel integral, analytical formulae for the average irradiance of circular and elliptical anomalous hollow beams propagating in a turbulent atmosphere are derived. The irradiance and spreading properties of circular and elliptical anomalous hollow beams in a turbulent atmosphere and in free space are studied numerically. It is found that circular and elliptical anomalous hollow beams at short propagation distance in turbulent atmosphere have similar propagation properties to those of free space, while at long propagation distance, circular and elliptical anomalous hollow beams eventually become circular Gaussian beams in a turbulent atmosphere, which is much different from their propagation properties in free space. The conversion from an anomalous hollow beam to a circular Gaussian beam becomes quicker and the beam spot spreads more rapidly for a larger structure constant, a shorter wavelength and a smaller waist size of the initial beam.     

Finite Element Analysis of the Field Patterns in Elliptical Waveguide

In this paper, finite element method is first used to discuss the field patterns in a hollow perfectly conducting pipe with elliptical cross section. The electrical field lines of the dominant TE mode as well as the magnetic field lines of the lowest TM mode are presented. The results are the same with literatures, and also give a correction to the field pattern of the lowest TM mode in elliptical waveguide.     

Multi-scale bending,buckling and vibration analyses of carbon fiber/carbon nanotube-reinforced polymer nanocomposite plates with various shapes

Using a finite element-based multi-scale modeling approach, the bending, buckling and free vibration of hybrid polymer matrix composites reinforced by carbon fibers and carbon nanotubes (CF/CNT-RP) are analyzed herein. Thick composite plates with rectangular, circular, annular and elliptical shapes are considered. First, the equivalent material properties of CF/CNT-RP are calculated for different volume fractions of CF and CNT. To accomplish this aim, a two-step procedure is presented through which the coupled effects of nano- and micro-scale are taken into account. In the first step, modeling of dispersion of CNTs into the polymer matrix is done with considering interphase formed by their chemical interaction with the matrix, and the equivalent properties of resulting composite material are determined accordingly. CFs are then dispersed into CNT-RP which is considered a homogenous material in this step. Both distributions of CNTs and CFs are assumed to be random. After computing the equivalent properties of CF/CNT-RP for different volume fractions of its constituents, the bending, buckling and free vibration analyses of plates with different shapes are performed. It is shown that the reinforcement of the polymer matrix with both CF and CNT significantly affects the bending, buckling and free vibration characteristics of plates.     

Surface magnetostatic oscillations in elliptical bubble domains

A theory of surface magnetostatic oscillations in magnetic bubble domains with an elliptical cross section is presented. The dependences of the eigenfrequencies of resonant modes on the applied magnetic field are analyzed for a barium hexaferrite sample with allowance made for the change in the domain size due to a variation in the bias magnetic field. The range of frequency tuning in response to a magnetic field ranging from the elliptical instability field to the collapse field is estimated. It is demonstrated that elliptical bubble domains can be used as microminiature resonators operating in the millimeter range.     

Configurations of high-frequency ultrasonics complex vibration systems for packaging in microelectronics

Ultrasonic high-frequency complex vibrations are effective for various ultrasonic high-power applications. Three types of ultrasonic complex vibration system with a welding tip vibrating elliptical to circular locus for packaging in microelectronics were studied. The complex vibration sources are using (1) a longitudinal-torsional vibration converter with diagonal slits that is driven only by a longitudinal vibration source, (2) a complex transverse vibration rod with several stepped parts that is driven by two longitudinal vibration source crossed at a right angle and (3) a longitudinal vibration circular disk and three longitudinal transducers that are installed at the circumference of the disk.     

Transverse and torsional complex vibration systems for ultrasonic seam welding of metal plates

Transverse and torsional complex vibration systems for ultrasonic seam welding of metal plate specimens, using a 27 kHz complex vibration disk welding tip vibrating in transverse and torsional vibration modes, were studied. Using a complex vibration welding system with a welding tip vibrating in elliptical or circular locus, thick plate specimens can be welded with a more uniform and larger area compared to a conventional ultrasonic welding system. The disk welding tip vibrates in an elliptical or circular locus. The complex vibration system can continuously weld multiple parts of metal plate specimens such as heat sinks with a large number of fins.     

Scattering from an elliptical cylindrical plasma for electromagnetic waves with wavelength much greater than the dimensions of the plasma cross-section

The distribution of the electric potential inside and outside a cold plasma column with elliptical cross-section when electromagnetic waves scatter from it are obtained. It is assumed that the wavelength of incident wave is much greater than the dimensions of the cross section of the plasma column. The electrical potential inside and outside a magnetized elliptical plasma column for an anisotropic scattering process are obtained. The graphs of the ratio of the electric field inside the plasma and the incident electric field versus the incident angle, the geometrical dimension of the elliptical plasma column and cyclotron frequency are presented separately. Finally, scattering of the same waves from an elliptical cylindrical inhomogeneous isotropic cold plasma is also investigated.     

Pressure potential and stability analysis in an acoustical noncontact transportation

Near field acoustic traveling wave is one of the most popular principles in noncontact manipulations and transportations. The stability behavior is a key factor in the industrial applications of acoustical noncontact transportation. We present here an in-depth analysis of the transportation stability of a planar object levitated in near field acoustic traveling waves. To more accurately describe the pressure distributions on the radiation surface, a 3D nonlinear traveling wave model is presented. A closed form solution is derived based on the pressure potential to quantitatively calculate the restoring forces and moments under small disturbances. The physical explanations of the effects of fluid inertia and the effects of non-uniform pressure distributions are provided in detail. It is found that a vibration rail with tapered cross section provides more stable transportation than a rail with rectangular cross section. The present study sheds light on the issue of quantitative evaluation of stability in acoustic traveling waves and proposes three main factors that influence the stability: (a) vibration shape, (b) pressure distribution and (c) restoring force/moment. It helps to provide a better understanding of the physics behind the near field acoustic transportation and provide useful design and optimization tools for industrial applications.     

Effects of structural factors on filtering operation of photonic band gap air bridges with circular and square shape holes

Applying the finite element analysis on the photonic band-gap materials with a cavity at the center for two types of structures, circular and square shape holes with the same cross section, filtering operation of these structures is simulated and compared. Any variations in the structure parameters, such as cavity length, period and hole dimensions, change the transmission peak and frequency bandwidth of these structures. The effects of rotation of square holes and ellipticity of circular holes on filtering operation are studied. Other new structures such as tapered, shortened and non-uniform rotated structures are proposed and filtering characteristics of them are discussed. It is found that, by rotating the square holes around their axis, it is possible to have a blue-shift in the transmission peak wavelength without notable variations in the filter peak and bandwidth. It is concluded that the increase of elliptical holes diameters length causes the decrease of transmission peak and increase of bandwidth with blueshift of the peak wavelength. This shift is larger for one of the elliptical diameter values considered that is along the waveguide length.     

Transmission loss predictions for dissipative silencers of arbitrary cross section in the presence of mean flow

A numerical technique is developed for the analysis of dissipative silencers of arbitrary, but axially uniform, cross section. Mean gas flow is included in a central airway that is separated from a bulk reacting porous material by a concentric perforate screen. The analysis begins by employing the finite element method to extract the eigenvalues and associated eigenvectors for a silencer of infinite length. Point collocation is then used to match the expanded acoustic pressure and velocity fields in the silencer chamber to those in the inlet and outlet pipes. Transmission loss predictions are compared with experimental measurements taken for two automotive dissipative silencers with elliptical cross sections. Good agreement between prediction and experiment is observed both without mean flow and for a mean flow Mach number of 0.15. It is demonstrated also that the technique presented offers a considerable reduction in the computational expenditure when compared to a three-dimensional finite element analysis.