Arbitrary Cross-sectional Shape Research Articles

Stability of fundamental nonlinear guided waves

We determine the stability of nonlinear guided waves, including solitons, nonlinear surface waves, and modes of nonlinear waveguides, by simply reading the familiar dispersion diagram without further calculation. The waveguide can be of arbitrary cross section and arbitrary profile shape and can be composed of arbitrary nonlinear materials distributed nonuniformly. This criterion is the first to our knowledge that is universal for the long-standing problem of stability of fundamental nonlinear guided waves, i.e., waves without nodes. We also show that the transverse stability of planar nonlinear guided fundamental waves demands that the material be self-defocusing in at least some portion of space, whereas planar black solitons are unstable in arbitrary self-defocusing material.

HARMONIC FINITE-ELEMENT THERMOELASTIC ANALYSIS OF SPACE FRAMES AND TRUSSES

A numerical procedure is devised for the thermoelastic analysis of three-dimensional frame- or truss-type space structures exposed to solar radiation. Thin-walled frame or truss members with cross sections of arbitrary shape are considered. Tension-compression, bending, shear, and torsional effects due to the temperature distribution induced by the solar radiation are all taken into account. The procedure proposed involves finite element discretization in the axial direction and a harmonic analysis in the circumferential direction of each member. This procedure is an extension of the one employed previously to obtain the temperature field in trusses. A multibay frame structure serves as a model to demonstrate the performance of the proposed method. The temperature, displacement, and stress fields in the frame are found in various cases.

Alpha-particle losses from toroidicity-induced Alfvén eigenmodes. Part I: Phase-space topology of energetic particle orbits in tokamak plasma

Phase-space topology of energetic particles in tokamak plasma with arbitrary shape of cross section is studied based upon the guiding center theory. Important phase-space boundaries such as prompt loss boundary, trapped passing boundary, and other boundaries between classes of nonstandard orbits (e.g., pinch and stagnation orbits) are studied. This phase-space topology information is applied to the study of anomalous phase-space diffusion due to finite amplitude Alfvén wave fluctuations of energetic particles. The separatrix between trapped and circulating particles contributes dominantly to the losses.

Coupling coefficients of synchronous modes on two arbitrarily-shaped weakly-guiding optical waveguides

Usually, coupling coefficients of parallel weakly-guiding waveguides of arbitrary crosssectional shape with uniform infinite cladding are calculated via two-dimensional overlap integrals of the refractive-index distribution of the concerned waveguide core and the field distributions of the two coupling isolated-core modes. In this paper it is shown that, in the case of synchronous coupled modes, the calculation can be reduced to the evaluation of a line integral involving only the field functions. Convenient formulations are obtained for typical forms of the field representation.

Interface phonons of quantum wires.

We have used the continuum dielectric approach to study the optical-interface-phonon modes of a quantum-wire structure consisting of one material buried within another. Wires with a number of cross-sectional shapes have been studied. Analytical results are presented for wires with elliptical cross sections, of which the circular cross section is a special case. Numerical results using an integral-equation approach are given for wires with arbitrary cross-sectional shapes including rectangles having rounded corners. The dependence of the modes on the wire cross sections and their relation to the vibrational modes of planar quantum wells are discussed. For large wave vectors parallel to the wire or around the wire circumference, the modes are found to approach those of the planar interface. Modes are found to be localized in the corners of the wires or regions of high curvature, and the degree of localization is found to increase with the increasing sharpness of the corners.

Approximate method for calculating the impedances of multiconductors with cross sections of arbitrary shapes

AbstractThis paper proposes an approximate impedance formula of a conductor with an arbitrary cross section, and also a method of approximating the conductor by an equivalent circular conductor. Thus, a multiconductor system consisting of arbitrary cross section conductors is represented by circular cross section conductors, the impedance of admittance of which are evaluated by the existing impedance and admittance formulas.The calculated results by the proposed method agree satisfactorily with measured results and numerical results by a finite‐element method which is, at present, the only way of calculating such impedance, but requires a large computation time and large memory. The proposed method might be very useful in evaluating the impedance and admittance of a multiconductor system consisting of arbitrary cross section conductors.

Boundary-marching method for discontinuity analysis in waveguides of arbitrary cross section

A recursive algorithm previously used in diffusion problems of geophysics and in electrostatics is extended to wave phenomena. It is used to construct a matrix representation for an infinitely long waveguide of arbitrary cross-sectional shape. This representation is used in finite-element analysis of waveguide discontinuities. In numerical tests, scattering matrices for the long guides converge to nearly full word-length in six to seven recursion steps, and discontinuity characteristics are within 1-2% of known results where they exist. >

Research on electromagnetic scattering from partially coated conducting cylinders

In this paper, moment methods are applied to solving the electromagnetic scattering problems (for both E-and H-polarizations) involving partially coated conduching cylinders. The computer programs have been compiled for general use. They can be used to solve the electromagnetic scattering from uncoated, partially coated or entirely coated cylinders of arbitrary cross sectional shape. Numerical examples are also presented to show the validity and versatility of the method.

Beam Theory and Its Suitability for the Analysis of Pipes

The use of the asymptotic expansion technique when applied to the three-dimensional elasticity equations is outlined and used to demonstrate the development of an asymptotic beam theory and associated boundary conditions. The formulation thus obtained holds for arbitrary cross section shapes and is applied here to pipes. It can be used to provide benchmark solutions to test the suitability of engineering beam and shell theories.

Efficiency of single noise barriers

A numerical model is described which enables the sound field in the region of outdoor noise barriers to be calculated by using the boundary element method. The non-uniqueness of solution of the method, producing unreliable results in some conditions, is discussed. The model can be applied to barriers of arbitrary cross-sectional shape and arbitrary distribution of surface cover. The model is two-dimensional, but results are shown to agree well with those obtained for the three-dimensional problem of propagation from a point source over a noise barrier of infinite length. The model is used to compare the efficiency of a wide range of constructions of single noise barriers of different height, cross-sectional shape and surface cover. The effects of the ground cover are also considered. Comparison is made by examining spectra of the insertion loss of the barriers, and also broadband insertion losses for a source with a characteristic A-weighted road traffic noise spectrum. Single-figure estimates are presented of the relative efficiency, in terms of insertion loss, in the deep shadow zone, of a wide range of barrier configurations.

Amplification of obliquely incident seismic waves by cylindrical alluvial valley of arbitrary cross-sectional shape. Part II. Incident SH and rayleigh waves

Amplification of ground motion in three dimensions due to cylindrical alluvial valleys of arbitrary cross section is investigated in this paper. The incident wave is either a plane SH or Rayleigh wave, propagating at an arbitrary angle to the axis of the valley. A hybrid numerical method combining boundary integral representation and finite element discretization has been employed. Numerical results show significant amplification depending on the angles of incidence and geometries of the valleys.

The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross-sectional shape

The general Kirchhoff theory of sound propagation in a circular tube is shown to take a considerably simpler form in a regime that includes both narrow and wide tubes. For tube radii greater than rw=10−3 cm and sound frequencies f such that rwf3/2<106 cm s−3/2, the Kirchhoff solution reduces to the approximate solution suggested by Zwikker and Kosten. In this regime, viscosity and thermal conductivity effects are treated separately, within complex density and complex compressibility functions. The sound pressure is essentially constant through each cross section, and the excess density and sound pressure (when scaled by the equilibrium density and pressure of air, respectively) are comparable in magnitude. These last two observations are assumed to apply to uniform tubes having arbitrary cross-sectional shape, and a generalized theory of sound propagation in narrow and wide tubes is derived. The two-dimensional wave equation that results can be used to describe the variation of either particle velocity or excess temperature over a cross section. Complex density and compressibility functions, propagation constants, and characteristic impedances may then be calculated. As an example, this procedure has been used to determine the propagation characteristics for a tube of rectangular cross section.

Bounds on Heat Transfer in a Periodic Graetz Problem

It is proven that the heat transfer coefficient and rate of decay of temperature with distance in a fully developed Graetz problem with temporally periodic inlet temperature are greater than or equal to the corresponding quantities in the corresponding steady Graetz problem. The proof is valid for arbitrary duct cross-sectional shapes and for either constant temperature, constant heat flux, or linearized radiation boundary conditions. A numerical solution of the energy equation demonstrates the validity of the theorem. The utility of the result is discussed in the context of heat exchanger design for pulsed gas lasers.

Nonlinear dynamic buckling of thin-walled beam-columns under ground excitations

A new analysis technique has been developed to study the non-linear elastic mode interaction in thin-walled beam columns under ground excitation. The technique is capable of handling arbitrary cross-sectional shapes and end conditions. In the analysis of P - Δ effects in the building frames, the technique incorporates the instantaneous loss of stiffness due to local buckling of the individual plates in a rational and convenient manner. The latter is achieved via use of the finite-strip technique which is found to be extremely efficient in the local and post-local buckling analysis of prismatic plate structures. The overall behaviour is modelled by a one-dimensional finite element in which the effects of local buckling are appropriately incorporated. It is observed that moment frames lose stability at an axial load significantly lower than the static buckling load, even for moderate levels of earthquake.

Diffraction tomography of strongly scattering infinite cylindrical objects of arbitrary cross-sectional shape

A new method for imaging an infinite cylindrical object with arbitrary cross-sectional shape, without any small-perturbation approximations, is proposed. In this method, the well-known integral equation equivalent to the inhomogeneous Helmholtz wave equation is discretized. The discretized equation expresses the scattered pressure field at any point in terms of the samples of the product of the unknown object function and the unknown pressure field present inside the object. Based on this relation, simultaneous equations are set up, relating these samples to the samples of the pressure field measured outside the object. By requiring the measurement points to lie on circles around the object, these equations are solved efficiently using the fast Fourier transform (FFT). From the product samples thus obtained, the samples of the unknown object function are extracted by means of a second set of FFT calculations. Details of illustrative computer simulations for the case of an elliptic cylinder are described.

Green's function approach to propagation in fibres of arbitrary cross section

An attempt has been made to obtain a formally exact solution, based on Green's function of the scalar wave equation for step-index fibres of arbitrary cross-sectional shape. The wave functions in the core and cladding are expanded in a series of basis functions (appropriate to cylindrical coordinates), and the expansion coefficients along with the characteristic equation of the problem are derived in a matrix notation. Compared with the earlier similar treatments of the problems, the present formalism is very general in the sense that it does not assume any special symmetry property of the cross-sectional curve or of the underlying solutions. The theory is applied to fibres that are only slightly deformed about a circular shape. Explicit algebraic and (or) numerical results are obtained for the allowed propagation constants, fields, and the group delay of a few low-ordered modes.

Finite element simulation of complex jets in a crossflow for V/STOL applications

The paper presents a prediction method for the flowfield and surface pressure distribution induced by three-dimensional jets injected from a flat surface into a crossflow. An eddy viscosity model extended from Prandtl's concept has been developed to account for the curved nature of the jets with arbitrary cross-sectional shape. The first-order influence of the fluctuating nature of the turbulent flow is reflected via axial turbulence information. The Reynolds-averaged, Navier-Stokes equations are solved using the finite-element method, and the penalty function method is used to discretize the pressure in a consistent manner. The eight-noded, isoparametric finite element is used to approximate the computational domain and the field variables. The performance of the present prediction method is verified for a single circular jet in a crossflow at R = 4, which has enough measured data available for detailed comparisons. The jet trajectory and axial velocity decay comparison are excellent, and the surface pressure distribution is well predicted except for the wake region right behind the jet. The same methodology is then applied to single- and dual-rectangular jets in a crossflow at the same velocity ratio, and most of the important features of the surface pressure distribution are predicted well. The general observation is that the entrainment process due to the turbulent mixing is modeled reasonably through a generalized eddy viscosity concept supported by an axial turbulence intensity correlation, and the agreement achieved here between the prediction and existing measured data is considered good for a three-dimensional, turbulent flow of this complexity.

Linear flood routing model for rapid flow

The linear flood routing model presented has been derived from the linearized St. Venant equation for the case of a uniform open channel with arbitrary cross-sectional shape and friction law. In order to filter out the downstream boundary condition the kinematic wave solution is used to approximate the diffusion term in the St. Venant equation. The hydrodynamic model obtained is called the rapid flow model (RFM). It provides the exact solution for a Froude number equal to one. Such characteristics of the RFM impulse response as cumulants, amplitude and phase spectra are analysed, and then compared with those of the complete linearized St. Venant equations for different reach lengths, values of Froude number and frequencies of flood waves. The RFM can be applied for mountainous rivers that have large Froude numbers and both quick and slow rising waves.

A consistent theory for torsion of thin-walled bars

A consistent theory for torsion of thin-walled bars with cross-sections of arbitrary shape (open, closed or mixed) is developed in this paper; it is an improvement on the classical torsion theory of thin-walled bars. All the basic relations, formulas and equations are derived and proved under the consistent assumptions. A torsional stiffness matrix for thin-walled bar elements is also formulated on the basis of the consistent theory. A computer program has been written which is applicable to the practical use of torsional analysis of thin-walled bar structures with arbitrary cross-sections.

Extending the effective index method for arbitrarily shaped inhomogeneous optical waveguides

A procedure for computing the propagation constant and field distribution for modes of dielectric waveguides with arbitrary cross-sectional shape and refractive index profile is described. This procedure, based on the effective index method, can be applied to a wide range of problems. The authors compare their results with those obtained by other methods for a circular dielectric waveguide with parabolic index profile.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>