Bodies Of Arbitrary Shape Research Articles

Application of the method of moments to acoustic scattering from fluid‐filled bodies of arbitrary shape

AbstractThe method proposed in this paper provides a computational technique for solving acoustic scattering problems associated with arbitrarily shaped two‐ or three‐dimensional fluid‐filled bodies. In particular, using free‐space Green's functions along with the associated boundary conditions on the surface of the body, a pair of coupled integral equations are derived. The equations are then solved by approximating scatterer geometry by either linear segments or triangular patches, for the two‐ or three‐dimensional cases, respectively, and employing the method of moments. The method presented in this work is simple, efficient and applicable to truly arbitrary geometries. Numerical results are presented for certain canonical shapes and compared with other available data.

Estimation of Impact Load by Inverse Analysis : Optimal Transfer Function for Inverse Analysis

The present study is concerned with a method for estimating impact load acting on a body of arbitrary shape. It is known that the impact load can be estimated from the impact response of the body by an inverse analysis. In practical situations, the impact response data involves noise caused by the measurement system. Since the inverse analysis is usually ill-conditioned, such noise tends to be expanded and the estimated impact load is obscured by noise. For solving this problem, we show a method to minimize the mean square error of estimation by applying the Wiener filtering theory. We demonstrate the availability of the present method by numerical simulation on the longitudinal impact of the rod.

Energy absorption mechanism by biological bodies in the near field of dipole antennas above 300 MHz

The energy absorption mechanism in the close near field of dipole antennas is studied by numerical simulations. All computations are performed and validated applying the three-dimensional multiple multipole software package. The numerical model of the plane phantom is additionally checked by accurate as possible experimental measurements. For the plane phantom, the interaction mechanism can be described well by H-field induced surface currents. The spatial peak specific absorption rate can be approximated within 3 dB by a formula given here based on the incident H-field or antenna current and on the conductivity and permittivity of the tissue. These findings can be generalized to heterogeneous tissues and larger biological bodies of arbitrary shape for frequencies above 300 MHz. The specific absorption rate is mainly proportional to the square of the incident H-field, which implies that in the close near field, the spatial peak specific absorption rate is related to the antenna current and not to the input power.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An approximate solution for free convection flows in a thermally stratified porous medium

A simple and sufficiently accurate method for finding the rate of heat transfer for buoyancy-induced flows over bodies of arbitrary shape embedded in a thermally stratified porous medium is given.

On the fluctuations of the Casimir forces. II. The stress-correlation function

For pt.I see ibid., vol.24, p.991 (1991). The quantized Maxwell field in a halfspace exerts stresses on the boundary plane, whose zero-point fluctuations are analyzed for a perfectly-conducting surface. The stress-correlation function on the surface is determined: its Fourier transform with respect to time and distance governs the mean-square deviation of the stress averaged over finite areas (diameters of order a) and over finite times of order T. Conditions guaranteeing physically sensible results are specified on the Fourier transforms of the averaging functions, with a systematic expansion for a/cT<<1, and the first few terms of an asymptotic approximation for a/cT>>1. The small-time behaviour of the surface-averaged correlation function appears to present a paradox which is elucidated. Finally, a very simple expression is found to leading order for the mean-square fluctuating force on perfectly conducting large bodies of arbitrary shape.

Second order wave diffraction around two-dimensional bodies by time-domain method

A time-domain second order method is developed to study the nonlinear wave forces and runupon a surface piercing body of arbitrary shape in two dimensions. The free surface boundary conditions and the radiation condition are satisfied to second order by a numerical integration in time and the field solution at each time step is obtained by an integral equation method based on Green's theorem. The solution is separated into a known incident potential and a scattered potential. The initial condition corresponds to a Stokes second order wave field in the domain, and the scattered potential is allowed to develop in time and space. The stability and numerical accuracy of the proposed solution and the treatment of the radiation condition to second order are discussed. Comparisons of wave forces are made with previous theoretical and experimental results for the case of a semi-circular cylinder with axis at the still water level and a favourable agreement is indicated.

Dynamics of rigid bodies rotating about an arbitrary fixed axis

The definitions of the angular momentum and torque about a fixed point are used to derive the equation of motion of a rigid body rotating about an arbitrary fixed axis. It is shown that the angular momentum (torque) and angular velocity (acceleration) vectors are parallel to each other if the fixed reference point is chosen as follows: (i) for a body of arbitrary shape rotating about a principal axis, to be at the origin of the principal axis coordinate system, which need not be the centre of mass of the rigid body; (ii) for a body rotating about an axis of symmetry, to be anywhere on the axis of rotation; (iii) for a body rotating about an axis perpendicular to the plane of symmetry, to be at the intersection of the axis of rotation with the symmetry plane. The method described is particularly useful as its leads in a natural way to the special case of rigid body rotation about an arbitrary fixed axis.

Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness

A simple and efficient numerical technique is presented to solve the electromagnetic scattering problem of coated conducting bodies of arbitrary shape. The surface equivalence principle is used to formulate the problem in terms of a set of coupled integral equations involving equivalent electric and magnetic surface currents which represent boundary fields. The conducting structures and the dielectric materials are modeled by planar triangular patches, and the method of moments is used to solve the integral equations. Numerical results for scattering cross sections are given for various structures and compared with other available data. These results are proved accurate by a number of representative examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Resonant frequencies of a fluid in containers with internal bodies

A number of problems are solved for the resonant frequencies of oscillation of a fluid in rectangular or circular containers having internal bodies such as surface or bottom-mounted vertical blocks or circular apertures in the top surface. The variation of these frequencies with the dimensions of the bodies is obtained. The method uses matched eigenfunction expansions and Galerkin expansions to derive explicit forms for the elementsSijof a 2×2 matrix required in the course of the solution. An approximate formula for an arbitrary-shaped body in a container which gives good agreement with the more accurate Galerkin approach is used to solve the resonant frequencies when the internal body is a submerged cylinder.

Scattering from multiple conducting and dielectric bodies of arbitrary shape

A simple moment-method solution is presented for the problem of electromagnetic scattering from structures consisting of multiple perfectly conducting and dielectric bodies of arbitrary shape. The system is excited by a plane wave. The surface equivalence principle is used to replace the bodies by equivalent electric and magnetic surface currents, radiating into an unbounded medium. A set of coupled integral equations, involving the surface currents, is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the bodies are approximated by planar triangular patches, and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. Results for the scattering cross sections are presented. The computed results are in very good agreement with the exact solutions and with published data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Measurement of Impact Load by using an Inverse Analysis Technique : Comparison of Methods for Estimating the Transfer Function and its Application to the Instrumented Charpy Impact Test

This paper is concerned with a method for measuring an impact load acting on a body of arbitrary shape. The impact load is determined from the strain response of the body by the deconvolution procedure which is performed in the frequency domain by using Laplace transformation. The transfer function is estimated from the result of the calibration experiment. The deconvolution is one of the ill-posed problems, and it is usually difficult to obtain a good result. In particular, high- frequency noise involved in the measured signal is often expanded to obscure the result. For this problem, we used five estimators of the transfer function and investigated which of them gives the most suitable transfer function for the deconvolution of experimental data. The efficiency of the method is demonstrated by applying it to the instrumentation of the Charpy impact testing machine.

Buoyancy-induced flow of non-Newtonian fluids over a non-isothermal body of arbitrary shape in a fluid-saturated porous medium

The buoyancy-induced flows of non-Newtonian fluids over non-isothermal bodies of arbitrary shape within saturated porous media have been treated using the boundary layer approximations and the power-law model to characterize the non-Newtonian fluid behavior. Upon introducing a general similarity transformation which considers both the geometrical effect and the wall temperature effect on the development of the boundary layer length scale, the governing equations for a non-isothermal body of arbitrary shape have been reduced to those for a vertical flat plate. The transformed equations reveal that a plane or axisymmetric body of arbitrary shape possesses its corresponding family of the wall temperature distributions which permit similarity solutions. Numerical integrations were carried out using the Runge-Kutta-Gill method, and the results of the heat transfer function were presented once for all plane and axisymmetric bodies. As illustrations, local wall heat flux distributions were discussed for wedges, cones, spheres, circular cylinders and other geometries. Furthermore, an approximate formula based on the Karman-Pohlhausen integral relation has been presented for speedy and sufficiently accurate estimation of heat transfer rates.

Measurement of impact load by using an inverse analysis technique. Comparison of methods for estimating the transfer function and its application to the instrumented Charpy impact test.

This paper is concerned with a method for measuring an impact load acting on a body of arbitrary shape. The impact load is determined from the strain response of the body by the deconvolution procedure which is performed in the frequency domain by using Laplace transformation. The transfer function is estimated from the result of the calibration experiment. The deconvolution is one of the ill-posed problems, and it is usually difficult to obtain a good result. In particular, high- frequency noise involved in the measured signal is often expanded to obscure the result. For this problem, we used five estimators of the transfer function and investigated which of them gives the most suitable transfer function for the deconvolution of experimental data. The efficiency of the method is demonstrated by applying it to the instrumentation of the Charpy impact testing machine.

Estimation of Impact Load by Inverse Analysis. Optimal Transfer Function for Inverse Analysis.

The present study is concerned with a method for estimating impact load acting on a body of arbitrary shape. It is known that the impact load can be estimated from the impact response of the body by an inverse analysis. In practical situations, the impact response data involves noise caused by the measurement system. Since the inverse analysis is usually ill-conditioned, such noise tends to be expanded and the estimated impact load is obscured by noise. For solving this problem, we show a method to minimize the mean square error of estimation by applying the Wiener filtering theory. We demonstrate the availability of the present method by numerical simulation on the longitudinal impact of the rod.

Flume confinement effect on diffracted wave field around vertical cylinders

Numerical solutions for a diffracted wave field around a rigid and surface-piercing single circular cylinder, multiple circular cylinders and cylinders of square and rectangular cross-sections, placed vertically in a wave flume, are obtained using the source distribution method. The wave flume confinement effect is introduced by the method of images, considering the fact that the flow field associated with an infinite row of cylinders is equivalent to a single cylinder placed between two parallel vertical walls. The results for a circular cylinder compare well with those of Spring and Monkmeyer [(1975), Interaction of plane waves with a row of cylinders. Proceedings of the 3rd Speciality Conference on Civil Engineering in Oceans, ASCE, University of Delaware, Vol. III, pp. 979–988]. The present method has the advantages that it can be applied to bodies of arbitrary shape and involves less computation than that used by Spring and Monkmeyer [(1975), Interaction of plane waves with a row of cylinders. Proceedings of the 3rd Speciality Conference on Civil Engineering in Oceans, ASCE, University of Delaware, Vol. III, pp. 979–988], which is applicable only to circular cylinders.

On Love wave propagation along the surface of an anisotropic body of arbitrary shape

Love wave propagation is examined along the surface of an anisotropic body of arbitrary shape. An analytic expression is determined for the wave field in the neighborhood of the surface to the accuracy of the principal terms.

A general theory for the motion of a body through a fluid at low Reynolds number

The motion of a body through a viscous fluid at low Reynolds number is considered. The motion is steady relative to axes moving with a linear velocity, U a , and rotating with an angular velocity, Ω a . The fluid motion depends on two (small) Reynolds numbers, R proportional to the linear velocity and T proportional to the angular velocity. The correction to the first approximation (Stokes flow) is a complicated function of R and T ; it is O ( R ) for T ½ ≪ R and O ( T ½ )for T ½ ≫ R . General formulae are derived for the force and couple acting on a body of arbitrary shape. From them all the terms O ( R + T ) or larger can be calculated once the Stokes problem has been solved completely. Some special cases are considered in detail.

A numerical solution for conducting bodies of arbitrary shape

An efficient numerical technique based on a Fourier expansion of the surface current is developed to study the electromagnetic scattering from three-dimensional geometries of arbitrary shape. In this method, the discrete domain representing the structure surface is geometrically represented by two orthogonal contours. One is selected along the intersection of the x–z plane with the object's surface, and the other along the corresponding one in the x–y plane. Entire domain basis functions are selected for the current component in the x–y plane, and subdomain linear basis functions are used to represent the other current component. The method of moments is used to solve the problem numerically. The technique is then applied to study the scattering from discrete surfaces such as squares and rectangles, to compare them with those of the coordinate-transformation technique developed earlier. The behavior of the solutions with the number of modes is investigated to determine their coupling.

A boundary integral equation solution of the stokes flow due to the motion of an arbitrary body near a plane wall with a hole

A boundary integral equation technique is presented for solving the low Reynolds number hydrodynamic interaction of a rigid body with a plane wall and a hole. Such a problem occurs during the process of filtration by a multipore or similar devices. The proposed technique utilizes the Green function of the Stokes equation for the infinite plane wall to eliminate all unknowns on the plane wall. A system of two integral equations is derived, for the stresses on the surface of the body and for the velocity in the hole; this system is later reduced to a single equation. The proposed technique is applicable to a hole and a body of arbitrary shape and no symmetry is required.

Conduction Shape Factor for a Region of Uniform Thickness Surrounding a Three-Dimensional Body of Arbitrary Shape

Conduction Shape Factor for a Region of Uniform Thickness Surrounding a Three-Dimensional Body of Arbitrary Shape