Ring-shaped Plate Research Articles

ANALYTICAL METHOD FOR CALCULATING ANNULAR PLATES ON A VARIABLE ELASTIC BASE

The paper considers the application of the method of direct integration to calculations of annular plates and slabs on a continuous variable elastic base. Ring-shaped plates with variable geometric and mechanical parameters are increasingly used. Not only the elastic base, but also the plate thickness and cylindrical stiffness can be variable parameters here. The need for an analytical method for calculating such structures raises no doubts, since it makes it possible to evaluate the accuracy of finite-element analysis. To date, there are no proposals in the literature regarding a general analytical method for the calculation of annular plates on a variable elastic base. A detailed description of the algorithm of the direct integration method is not given in the paper, and all the calculation formulas for the annular plate are taken from the authors' already published article. The results of numerical implementation of this algorithm for specific examples are considered: a concrete plate, which is rigidly pinch on the inner contour, and its outer contour is free, and a steel plate, which is rigidly pinch on the outer contour, and its inner contour is free. To estimate the results of calculation by the author's method, computer modeling of the considered structures in PC LIRA-SAPR and their calculations by the finite-element method have been executed. The foundation reaction is described by Winkler model with a variable bedding factor. In the first case a bed factor is assumed constant, and in the second case it changes under the linear law. Calculations have shown that discrepancy between deflections calculated by the finite-element method and the author's method does not exceed 1 %, and the results of radial and circumferential moments calculation differ more considerably, amounting to 10 %. The authors explain this difference by the inaccuracy of the numerical analysis associated with the semi-automatic method of constructing a finite-element mesh, which should be made finer. The densification of the mesh in the manual mode of its partitioning significantly reduces the discrepancy between the results of calculating the deflections, radial and circumferential bending moments by the finite-element method and the author's method.

Development of a wind turbine driven by longitudinal vortex: Wind tunnel experiment to investigate the basic characteristics of the wind turbine using a single circular cylinder blade

In this study, the basic rotation and output torque characteristics of a longitudinal vortex wind turbine (LV-WT) were investigated by using a wind tunnel experiment. This wind turbine uses a circular cylinder with a diameter d as the driving blade, and a ring-shaped plate with width w ​= ​d is installed behind the cylinder blade with a gap s. A steady lift force to sustain the rotational motion is generated by the longitudinal vortex formed near the intersection of the cylinder blade and the ring plate. The gap ratio s/d is the most dominant parameter for the performance of the LV-WT, and the output torque and efficiency are maximum at s/d ​= ​0.35. A wider ring plate and flanges attached to the blade are promising techniques to improve the performance of the LV-WT. The lift coefficient Cl is approximated by a decreasing linear function of the velocity ratio λ = (rotational velocity V)/(free flow velocity U), as predicted in the preceding numerical study of the authors. Using the drag coefficient determined by the loaded experiment, the performance characteristics of LV-WT are predicted for the widely varying conditions.

A longitudinal vortex wind turbine: Numerical study

The longitudinal vortex wind turbine (LV-WT) is a new windmill concept which uses circular cylinders as the turbine blades and not Magnus rotors. The driving force is produced by the longitudinal vortex (LV). A ring-shaped plate is installed behind the circular blades for employing the LV. In this study, the aerodynamic mechanism of the LV-WT system is numerically investigated using the unsteady Reynolds-averaged Navier-Stokes (URANS) simulation. A small model of the two blades is evaluated in a wind tunnel for comparison with the CFD results. The computational and experimental predictions correlate very well with only a small difference. The numerical visualizations show the vortical structure near the crossing includes the necklace vortex (NV) and the trailing vortices (TVs). The driving force (lift) is produced due to the longitudinal vortex induced suction-flow in the leading region. The distributions of the aerodynamic force coefficients are continuously evaluated along the blade length in order to examine the 3D effects of the LV, and visualizing the flow fields around the system is employed to discuss the aerodynamic reasons. Cross-flow over a stationary isolated-cylinder is also simulated to compare the mechanism by visualizing the limiting streamlines on the cylinder surface.

Depth profiles of oxygen precipitates in nitride-coated silicon wafers subjected to rapid thermal annealing

Silicon wafers, coated with a silicon nitride layer and subjected to high temperature Rapid Thermal Annealing (RTA) in Ar, show—upon a subsequent two-step precipitation anneal cycle (such as 800 °C + 1000 °C)—peculiar depth profiles of oxygen precipitate densities. Some profiles are sharply peaked near the wafer surface, sometimes with a zero bulk density. Other profiles are uniform in depth. The maximum density is always the same. These profiles are well reproduced by simulations assuming that precipitation starts from a uniformly distributed small oxide plates originated from RTA step and composed of oxygen atoms and vacancies (“VO2 plates”). During the first step of the precipitation anneal, an oxide layer propagates around this core plate by a process of oxygen attachment, meaning that an oxygen-only ring-shaped plate emerges around the original plate. These rings, depending on their size, then either dissolve or grow during the second part of the anneal leading to a rich variety of density profiles.

A low profile post‐type monopole antenna with a ring and four small posts

AbstractThis article presents a low profile wideband top‐loading monopole antenna with a ring and four small post‐shape plates. And an inserted ring‐shaped plate makes a gap from the post element and leads to enhance wider and higher gain than the conventional top‐loading monopole. Four small post‐shape plates also lead to obtain higher antenna gain, uniformity radiation patterns. Moreover, top‐load also leads to reduce the height of antenna (a small antenna size). The experimental impedance bandwidth is approximately 1.55–2.73 GHz (% bandwidth is 55.14%) below with VSWR ≤2.0. This antenna also presents a wideband, a uniformity radiation patterns characteristic, respectively. The proposed antenna can be applied PCS, DCS, IMT‐2000, WLL. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52:910–912, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25086

Motion planning and open loop control design for linear distributed parameter systems with lumped controls

Motion planning and open loop boundary control schemes for linear spatially one dimensional distributed parameter systems with lumped control are discussed. Using Mikusiński's operational calculus the models are formulated as ordinary (operational) boundary value problems. Their solutions are parameterized by introducing a so-called basic variable as an appropriate free parameter. Particular classes of models considered lead to series representations involving derivatives of the basic variable of arbitrary order or to convolution operators which can be interpreted as distributed delays and advances. Examples of bending motions on a ring-shaped plate and a heat exchanger illustrate the results.

A low profile wideband top-loading monopole antenna with a ring-shaped plate

This paper presents a low profile wideband top-loading monopole antenna with ring-shaped plate. The ring-shaped plate is used to enhance the impedance matching and to increase the antenna gain, due to the low radiation resistance in the usable band. That is, an additional ring-shaped plate allows us to obtain multiband and omnidirectional patterns. Moreover, top-loading also allows us to reduce the height of the antenna for a small-size antenna. We experimentally 53.3% (1.6200–2.6867 GHz) bandwidths with VSWR ≤ 2.0. This antenna also obtains a wideband and high-gain characteristics. The proposed antenna can be applied to PCS, DCS, IMT-2000, and WLL. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1458–1460, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21731

Hydroelastic Behavior of a Floating Ring-Shaped Plate

The interaction between incident surface water waves and floating elastic plate is studied. This paper considers the diffraction of plane incident waves on a floating flexible ring-shaped plate and its response to the incident waves. An analytic and numerical study of the hydroelastic behavior of the plate is presented. An integro-differential equation is derived for the problem and an algorithm of its numerical solution is proposed. The representation of the solution as a series of Hankel functions is the key ingredient of the approach. The problem is first formulated. The main integro-differential equation is derived on the basis of the Laplace equation and thin-plate theory. The free-surface elevation, plate deflection and Green’s function are expressed in polar coordinates as superpositions of Hankel and Bessel functions, respectively. These expressions are used in a further analysis of the integro-differential equation. The problem is solved for two cases of water depth infinite and finite. For the coefficients in the case of infinite depth a set of algebraic equations is obtained, yielding an approximate solution. Then a solution is obtained for the general and most interesting case of finite water depth analogously in the seventh section. The exact solution might be approximated by taking into account a finite number of the roots of the plate dispersion relation. Also, the influence of the plate’s motion on wave propagation in the open water field and within the gap of the ring is studied. Numerical results are presented for illustrative purposes.

Waveguide properties of a plane ring-shaped plate. I. flexural waves

A new type of the so-called “angular” waves for flexural normal modes propagating in a ringshaped plate is studied. A dispersion equation for wave numbers, an equation for critical frequencies, and expressions for the eigenfunctions of such a waveguide are derived. Solutions to these equations are obtained by numerical methods for various values of parameter d, which represents the relative width of the ring. The solutions are analyzed, and the main properties of dispersion curves are described. Individual normal modes are identified on the basis of the calculation and further analysis of eigenfunctions.

Barotropic instability of a boundary jet on a sloping bottom

Abstract The stability of a shear flow on a sloping bottom in a homogeneous, rotating system was investigated by means of a laboratory experiment. The basic flow was driven near a vertical wall of a circular container by a ring-shaped plate that contacted with a free surface of the working fluid and rotated relative to the fluid container. The velocity profile was asymmetric in the radial direction and had only one inflection point. The velocity profile was well expressed by a linear theory for the vertical shear layer. The effect of the circular geometry was checked by comparing experimental results obtained in two fluid systems in which only the sign of the curvature was opposite and it was confirmed that circular geometry was not essential for the shear flow on the sloping bottom in this experiment. It was found that the sloping bottom stabilizes the basic flow only when the drift direction of the topographic Rossby wave is opposite to that of the basic flow. The viscous dissipation in both the Ekman layer and the interior region was also important in determining the critical Rossby number. The eddy fields caused by the instability can be classified into two types: One is the stationary eddy field in which a row of eddies moves along the basic flow without changing form. The other is the flow pattern in which eddies have finite life times and their configuration is not well organized. When the sloping bottom does not stabilize the basic flow, the former flow pattern is realized, otherwise the latter flow pattern appears. The wave numbers of the eddies in the regular flow pattern were observed as a function of the Rossby number. The relation did not fit to linear preferred modes predicted by an eigenvalue problem.

Free flexural vibrations of a ring-shaped plate bounded by confocal ellipses

This paper studies free flexural vibrations of a confocal elliptical ring-shaped plate using Mathieu functions and modified Mathieu functions which are solutions of the differential equation of motion. We give the procedure leading to the frequency equations by making use of the orthogonal property of Mathieu functions in order to satisfy the boundary conditions. Some numerical results are shown graphically in comparison with experimental ones.

Stability of a ring-shaped plate with a small hole

Stability of a ring-shaped plate with a small hole

Forced Vibrations of a Circular Plate

Abstract A solution is presented for the response of a clamped, circular plate to the action of an arbitrarily placed, harmonically oscillating, transverse, concentrated force. The method may be extended to a variety of loading and boundary conditions and can also be applied to ring-shaped plates.

Closure to “Discussions of ‘Bending of Circular and Ring-Shaped Plates on an Elastic Foundation’” (1954, ASME J. Appl. Mech., 21, p. 415)

Closure to “Discussions of ‘Bending of Circular and Ring-Shaped Plates on an Elastic Foundation’” (1954, ASME J. Appl. Mech., 21, p. 415)

Bending of Circular and Ring-Shaped Plates on an Elastic Foundation

Abstract This paper develops a method for the evaluation of deflections, moments, shears, and stresses of a circular or ring-shaped plate on an elastic foundation under transverse loads. A series solution is derived for plates subjected to edge and/or concentrated loads and is given in terms of tabulated functions. It is exact within the assumptions underlying the classical theory of plates and includes, as a particular case, the known solution of the corresponding radially symmetric problem. Two examples displaying radial asymmetry are worked. A solution is given for (a) a circular plate resting on an elastic foundation, clamped at the boundary and subjected to an arbitrarily placed concentrated load, and (b) a plate of infinite extent, resting on an elastic foundation and clamped to the boundary of a rigid circular disk to which a pure moment is applied.

Concentrated-Force Problems in Plane Strain, Plane Stress, and Transverse Bending of Plates

Abstract A general method is described for the solution of problems of transverse bending of thin plates acted on by concentrated normal forces, and of problems of plane stress or plane strain, in which concentrated forces are applied to the boundaries. The solution is taken in two parts: (a) The special functions which give the stresses or deflections in the neighborhood of the concentrated forces. (b) A complementary function, satisfying the appropriate biharmonic equation, such that the complete solution satisfies the boundary conditions of the problem. For certain types of boundaries, this complementary function can be determined by expanding the concentrated-force functions as infinite trigonometric series. Then by addition of general solutions of the appropriate biharmonic equation, the required boundary conditions may be satisfied. The method is first illustrated by solving the plate-bending problem, for which the solution is known, of a clamped circular disk loaded by a transverse force at any point. It is then applied to the problem of an infinite plate fixed at an inner circular boundary, with outer edge free, and loaded by a transverse force at any point. This solution is obtained in finite form, and typical curves of deflection, bending moments, and shear forces are given in Figs. 3 to 8, inclusive. Using this result, solutions are next obtained for ring-shaped plates of finite outer radius, with the force applied either at the outer edge or at any point between the inner clamped edge and the outer free edge. The former case was previously solved by H. Reissner. Curves comparing the maximum moments and shears in the infinite plate with those of the annular plate with force either at the outer edge, or inside the ring are given in Figs. 9 to 12, inclusive. Finally, a solution is given of the problem in plane stress of a large plate containing an elliptical hole, which is loaded by line forces at the ends of the minor axes of the ellipse. Curves showing results of this solution are given in Figs. 14 and 15.