Numerical and Analytical Investigations of Nonlinear Synthesis Problems of Antenna with the Flat Radiating Aperture

The review article contains results of researches of the synthesis problems of radiating systems with incomplete input information arising in particular during optimal design of radio, acoustic or other types of radiating systems (RS) by the given requirements to energy characteristics of radiated field. In mathematical terms, these tasks are reduced to study and nume­rical solution of one class of two-dimensional nonlinear integral equations of Hammerstein type that depend on two real para­meters. It was established that a characteristic feature of this class of equations is nonuniqueness and the branching (or bifur­cation) of existing solutions. Methods of solving two-parametric nonlinear spectral problem, which is necessary to finding the set of points of branching are proposed. Algorithms and numerical methods for the finding of branching solutions are built and founded. Numerous examples of specific synthesis problems are presented.

Five Position Synthesis of a Slider-Crank Function Generator

In this paper, we present a synthesis procedure for the coupler link of a planar slider-crank linkage in order to coordinate input by a linear actuator with the rotation of an output crank. This problem can be formulated in a manner similar to the synthesis of a five position RR coupler link. It is well-known that the resulting equations can produce branching solutions that are not useful. This is addressed by introducing tolerances for the input and output values of the specified task function. The proposed synthesis procedure is then executed on two examples. In the first example, a survey of solutions for tolerance zones of increasing size is conducted. In this example we find that a tolerance zone of 5% of the desired full range results in a number of useful task functions and usable slider-crank function generators. To demonstrate the use of these results, we present an example design for the actuator of the shovel of a front-end loader.

Steady and Transient Analyses of Natural Convection in a Horizontal Porous Annulus With the Galerkin Method

Steady and transient analytical investigation with the Galerkin method has been performed on natural convection in a horizontal porous annulus heated from the inner surface. Three families of convergent solutions, appearing one after another with increasing RaDa numbers, were obtained corresponding to different initial conditions. Despite the fact that the flow structures of two branching solutions are quite different, there exists a critcal RaDa number at which their overall heat transfer rates have the same value. The bifurcation point was determined numerically, which coincided very well with that from experimental observation. The solutions in which higher wavenumber modes are dominant agree better with experimental data of overall heat transfer.