Characterizations for the family of functions classes {B^r_p,q,N} and their connection with Besov’s spaces

In this paper we define families of classes of functions related to best approximations in harmonic intervals. These families of function classes characterize the order of approximation of functions by trigonometric polynomials with a spectrum from harmonic intervals. The article contains an investigation of various characterizations of the indicated families of function classes, introduces imbedding theorems, and shows the connection between the introduced families of functions classes and the classical Besov spaces. The article is intended for researchers specializing in the theory of approximation and functional analysis, and all those whose interests lie in these areas

On the finite element method for calculation of rectangular plates

The article is devoted to the study of bending problems for rectangular plates, which are of great applied importance and are found everywhere in various branches of science and technology. The calculation of plate bending is performed by the finite element method. In this article the structure of the method for calculating the deformed and stress state of a rectangular finite element of the plate is described, their main components are highlighted; the classical approach of calculating rectangular plates is characterized. The mathematical apparatus of the calculation is presented in the volume necessary for calculating the plates. This article is focused mainly on mechanics, physicists, engineers and technical specialists

On the calculation of the rectangular finite element of the plate

The article is devoted to the study of the thin plate bending by the finite element method. The application of the finite element method to solving the problem of the plate bending leads to the necessity of studying the rectangular finite element of the plate. All deformation and statics characteristics of the plate are functions of the displacement in the direction of the normal to the middle surface of the plate, which is determined by the deflection function. In the article, the formation of the plate deflection function in explicit form is carried out. The ways for finding the deflection function by division of the variables in the equilibrium equation of the plate, through an incomplete fourth - degree polynomial and in the form of Hermite polynomials are presented. The article is focused mainly on mechanics, engineers and scientific employees of technical specialties

On mathematical and analytical methods for solving problems on vibrations of membranes and plates

The problems about determination of the frequencies and forms of natural vibrations of plates and shells lead to the necessity of partial differential equations integration. The well - researched cases are those where it is possible to separate the variables. In particular, these include the vibrations of a rectangular plate hinged on opposite sides, umbrella and fan vibration of circular axisymmetric plates and vibrations of cylindrical shells, closed or hinged along generating curves. In this work, the vibration of a flat homogeneous membrane is investigated for the general case of boundary conditions

On the calculation of rectangular plates by the collocation method

The article is devoted to the application of the collocation method to solving differential equations, which are the basis for calculating many problems of mechanics. In this article the structure of this method is presented, its main components are highlighted; its types are characterized, as well as its classical approaches. The research of the problem of rectangular plates bending is carried out by the method of collocations in this article. The collocation method, like all numerical - analytical approximate methods, has a number of advantages and disadvantages, which are also noted in this article. The article is focused mainly on mechanics, engineers and technical specialists