This paper presents a mathematical model of nonlinear supersonic flutter of viscoelastic shells. To describe the strain processes in shallow shells, the Boltzmann-Volterra integral model is used. Based on linear integral models in geometrically nonlinear formulations, equations of nonlinear oscillations of shallow shells are derived. The Koltunov-Rzhanitsyn kernel is used as a relaxation kernel. The equations of motion of shallow shells after applying the Bubnov-Galerkin method in axial coordinates are reduced to solve a system of nonlinear integro-differential equations (IDE) with variable coefficients relative to the time function. The IDE solution is found numerically using quadrature formulas.
One of the main problems in the theory of partial differential equations is the study of equations of mixed type. the modified Cauchy problem for some values of α is stated and investigated. The equations of the mixed type began to be studied systematically, after FI Frankl indicated their applications to the problems of transonic and supersonic gas dynamics. In this regard, the purpose of this work was to find out whether it is possible to find a more convenient form of representation of the solution of the Cauchy problem for a differential equation, with the help of which it would be possible to solve boundary value problems for a mixed type equation of both parabolic-hyperbolic and elliptic-hyperbolic types. The modified Cauchy problem for some values of α is stated and investigated. A convenient representation of the generalized solution of the modified Cauchy problem is obtained.
One of the characteristic features of the development of the hereditary theory is the wide possibilities for describing the dynamic processes of deformation of various materials. However, due to the lack of an adequate mathematical apparatus, the implementation of these possibilities is in many cases difficult, especially when studying nonlinear dynamic processes. In recent years, the power of computing has increased interest in nonlinear problems. Under these conditions, it is important to create and develop such effective methods of solution that could be applied to the widest possible class of problems. In this work, a mathematical model of the problem of the dynamics of thin-walled structures is constructed taking into account the hereditary properties of the material. Using the Bubnov-Galerkin method under various boundary conditions, the problem under consideration is reduced to solving systems of integro-differential equations. The analysis of the influence of various properties of the construction material on the amplitude-frequency characteristics is carried out.
The operation of Bradley's algorithm is simple. After that, we divide the image into several areas alongside d, take the average value of the sum of the values of Im pixels in this area, add the value, and compare the value of each pixel with the obtained result. 1/8 of the image width and 15% of the average pixel brightness across the area. In general, both of these parameters can and should be changed according to the specific situation. Thus, if the size of the object is larger than the area of a square with a side equal to d, then the center of this object can be taken as the background by the algorithm, and the problem is solved by reducing the value of d, but fine details of the image may be lost. This article provides an overview of some research and image processing analysis on the problem of crop and vegetation image recognition. Remote identification of crops and plants and their cultivation, assessment of horticulture status startup projects are presented. A computer vision system for obtaining images from a drone and assessing the condition of a garden is provided. Digitization methods for data processing are considered.
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