Testing and Diagnostics of Carbon Polymer Composite Materials by Radio Wave Method Used in Aircraft Construction

The article is devoted to the applicability of radio wave methods of testing and diagnostics of aviation composites for newly launched products. The description of the measurement process is also considered by the method of integral equations.

Stress Concentration in Bounded Compositeplates with Carbon Reinforcement

The research purpose is to develop an approach for determining the stress concentration near the holes in composite structure elements reinforced with carbon fibres. The research is performed on the basis of a numerical-analytic approach using the method of singular integral equations. The paper studies the stress concentration near the holes in composite plate elements of the structures, which are reinforced with carbon fibres. The stresses are determined based on the singular integral equations. The integral equations are solved numerically using the mechanical quadrature method. The stress in the strip is studied at: longitudinal tension; pure bending; three-point bending; with periodically spaced holes. An approach to calculating the stresses in composite strips weakened by holes of different shapes, based on the method of integral equations, has been developed. The equation kernels are formulated on the basis of Green's functions, under which the boundary conditions on straight-line boundaries are satisfied identically. A methodology for calculating the stress concentration near the holes of arbitrary shape in plate elements of the structures has been developed. The results obtained can be used when calculating the strength of composite materials reinforced with carbon fibres.

INVESTIGATION OF THE BOUNDARY-VALUED PROBLEM ON RESONANCE MHD NON-UNIFORMITY BY INTEGRAL EQUATIONS USING

Numerical simulation of interior field velocity is studied on the basis of the rigorous analytical solution of the boundary-valued magnetohydrodynamics problem on the sphere type non-uniformities. The basis for the analytical solution is the method of integral equations of linear magnetohydrodynamics. The analysis of the obtained results is carried out.

A boundary value problem for mixed type equation with singular coefficient

В работе изучается краевая задача для уравнения смешанного типа с сингулярным коэффициентом в области, эллиптической частью которой является первая четверть плоскости, а гиперболической частью — характеристический треугольник. Методами интегральных уравнений и принципа экстремума доказывается однозначная разрешимость рассматриваемой задачи. In this paper we study a boundary value problem for a mixed type equation in a domain whose elliptic part is the first quadrant of the plane and the hyperbolic part is the characteristic triangle. With the help of the method of integral equations and the principle of extremum we prove the unique solvability of the considered problem

Investigation of nonlinear static displacements during the ship’s motions in various confined waterways

В статье проводится исследование нелинейных статических перемещений, возникающих в случае качки судна на мелководье, качки судна параллельно вертикальной стенке и при совместной качке двух судов на мелководье. Определение статических перемещений осуществляется на основании определения соответствующих сил волнового дрейфа по методам, разработанным в предшествующих работах. Данные методы основаны на применении метода интегральных уравнений и зеркальных отображений для случая качки судна параллельно вертикальной стенки. Проведенное исследование в отечественной практике является новым. В статье приводятся результаты расчетов нелинейных статических перемещений, возникающих при вертикальной, бортовой и килевой качки различных типов судов. Проводится исследование влияния различных факторов на их величины, а именно: изменения относительной глубины фарватера, изменения расстояния между судном и вертикальной стенкой, изменения расстояния между судами, курсового угла. Показано увеличение значений нелинейных статических углов крена и дифферента, а также вертикальных перемещений при уменьшении относительной глубины, уменьшении расстояния между судами и расстояния между судном и стенкой. Приведено сравнение значений статических перемещений, возникающих в различных стесненных фарватерах при прочих равных условиях. The article investigates nonlinear static displacements arising in the case of a ship’s motions in shallow water, motions of a ship parallel to a vertical wall and during coupled motions of two ships in shallow water. The determination of static displacements is carried out on the basis of determining the corresponding forces of wave drift according to the methods developed in previous works. These methods are based on the application of the method of integral equations and mirror images for the case of the ship’s motions parallel to the vertical wall. The research carried out in domestic practice is new. The article presents the results of calculations of nonlinear static displacements occurring during heaving, rolling and pitching of various types of ships. A study of the influence of various factors on their values is being carried out, namely: changes in the relative depth of the waterway, changes in the distance between the ship and the vertical wall, changes in the distance between ships, heading angle. An increase in the values of nonlinear static angles of roll and trim, as well as vertical displacements with a decrease in the relative depth, a decrease in the distance between ships and the distance between the ship and the wall, is shown. A comparison of the values of static displacements arising in various confined waterways, all other things being equal, is given.

Solvability of BVPs for the Parabolic-Hyperbolic Equation with Non-linear Loaded Term

This work is devoted to prove the existence and uniqueness of solution of BVP with non-local assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation involving Caputo derivatives. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of integral equations

Digital Modeling of Electromagnetic Processes in Technological Induction Devices

Development of an electrical calculation method plays the leading role in simulating induction devices. In modeling electrical devices and complexes, it is often necessary to simultaneously solve both chain and field problems, i.e., to deal with both lumped and distributed parameters. The article considers the method of integral equations for induction systems with non-magnetic and ferromagnetic loading, which is based on the theory of long-range action. The method’s key statement is that the field at any point is determined as the sum of the fields produced by all sources, including primary and secondary ones. Another finite element method is based on the theory of short-range action, which describes the electromagnetic wave propagation from point to point, its refraction and reflection at the boundaries of media. The article substantiates the development of a combined method based on using the method of integral equations for calculating the input parameters of inductors (an external problem) and the finite element method for calculating the field distribution in the load (an internal problem). The combined method has well proven itself in modeling induction heating and melting of metals and oxides, heating a tape in a transverse magnetic field, induction plasmatrons, and casting aluminum into an electromagnetic crystallizer.

Calculation of the impedance characteristics of a microstrip loop antenna with a metallized dielectric substrate

In connection with the intensive development of electronic technology, an urgent task is the development of antennas in a microstrip way, the advantages of which are small dimensions, a relatively simple manufacturing technology, and the ability to control their characteristics by using various materials and forms of radiators in their design. Currently, there are many mathematical models of microstrip antennas with vibrator radiators located on dielectric substrates, while models of microstrip antennas with other radiator shapes are presented much less often. As a rule, the calculation of the characteristics of such antennas is performed in electrodynamic modeling systems based on the use of «closed» algorithms. In this regard, there is a need to develop rigorous mathematical models of microstrip antennas with radiators of various shapes. This work is dedicated to the development of a rigorous model of a microstrip antenna with a frame radiator located on a dielectric substrate, based on the use of the method of integral equations. An integral equation is obtained for the unknown distribution function of the radial component of the current density over a frame radiator, the numerical solution of which is a correct mathematical problem. In addition, the numerical results of calculating the current density distribution, as well as the input impedance of such an antenna for various parameters of the radiator and substrate, are presented.

Determination of stress concentration near the holes under dynamic loadings

Purpose. To develop an approach for determining the stress state of plate structural elements with holes under dynamic loads with controlled accuracy. Methodology. The study was carried out on the basis of the Laplace transform and the method of integral equations. Findings. An approach to determining the dynamic stresses at the holes in the plates is proposed, which includes: the Laplace transform in the time coordinate; a numerical method for determining transformants of displacements and stresses based on the method of integral equations; finding originals on the basis of Prudnikovs formula adapted to dynamic problems of elasticity theory. The problem of determining the Laplace images for displacements is reduced to solving singular integral equations. Integral equations were solved numerically based on the approaches developed in the boundary element method. To find displacements and stresses, the Laplace transform inversion formulas proposed by Prudnikov are adapted to dynamic problems. The study on dynamic stresses at holes of various shapes was carried out. Originality. A new approach to the regularization of the Prudnikov formula for inverting the Laplace transform as applied to dynamic problems of the theory of elasticity has been developed. For its implementation: convergence of Fourier series based on pre-set stresses at the initial time is improved; the remainder is taken into account in the conversion formula. Practical value. A method has been developed for calculating the stress concentration at holes of arbitrary shape in lamellar structural elements under dynamic loads. The proposed approach makes it possible to determine stresses with controlled accuracy. The studies performed at circular and polygonal holes with rounded tops can be used in strength calculations for dynamically loaded plates. The influence of Poissons ratio on the concentration of dynamic stresses is analyzed.