Том 226, № 2 (2017)

We consider the problem of radiation of sound during the takeoff of an aircraft in the stage of its elevation over the runway with regard for the action of the wind. The role of the sources of noise are played by the engines of the aircraft modeled by point sources moving in air with a constant velocity at an angle to the plane interface of acoustic and elastic half spaces. The solution of the problem is obtained by using the Fourier integral transformations with respect to time and space variables with regard for the properties of generalized functions and the method of stationary phase. We perform the numerical analyses of the space-and-time distributions of the pressure of sound and the energy characteristics of the acoustic field on the example of modeling of the process of takeoff of the six-engine An-225 “Mriya” aircraft.

We describe an approach to the determination of viscoelastic stresses in plates with inclusions. It is based on the method of boundary integral equations and the Laplace integral transformation. The formal solution of the problem of elasticity theory in which the differential operators are replaced with constants is constructed by the method of boundary integral equations and reduced to the solution of a system of algebraic equations. The corresponding system for the viscoelasticity problem is solved with the help of the Laplace integral transformation and a refined numerical-analytic formula for its inversion.

By using the concept of the local displacements of mass as a measure of the gradient character of mechanical fields, we propose the relations of nonlocal electrothermoelasticity of nonferromagnetic dielectric solids. The theory takes into account the tensor nature of the local displacements of masses. By using the relations of this theory, we deduce a formula for the surface strain energy of dielectric solids.

We consider a hollow elastic cylinder of finite length subjected to the action of its own weight and an axisymmetric normal load applied to the upper base. The lower base of the cylinder is immovably fixed. The inner cylindrical surface is under the conditions of sliding restraint and its outer surface is immovably fixed. The problem is reduced to an integral equation of the first kind for normal stresses on the fixed lateral surface. We determine the character of singularity of the required function and propose an efficient algorithm for the solution of the obtained equation based on the expansion of the required function in a series in Jacobi polynomials. We present the results of calculations of normal stresses on the lateral surfaces of the cylinder, which show that, in the case of rigid fixing, the influence of the weight of the cylinder is much weaker than in the case of sliding restraint.