Doklady Rossijskoj akademii nauk. Fizika, tehničeskie nauki

A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities that is called energy is constant. This paper presents an alternative approach, namely derivation of a general form of equations of motion that keep the system energy, expressed as a function of generalized coordinates and corresponding velocities, constant. These are Lagrange’s equations with addition of gyroscopic forces. The important fact, that the energy is defined as the function on the tangent bundle of configuration manifold, is used explicitly for the derivation. The Lagrangian is derived from a known energy function. A development of generalized Hamilton’s and Lagrange’s equations without the use of variational principles is proposed. The use of new technique is applied to derivation of some equations.

The possibility of shock wave amplification in a two-phase mixture of superheated steam and liquid triethylaluminum (TEA, Al(C2H5)3) has been experimentally demonstrated for the first time. Fine synchronization of TEA injection of TEA into a flow of superheated steam with the arrival of an attenuating shock wave is shown to ensure the self-sustaining propagation of the shock wave in the two-phase medium at a speed of about 1500 m/s.

For the first time, an exact solution to the contact problem of the action of a strip rigid stamp of finite width on a composite layered material having an anisotropic structure is constructed. Problems of this kind have been studied in sufficient depth for isotropic materials. Contact problems for non-classical shaped stamps acting on composite materials have been poorly studied. The applied numerical methods for composite materials do not take into account the contact stress concentrations occurring at the boundary, which are characteristic of contact problems, do not fully reveal the malleability of the stamp insertion into an anisotropic medium when the stamp size changes, and are difficult to analyze in dynamic cases. In contrast to the isotropic case, when the symbol of the kernel of the integral equation is described by a meromorphic function, in the anisotropic case one has to meet with an analytical function of two complex variables of complex structure. Contact problems for anisotropic materials arise in many areas when creating various engineering equipment and products, in construction, when creating an electronic element base, as well as in the mechanics of natural processes.. In this paper, using the example of the effect of a strip rigid stamp of finite width on a composite laminated material, an exact solution of a static problem for one type of anisotropy is constructed using the block element method. The practice of constructing exact solutions to boundary value problems shows that with their help it is possible to capture and identify properties of solutions, the study of which is inaccessible to numerical methods. Examples are the identification of new types of earthquakes, starting ones, a new type of cracks not previously described, new types of earthquake precursors and resonances of structures. On the basis of exact solutions, it is possible to build high-precision approximations, the application of numerical methods to which already turns out to be more effective than as a result of direct inversion of volumetric and boundary differential operators of boundary problems. The result of this article can be useful both in engineering practice and in geophysics in describing the behavior of a mountain range on an anisotropic bedrock. In addition, the method opens up the possibility to investigate anisotropic cases in a dynamic formulation using contour integrals in the representation of solutions.

Progressive motion in the fluid of a body (housing) with an internal movable mass is considered. The external resistance is proportional to the squared velocity of the body and depends on the direction of motion. The control is implemented by the force of interaction of the internal body with the housing. Motions with periodic change of the velocities are obtained an analyzed. The average speed of the motion of the system is evaluated.

A method of solving the problem for an infinite elastic strip with a transverse crack located on the vertical axis of symmetry is proposed. The solution is sought in the form of series in Papkovich–Fadle eigenfunctions, the coefficients of which are determined explicitly. The solution method does not depend on the type of homogeneous boundary conditions on the sides of the strip. To solve the problem, a function is constructed from the Papkovich–Fadle eigenfunctions that allows an analytical continuation outside the crack into the entire strip. The analytic continuation is constructed using the Borel transform. The solution sequence is shown using the example of an even-symmetric problem for a free strip with a central crack, on the sides of which normal stresses are specified.

It is shown that the problem of describing the technology of additive laser deposition can be considered within the framework of a self-similar thermal conductivity equation. It is shown that, under certain conditions, the depth of substrate penetration is well described by a self-similar solution. Based on the obtained self-similar solution, a two-parameter dependence of the penetration depth on the Peclet number (the ratio of the scanning speed to the rate of temperature change in the material) and dimensionless enthalpy (the ratio of the specific energy absorbed by the material and the energy required for melting) was obtained. It is shown that the obtained analytical dependence describes the experimental data quite accurately.

In recent years, the application of low-temperature plasma in biomedical and agricultural research has attracted significant interest due to the plasma’s ability to effectively sterilize, modify surfaces, and generate reactive oxygen and nitrogen species. Accurate positioning of plasma sources and characterization of source operating modes are primary tasks when implemented in real practice. This paper presents a universal device for positioning of plasma sources and measuring equipment. The device is manufactured by FDM 3D printing and has a relatively high structural strength in the absence of metal-containing elements. The developed device allows the active elements of plasma sources to be positioned with high accuracy over objects of various sizes and compositions, and also allows the implementation of sensitive methods for diagnosing plasma characteristics and parameters of processed objects.