Journal of Applied Mathematics and Mechanics

The motion of a holonomic mechanical system with many degrees of freedom exposed to potential and vortex force fields is considered. The Riemannian space, expanded by two units, is introduced, similar to the space with torsion, in which the motion of the same mechanical system is studied in the absence of force fields, but interacting with another mechanical system moving in the expanded space. The interaction between mechanical systems is taken into account by the dependence of the inertial coefficients of the additional system on the coordinates of the original one. The equations of both holonomic and non-holonomic constraints are determined, which are superimposed on the motion of the initial but free mechanical system in an expanded space and ensure the identity of motion under the action of potential and vortex forces in the initial space. As an example, the motion of a charged material particle in both electromagnetic and gravitational fields is considered.

This study investigates acoustic waves in one-dimensional periodic functionally graded rods using a modified Cauchy formalism previously applied to analyze the dispersion of surface acoustic waves in layered media. During the propagation of harmonic waves in a semi-infinite rod with harmonic periodicity of acoustic properties, phenomena were observed, including non-periodic spatial variation of the wave's phase velocity and amplitude, along with spatially periodic changes in kinetic energy and strain energy.

A review of works on submerged jets, the evolution of which occurs in the presence of infinite solid planes, is presented. In the first part of the review, problems related to jets emerging from an orifice perpendicular to an infinite plane are considered. The second part of the review will be devoted to jets emerging parallel to an infinite plane, as well as the interaction of jets.

The strengthening of a hollow cylindrical tube by using rotational autofrettage is investigated. The problem statement is based on the theory of infinitesimal elastic-plastic deformations, the unified yield criterion, the associated flow rule and the law of linear isotropic hardening. During unloading, the cylinder material can exhibit the Bauschinger effect. Exact analytical solutions are obtained for the stages of loading, unloading and operation. It is established that the material parameter reflecting the influence of the intermediate principal stress has a significant effect on the stress-strain state in the cylinder and the choice of optimal autofrettage parameters.

The problem of relaxation of residual stresses under conditions of high-temperature creep in surface-hardened cylinders with incisions of semicircular, square and V-shaped profiles cantilevered on an absolutely rigid rotating disk is considered and numerically solved. A series of variable calculations has been performed for cylinders made of EI698 alloy with a radius of 3.76 mm and a length of 150 mm, hardened by shot peening: smooth, with a semicircular incision with a radius of 0.1 and 0.3 mm, a square incision with a depth of 0.1 mm, with a V-shaped incision with a depth of 0.1 mm and an opening angle of 5°, 10°, 20° and 30°. In accordance with the technology of advanced surface plastic deformation, the incisions were applied to a pre-hardened smooth sample. First, the stress-strain state in a smooth sample was determined, and then the problem of redistributing residual stresses after incision application was solved in the elastic formulation for a semicircular incision and in the elastoplastic formulation for cylinders with square and V-shaped incisions. When solving boundary value relaxation problems of residual stresses, the rotation speed and the location of the incision varied — the distance from it to the cantilevered end of the cylinder. The relaxation of residual stresses was calculated on a time base of 300 hours for a smooth cylinder for comparison with a similar solution based on the grid method and on a time base of 100 hours for cylinders with incisions. The flow theory was chosen as the law of creep. The parameters of the law are determined from experimental data on creep deformation for the EI698 alloy at a temperature of 700 °C. The stages of solving the problem correspond to the full loading cycle: “hardening at 20 °C — force load from rotation — temperature load up to 700 °C — creep for 100/300 hours — force unloading — temperature unloading up to 20 °C”. When solving all the boundary value problems, at the end of the loading cycle, a significant level of compressive residual stresses is observed on the incision surface, which is a positive fact of using plastic surface deformation technology even under conditions of high-temperature creep. The results of calculations of the kinetics of residual stresses during creep are presented in graphical and tabular forms.