In this paper the results of a study of the dynamic characteristics of thin-walled composite curved viscoelastic pipes under the influence of internal pulsating pressures is presented. The relationship between stress and strain is described by the Aviary equations. Based on the principle of calculus of variations, the equations of the dynamics of curvilinear shells are obtained. The obtained integral and integro-differential equations are solved using the finite element method, the Mueller and Gauss methods. The results of calculations of the natural frequencies of the shell and the curved rod are compared. As a result of the calculation, it was found that, shell vibrations occur at higher frequencies than rod vibrations (manifestation of a boundary effect). With this difference, the natural frequency, which has no analogue in the rod model decreases. This is due to the fact that, in this case the transverse vibrations of the section itself become significant, the rod. Some mechanical effects were discovered when taking into account the rheological properties of the pipe material.
The mathematical model of hardening the disk-shaped saw teeth with laser beams has been developed, and in terms of results of theoretical research based on this mathematical model, it has shown that it is advisable to use laser heat treatment technology for disc saws. At the same time, elements with a larger mass are less likely to collide with an increase in mass during operation. If the mass of the element increases by two times, the probability of collision decreases by three times. In general, it has been known that thermal treatment of the material with laser beams reduces the probability of damage to the saw teeth by 1.33 times, which in turn leads to an increase in the service life of saws. Graph of the dependence of changes in microhardness when load resistance is increased by changing the specific parameters by sharpening disc saw materials using laser beams has been developed. The 3D image shows the load resistance of the saw material, the mass of the element acting on it and the connection of its impact surface. Surfaces exposed to strong impact are four times smaller than the standard material with increased material strength, i.e. resistance to hard elements is increased by four times.
In this paper, we consider the natural vibrations of inhomogeneous mechanical systems, i.e., cylindrical bodies located in a deformable viscoelastic medium. The theory and methods for studying the natural vibrations of a cylindrical shell in a viscoelastic medium are constructed. The viscoelastic properties of the medium are taken into account using the hereditary Boltzmann-Walter theory. For the statement of the problem, the general equation of the theory of viscoelasticity in the potentials of displacements in a cylindrical coordinate system is used. An algorithm has been developed to solve the tasks posed on a computer using the Bessel, Hankel, and Mueller and Gauss methods. The considered problems were reduced to finding complex natural frequencies for the system of equations of motion of a cylindrical shell in an infinite viscoelastic medium using radiation conditions. It is shown that the problem has a discrete complex spectrum. The eigen frequencies of oscillations of a low-contrast heterogeneity are found. Revealed that the imaginary part of the eigen frequencies is comparable with the real one, which can lead to aperiodic movements of the systems considered.
A mathematical model and a technique for assessing the efficiency of the dissipative ability of structurally inhomogeneous mechanical systems consisting of multilayer cylinders bonded to a thin viscoelastic shell of finite length have been developed. A detailed analysis of the known works devoted to this problem is given. A model, methodology, and algorithm for studying the natural and forced oscillations of a system to assess the damping ability of structurally inhomogeneous elastic and viscoelastic mechanical systems, taking into account the influence of the geometric and physico-mechanical parameters of the shell and cylinderhave been developed. In solving the problems considered, the method of divided variables, the method of the theory of potential functions, the Mueller method, the Gauss method and the orthogonal sweep method were used. The complex eigenfrequencies, amplitudes of forced oscillations are determined, and the largest dephasing abilities of the considered structurally inhomogeneous systems are estimated. It has been revealed that, the effect of the greatest damping ability in structurally heterogeneous systems is manifested when the real parts of complex natural frequencies come closer due to the interaction of close natural forms with each other.
In this article an analysis of well-known works related to wave propagation and dispersion dependences in a cylindrical waveguide are presented. A mathematical model, methodology and algorithm for solving the problem of wave propagation in a cylindrical waveguide, having a sector cut are developed. The obtained equations are solved by the orthogonal sweep method in combination with the Mueller and Gauss methods. The dispersion relation for a viscoelastic cylindrical waveguide, having a sector cut in cross section at an arbitrary angle is obtained. Based on the obtained results, it was found that, there are no waves in the elastic cylinder of a sector section with real parts of the phase velocity. It has been established that, in the case of a wedge-shaped viscoelastic cylindrical panel, for each mode, there are limiting wave propagation velocities and they change with a change in the radius of curvature. The spectral sets of normal waves with an increase in the angular parameter of the sector cut-out, corresponding to lower non-zero frequencies of wave locking, slowly decrease.
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