M. A. Ilgamov

Influence of the ambient pressure on thin plate and film bending

The distributed lateral load on a plate located in a gas medium has been determined. The difference in the gas pressures of the plate surfaces results in a pressure drop and a lateral force, which depends on the middle surface curvature. It is shown that both these components of the lateral force must be taken into account in the general case. The influence of the second load component is small at a small ratio of the average pressure to the elastic modulus of the plate material and at a large relative thickness of the plate. At a small relative plate thickness and a large ratio of the average pressure of the medium to the elastic modulus of the plate material, the influence of the second component of the lateral load on the bending becomes significant. Cases of both linear and nonlinear plate bending are considered.

Bending and Stability of a Thin Plate under Vacuuming Its Surfaces

The effect of mean excessive pressure on the cylindrical bending of a plate is studied. An increase in this pressure leads to a decrease in deflection and vice versa. In the first case, the plate shape is stabilized under the action of longitudinal forces; in the second case, it is destabilized. The critical value of the mean pressure, upon achieving which an unlimited increase in the linear solution takes place, is determined. The dependence of the effect of the mean pressure on the bending on the boundary conditions, as well as on the ratio of pressures at the surface of the plate and at its edges, is shown.

Deformation of a bubble formed by coalescence of cavitation inclusions and shock wave inside it at strong expansion and compression

Dynamics of a cavitation bubble is considered at its strong expansion and subsequent compression. The bubble is formed by merging of two identical spherical cavitation microcavities in the pressure antinode of the intensive ultrasonic standing wave in the half-wave phase with negative pressure. Deformations of bubble and deformations of radially converging shock waves occurring therein at bubble compression are studied depending on the size of microcavities forming the bubble. It is found that compression of the medium in the bubble by the converging shock wave is kept close to the spherical one only in the case, when the radius of merging microcavities is 1800 times smaller than the radius of the bubble formed by merging at the time of its maximal expansion.

Resilient reaction of a pipeline to an internal impact pressure

The theory of dynamic stability of a the pipeline is developed on the basis of the linear bending equation, an assumption that the cross section is normal to the deformed axis of the pipe, the incompressibility of the transported fluid, and the instant establishment of impact pressure along its entire length. The calculation scheme is as follows: a pipe connecting two volumes and a pipe with one closed end and with a piston acting at a fluid at the other end. The relations between the input parameters for determining the dynamic reaction and the stress−strained state of the pipeline under the action of the internal shock wave are presented.

Evolution of disturbances of the sphericity of a bubble under strong compression

The growth in the amplitude of the small nonsphericity of cavitation bubbles in acetone and water under strong compression is considered. A hydrodynamic model is used in which the compressibility of the liquid, the nonstationary thermal conduction of the vapor and the liquid, and nonequilibrium evaporation–condensation processes, as well as imperfection of the vapor, are considered. It has been shown that the increase in the amplitude of the small nonsphericity of cavitation bubbles in the form of separate spherical harmonics during compression in water is substantially (more than 10 times) higher than during compression in acetone. This indicates that acetone is much more advantageous over water to implement a process of the nearer-to-spherical extreme compression of the medium in the cavitation bubbles.