In this work boundary value problem for a circular plate under the action of two-sided gas pressure is considered. The problem relations use a refined expression for the transverse distributed force. The force consists of the average overpressure and the difference of pressures acting on both surfaces of the plate as well as in the curvature that arises during bending. The effect of the boundary conditions on the deflection values is shown, and the compression force of the middle surface resulting from the thickness reduction of the plate has been also taken into account. Linear and nonlinear axisymmetric bending has been investigated.

We study how the fixing conditions along edge of a circular plate under pressure effects its axisymmetric bending. In our calculations we take into account refined transverse distributed load, which depends on a gas pressure and on an area difference between convex and concave surfaces. Furthermore we take into consideration a compression force of a middle surface, which is created by compression of the plate over the thickness. The deflections are defined in linear and nonlinear settings.

This article gives a review of three approaches to solving the problems of detecting local rod and pipeline defects and related problems. In the first approach, local defects are modeled by the matching conditions; in the second approach, by delta functions entering into the differential equation; and in the third approach, longitudinal cavities and cracks are modeled by continuous rod sections with modified stiffness, cross-sectional area, and density. This two-part review describes the works devoted to the detection of defects in distributed mechanical systems using natural frequencies, as well as using transmitted and reflected waves. The second part of the review is devoted to works that use the second and third approaches, i.e., defect modeling by delta functions and continuous rod sections with modified stiffness, cross-sectional area, and density.

In this paper, we considered the bending of a round shallow panel under the effect of excessive pressures on the lower and upper surfaces. A refined expression of the distributed transverse force that depends on both the pressure drop on the surface and the interaction of the average overpressure and curvature of the middle surface is used. This refinement is performed in a linear approximation. The panel edge is assumed to be isolated from excessive pressure. The classical theory of nonlinear bending of a round shallow panel under the effect of pressures on its surface is supplemented.

The influence of the shape of the jet head on its impact on a wall covered with a thin liquid layer has been studied. The conditions characteristic of the impact of the jet arising on the surface of a cavitation bubble upon its collapse near a wall have been considered. It has been established that a change in the shape of the jet head can lead to a significant change in the size of the maximum loading area of the wetted wall and in the magnitude and pattern of loading. In particular, with an increase in the degree of sharpening of the jet head, the wall pressure decreases and its spatial distribution becomes more uniform. Dependences of the maximum pressure and integral wall load on the jet shape were obtained.

Static cylindrical bending of nanofilms is considered in linear and nonlinear formulations. The frequency spectrum of bending vibrations and the parametric resonance are determined. In this case, two surface effects are taken into account. The first one is associated with different elastic properties in the surface layer and in the bulk of the material. It is manifested in stretching and bending of nanometer-thick films. The second effect is due to the difference, caused by bending, between the areas of the convex and concave surfaces subjected to gas pressure. The greater the ratio of the mean pressure to the elastic modulus of the material and the ratio of the length of the film to its thickness, the stronger this effect. The loading conditions of the end surfaces of the film are also important, as well as the strain over the film thickness under the action of the mean pressure. A positive mean pressure leads to an increase in effective stiffness, a decrease in deflection, and an increase in natural frequencies. A negative mean pressure reduces stiffness and natural frequencies. It is shown that, in this case, film bending may occur as a result of the longitudinal in stability. Oscillations of the mean pressure lead to a parametric amplification of bending vibrations. These results cannot be obtained on the basis of the classical equations of bending of plates and films.

The effect of the average excess pressure of the environment on the linear and nonlinear bending of a round plate is studied. Different values of the gas pressure on both surfaces of the plate form a transverse distributed load, consisting of a differential pressure and the interaction of the average pressure with the curvature of the middle surface. With a small ratio of the average pressure to the elastic modulus of the material and with a large relative thickness, the influence of the second component of the bending load is small. With a large ratio of the average pressure to the elastic modulus and a small relative thickness, this effect is significant.

In this paper, we compare the features of the shock compression of 1-mm vapor bubbles and the nonsphericity growth during their collapse in hydrocarbon (acetone, benzol, and tetradecane) liquids. At the beginning of compression, the vapor is in a saturation state at 1.03 MPa, and the bubble collapse is caused by a liquid pressure of 5 MPa. It has been found that, during the collapse of the bubble in acetone, only weak compression waves occur in its cavity, while intense, radially convergent compression waves that transform into shock waves arise in the bubbles in benzol and tetradecane, which have a significantly greater molecular weight and, consequently, a lower speed of sound in the vapor. This leads to an extreme focusing of energy at the bubble center. A shock wave in tetradecane appears shortly after the onset of collapse, whereas a shock wave in benzol forms only during the reconvergence of the unstressed compression wave to the center of the bubble after its reflections from the center and the interface. As a result, the highest values ​​of thermodynamic parameters are achieved in tetradecane, while the lowest values are attained in acetone. The bubble nonsphericity is shown to increase by two orders of magnitude less in tetradecane than in acetone and benzol by the time it reaches the extreme values ​​of the thermodynamic parameters.

The motion of a liquid column in a vertical tube caused by a moving piston that contacts its lower boundary is considered. The law of the piston’s motion is defined based on experimental data. The acceleration of the piston exceeds the acceleration due to gravity. The separation of the liquid from the piston and the change in the volume of the cavitation pocket are accepted. The simplest model of the phenomenon is proposed. A qualitative analytical solution of the one-dimensional problem is presented; the results are compared with experimental data. The pressure upon the collapse of the pocket, the subsequent elastic oscillations of the tube bottom, and the resulting stresses are assessed.

The static bending of a thin plate that separates two liquids with different densities and velocities has been considered under the assumption that the liquids and the midsurface of the plate are incompressible. Wavelengths in this simple model are small compared to the sizes of the plate and liquid-filled spaces. Static interaction between the Euler, Helmholtz, and Rayleigh instabilities as a function of the compression force acting on the plate normally to the contact boundary has been studied. The ranges of the corresponding parameters have been found for the cases when the flatness of the plate and contact boundaries becomes stable and unstable.

The spatial vibrations of a pipeline and the fluid inside it are considered with respect to the horizontal axis passing through supports under the action of internal shock pressure. The coupling between the internal pressure, curvature variation, and deformation of the pipeline circumference is taken into account. The bending and torsional deformations of the pipeline are divided into two sequential stages: inertial and inertial-elastic. The first support is rigid and fixed, and the second support may translate frictionlessly in the horizontal direction. Numerical modeling is performed. The analysis of the calculation results is given for special parameter values. The approximated analytical solutions are also presented.

The influence of the average value and amplitude of the transient internal pressure in the pipelines on the spatial vibrations of the latter has been assessed. The graphic dependences of the spatial vibrations, their phase patterns, Fourier spectra, and Poincare maps have been presented. The latter have been analyzed depending on the input parameters and time. Brief conclusions have been formulated.

The static and dynamic bending of a pipeline in the vertical plane under the action of its own weight is considered with regard to the interaction of the internal pressure with the curvature of the axial line and the axisymmetric deformation. The pressure consists of a constant and timevarying parts and is assumed to be uniformly distributed over the entire span between the supports. The pipeline reaction to the stepwise increase in the pressure is analyzed in the case where it is possible to determine the exact solution of the problem. The initial stage of bending determined by the smallness of elastic forces as compared to the inertial forces is introduced into the consideration. At this stage, the solution is sought in the form of power series and the law of pressure variation can be arbitrary. This solution provides initial conditions for determining the further process. The duration of the inertial stage is compared with the times of sharp changes of the pressure and the shock waves in fluids. The structure parameters are determined in the case where the shock pressure is accepted only by the inertial forces in the pipeline.

The simplest model of longitudinal vibrations of a bar with incipient transverse cracks is considered under the essential assumption that the crack size is small compared with the bar cross-section area and the difference between the mode shapes of the bar with incipient cracks and the undamaged bar is small. The different manifestation of cracks in the phases of extension and compression strains is taken into account. The natural vibration frequencies and the crack coordinates and dimensions are determined from experimental values of natural frequencies.

From preset pressure values on both surfaces of a plate, its bending is determined depending not only on the pressure difference but also on the product of the average pressure and the curvature of the middle surface. The latter component of this action is determined according to the models of Kirchhoff and Timoshenko for the case of a cylindrical linear bending of a plate. It is shown that taking into account the average pressure leads to an increase in the effective flexural rigidity. The value of deflection according to the models of Kirchhoff and Timoshenko is compared with a classical result. A criterion is established for the situation where the influence of the ambient pressure on the plate bending can be significant. The effect of the average pressure exerted on the longitudinal stability of the plates is determined.