No 3 (2023)

Based on experiments carried out: in ice basins; with large-scale models of hovercraft in the field; with full-scale hovercraft, as well as using theoretical dependencies for calculating the stressstrain state of the ice cover from the action of moving loads, the possibilities (patterns) of the resonant method of ice destruction, i.e., by excitation of resonant flexural-gravity waves (FGW), were studied. Its physical essence, the expediency of its implementation by a hovercraft are explained, the possible areas of effective use of this method are indicated. The results of the information review on the topic of the work are given, on the basis of which the purpose of the research is set. When describing the viscoelastic nature of the relationship between stresses and strains in ice, the Kelvin-Voigt law of deformation of an elastically retarded medium was used. The theoretical bending potential energy density of an infinite plate was taken as a criterion for the ice breaking capacity of FGW. In this case, the condition is used that when it reaches a certain value, complete (with the opening of cracks) destruction of ice occurs. The initial data for these calculations are taken from the performed experiments. Dependences are given that make it possible to determine the parameters of a load moving at a resonant speed (hovercraft parameters) sufficient to destroy an ice cover of a given thickness under given ice conditions.

The technique of asymptotic averaging has been developed for three-dimensional partial differential equations with rapidly oscillating coefficients. For example, for the equations of elasticity theory. Then it was modified and applied to thin bodies in the form of plates (homogeneous or inhomogeneous, with even front surfaces or not), described by the three-dimensional theory of elasticity. In these cases, asymptotic solutions were constructed with respect to one small parameter, which is usually the ratio of the plate thickness to the characteristic plan size. The averaging technique in this case also reduces the dimension of the problem, i.e. reduces the three-dimensional boundary value problem to some two-dimensional one.

In this article, we substantiate the application of the method to a problem with two small parameters in the case of a homogeneous thin, highly orthotropic plate bent by a surface load without taking into account body forces. The second small parameter is the ratio of the transverse elastic moduli to the moduli in the plan of the plate. It is shown that strong orthotropy is equivalent to an increase in the thickness of the equivalent plate.

A procedure for obtaining the stress distribution over the plate thickness is described for three approximations. The first approximation gives the classical Kirchhoff theory, also called the Kirchhoff-Love theory, and the third approximation coincides with the Ambartsumian theory and allows one to find transverse shear and normal stresses. The consideration of cylindrical bending makes it possible to find solutions in the framework of classical plate theories in the form of formulas, as well as three approximations of the asymptotic theory, which simplifies comparison. Examples are considered when the averaged orthotropic moduli are taken for a single-layer fibrous composite.

 By using nonlinear equations of constraints between macro- and micro-states, the regularities of changes in the limiting values of stress and strain invariants in microinhomogeneous media are studied. It is shown that the extreme relative moduli of stress tensor deviators in polycrystals with a cubic lattice are invariant with respect to external conditions of reversible force and depend only on the crystal anisotropy factor. In the irreversible region of deformation, analytical relations are obtained for bulk and tensile normal stresses. The effect of cyclic change in bulk and tensile stresses in some subelements under external monotonic loading has been established. It is shown that, on the basis of nonlinear equations of constraints, a complex pattern of material failure can be described using the theory of maximum normal stresses at the local level.

 This article proposes a method for the justified choice of the fixing method, the type of supports and their stiffness for flat beam structures of an axisymmetric cross section in order to ensure the specified values of the first frequency of natural bending vibrations and the first critical load, by taking into account the action of longitudinal forces and temperature changes. The technique is based on the well-known provisions of the theory of beam oscillations, the Euler’s theory of stability, and uses the coefficients of supports as a criterion for choosing a fixing method, which are pre-normalized to achieve comparable values. The selected fixing provides the specified value of the first natural oscillation frequency, the value of the first critical temperature, or simultaneously both conditions of working efficiency. According to the developed method, comparative calculations of a flat bar structure using the finite element method have been performed. They has shown good convergence of the results for all controlled parameters. The proposed approach can be used in the design of support fixing of flat beam structures for various purposes to ensure their dynamic behavior.

 The present study is devoted to mathematical modeling of the proposed new architecture of a microelectromechanical modally localized acceleration sensor (MEMS accelerometer/gravimeter) with a sensitive element in the form of a microbeam pinched at both ends with an initial deflection, made in the form of the first asymmetric mode of free vibrations. The article demonstrates that with an asymmetric form of the initial deflection in the region of positive axial forces, there are zones of proximity of the frequency branches corresponding to the second symmetric and the first asymmetric vibration modes. When the required value of the axial tensile force in the microbeam is provided structurally, this effect can be used, in particular, to measure the axial component of the transfer acceleration according to the principle of amplitude modal localization. The possibility of heating the sensitive element with the help of an electric current flowing through the microbeam, provided in the sensor layout, makes it possible to control the operating point of the oscillation mode and, thus, to vary the range of measured accelerations and the degree of sensor sensitivity within a very wide range. The configuration of the oscillation excitation and output signal pickup electrodes proposed in the article makes it possible, with the help of a feedback loop, to stabilize the oscillation amplitude at the required level in the working (third) symmetrical form and, at the same time, to measure the oscillation amplitude associated with the change in the value of the measured component of the portable acceleration according to the asymmetric form. Thus, a mathematical model of an original modal-localized accelerometer (gravimeter) containing a single sensitive microbeam element and involving the effect of energy exchange between its various modes of vibration is proposed and investigated in the article.

The present paper deals with the problem of deriving the constitutive equations for the micropolar thermoelastic continuum GN-I in terms of the standard pseudotensor formalism. In most cases, the pseudotensor approach is justified in modeling hemitropic micropolar solids, the thermomechanical properties of which are sensitive to mirror reflections of three-dimensional space. The requisite equations and notions from the theory of pseudotensors are revisited. General thermodynamic approaches are used, entropy and energy balance equations are discussed. The weights of the main thermomechanical pseudotensors are established. In a linear approximation, the constitutive equations of the hemitropic micropolar thermoelastic continuum (GN-I) of the first type are derived. A coupled system of differential equations of heat conduction and dynamic equations of the micropolar thermoelastic continuum GN-I is obtained.