Analytical Solution for Bending and Free Vibrations of an Orthotropic Nanoplate based on the New Modified Couple Stress Theory and the Third-order Plate Theory

In the present work, the equations of motion of a thin orthotropic nanoplate were obtained based on the new modified couple stress theory and the third-order shear deformation plate theory. The nanoplate was considered as a size-dependent orthotropic plate. The governing equations were derived using the dynamic version of Hamilton’s principle and natural boundary conditions were formulated. An analytical solution in the form of a double Fourier series was obtained for a simply supported rectangular nanoplate. The eigenvalue problem was set and solved. It was analytically shown that the displacements of the median surface points in the plane of the plate do not depend on the material length scale parameters in the same directions; these in-plane directional displacements depend on the material length scale parameter in the out-of-plane direction only. On the other hand, the out-of-plane directional displacement depends on the length scale parameter in the plane directions only. The cross-section rotation angles depend on all length scale parameters. It was shown that the size-dependent parameters only have a noticeable effect on the deformed state of the plate if their order is not less than the order (plate height)-1

Analytical Solution for Bending and Free Vibrations of an Orthotropic Nanoplate based on the New Modified Couple Stress Theory and the Third-order Plate Theory

In the present work, the equations of motion of a thin orthotropic nanoplate were obtained based on the new modified couple stress theory and the third-order shear deformation plate theory. The nanoplate was considered as a size-dependent orthotropic plate. The governing equations were derived using the dynamic version of Hamilton’s principle and natural boundary conditions were formulated. An analytical solution in the form of a double Fourier series was obtained for a simply supported rectangular nanoplate. The eigenvalue problem was set and solved. It was analytically shown that the displacements of the median surface points in the plane of the plate do not depend on the material length scale parameters in the same directions; these in-plane directional displacements depend on the material length scale parameter in the out-of-plane direction only. On the other hand, the out-of-plane directional displacement depends on the length scale parameter in the plane directions only. The cross-section rotation angles depend on all length scale parameters. It was shown that the size-dependent parameters only have a noticeable effect on the deformed state of the plate if their order is not less than the order (plate height)-1

Bending oscillations of a cylinder, surrounded by an elastic medium and containing a viscous liquid and an oscillator

The article considers dynamic processes mathematical modeling in a mechanical system, consisting of an elastic hollow cylinder, surrounded by an elastic medium and containing viscous liquid and vibrating coaxial rigid cylinder. The amplitude frequency characteristic for investigating bending cylinder oscillations as one-mass system is defined. It is shown, that the constructed amplitude characteristic makes it possible to define the considered system resonance frequencies oscillations. The calculations demonstrated the significance of taking into account viscous liquid inertia and the surrounding elastic medium

Hydroelasticity of three elastic coaxial shells interacting with viscous incompressible fluids between them under vibration

Elastic cylindrical shells interacting with a viscous incompressible fluid are widely used in various branches of science and technology, such as engineering and aviation engineering. They provide the possibility for solving a lot of problems, such as: reducing constructing weight and dimensions, equalizing dynamic influences and vibration level, as well as reducing friction and wearing, cooling. Mathematical model of the system, representing three coaxial cylindrical shells, freely supported at the ends, and interacting with viscous incompressible fluid between them under mechanical system harmonic vibration is constructed. This mathematical model represents a coupled system consisting of the Navier-Stokes, continuity for each fluid and equations and the ones of elastic coaxial cylindrical shells dynamics which are based on the Kirchhoff-Love hypotheses and the corresponding boundary conditions, namely: for the fluid non-flow and for free attaching for the shells. The constructed mathematical model allows to investigate the oscillations of a mechanical system consisting of coaxial elastic cylindrical shells interacting with viscous incompressible liquids in order to identify dangerous operating modes

Mathematical model of elastic ribbed shell dynamics interaction with viscous liquid under vibration

The mechanical model of the system, formed by two surfaces of the coaxial cylindrical shells interacting with viscous incompressible liquid between them under vibration, is considered. The outer shell is geometrically irregular, and inner one is an absolutely rigid cylinder. The mathematical model of this system, consisting of differential equations in partial derivatives for describing dynamics of viscous incompressible liquid and an elastic ribbed shell together with boundary conditions is constructed. The expressions for amplitude frequency characteristics of outer geometrically irregular shell are discovered

Core Proteome of the Minimal Cell: Comparative Proteomics of Three Mollicute Species

Mollicutes (mycoplasmas) have been recognized as highly evolved prokaryotes with an extremely small genome size and very limited coding capacity. Thus, they may serve as a model of a ‘minimal cell’: a cell with the lowest possible number of genes yet capable of autonomous self-replication. We present the results of a comparative analysis of proteomes of three mycoplasma species: A. laidlawii, M. gallisepticum, and M. mobile. The core proteome components found in the three mycoplasma species are involved in fundamental cellular processes which are necessary for the free living of cells. They include replication, transcription, translation, and minimal metabolism. The members of the proteome core seem to be tightly interconnected with a number of interactions forming core interactome whether or not additional species-specific proteins are located on the periphery. We also obtained a genome core of the respective organisms and compared it with the proteome core. It was found that the genome core encodes 73 more proteins than the proteome core. Apart of proteins which may not be identified due to technical limitations, there are 24 proteins that seem to not be expressed under the optimal conditions

Optimization of the energy efficiency of an integrated security system based on modeling its optimal structure

As a result of system modeling we built a global model of the integrated security system as an information system. The proposed model allows us to differentiate one model into a set of private models, the elements of which one by one form the stages of its operation. The model of structural functioning proposed in the work, based on the analysis of the schedule of different states gave the key to understanding the permissible-possible stages of reducing the time of decision-making and thereby optimize its energy efficiency

Modeling Nonlinear Hydroelastic Response for the Endwall of the Plane Channel Due to Its Upper-Wall Vibrations

A mathematical model for studying the nonlinear response of the endwall of a narrow channel filled with a viscous fluid to the vibration of the channel’s upper wall was formulated. The channel, formed by two parallel, rigid walls, was investigated. The right end-channel wall was supported by a nonlinear spring. At the end of the left channel, the fluid flowed into a cavity with constant pressure. The upper channel wall oscillated according to a given law. As a result of the interaction between the endwall and the upper wall via a viscous fluid, the forced, nonlinear oscillations of the channel endwall arose. The fluid motion was considered in terms of the hydrodynamic lubrication theory. The endwall was studied as a spring-mass system with a nonlinear cubic restoring force. The coupled hydroelasticity problem was formulated, and it was shown that the problem under consideration was reduced to a single equation in the form of the Duffing equation. The nonlinear hydroelastic response of the end wall was determined by means of the harmonic balance method. The results of numerical experiments on nonlinear hydroelastic response behavior and a comparison with the case when the support spring is linear were presented. The obtained results are of a fundamental nature and can be used in modeling various devices and systems that have narrow channels filled with viscous fluid and are subjected to vibrations on one side of the channel. For example, coolant pipes are subjected to vibrations from the engine. Of particular interest is the application of the presented solution to the mathematical modeling of nano- and micro-spacecraft systems with fluids since the proposed decision allows for the consideration of some boundary effects, which is important for nano- and micro-spacecraft due to their small size

Increasing the energy efficiency of electronic document management systems

This paper proposes a comprehensive set of characteristics of integrated security systems of electronic document management. We give a classification description and data analysis for modeling decision-making processes in integrated security systems by the example of responding to the threats of information leakage through parametric channels. The optimal set of measures to respond to an attacker’s operations of illegal interception of information via parametric channels by using the appropriate modes of operation of the TCP protocol, which reduces the decision-making time, optimizes the performance of the system as a whole and significantly contributes to the optimization of its energy efficiency is given