Dimensionless Scale Research Articles

Size-dependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory

The governing equations of motion are derived for analysis of a sandwich microbeam in this paper. The sandwich microbeam is including an elastic micro-core and two piezoelectric micro-face-sheets. The microbeam is subjected to transverse loads and two-dimensional electric potential. Higher-order sinusoidal shear deformation beam theory is used for description of displacement field. To account size dependency in governing equations of motion, strain gradient theory is used to mention higher-order stress and strains. An analytical approach for simply-supported sandwich microbeam with short-circuited electric potential is proposed. The numerical results indicate that various types of parameters such as foundation and material length scales have significant effects on the free vibration responses and dynamic results. Investigation on the influence of material length scales indicates that increase of both dimensionless material length scale parameters leads to significant changes of vibration and dynamic responses of microbeam.

Dynamic stability analysis of microcomposite annular sandwich plate with carbon nanotube reinforced composite facesheets based on modified strain gradient theory

In this article, dynamic stability of annular sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core are presented based on first-order shear deformation theory and modified strain gradient theory. The generalized rule of mixture is employed to predict mechanical properties of microcomposite sandwich plate. The equations of motion are derived from Hamilton’s principle and solved by differential quadrature method. The fast rate of convergence of the method is shown and the results are compared against existing results in the literature. The results indicate that volume fraction of carbon nanotubes in facesheets and dimensionless length scale parameter has significant effects on the dynamic stability region and the parametric resonance. Dynamic stability region increases with considering of dimensionless length scale parameter, increasing of volume fraction of carbon nanotubes, and static load factor. Also, the influence of inner-to-outer radius ratios, radius-to-thickness ratios, and core-to-facesheets ratios are considered. The results can be employed for design of materials science, in junction high pressure micropipe connections, solid-state physics, micro-electro-mechanical systems, and nano electromechanical systems such as microactuators and microsensor.

DETERMINATION OF GENDER SENSITIVITY LEVEL OF THE ENTERPRISE CORPORATE CULTURE

In the article the main methods of assessing the level of enterprise corporate culture are studied, as well as the gender aspects affecting its formation. Certain gender relations are formed in the enterprise organizational culture; they influence on the opportunities for the self-realization of some gender groups. The study of gender aspects of corporate culture is important both in terms of theory and practice. The main purpose of the research is to improve the methodological foundations for assessing the enterprise corporate culture based on the use of system and gender-based approaches. The methodical framework for assessing the level of gender sensitivity of the enterprise corporate culture based on a three-dimensional matrix, formed by the indicators of the perception of corporate culture by managers, subordinates and subjects of the direct enterprise environment have been improved. On this basis, an enterprise can assess the perception of the enterprise corporate culture by different categories of entities taking into account the special nature of gender. The offered methodological framework will allow to conduct a comprehensive assessment of the gender sensitivity of the enterprise corporate culture in a single dimensionless scale based on the semantic differential method, which will make it possible to determine the attitude to the corporate culture both within the enterprise and in the external environment, and to detect the ways of forming the culture with insufficient gender perspective. The methodological basis for assessing the level of gender sensitivity of enterprise corporate culture can be applied to any enterprises and organizations. The offered methodology allows to identify the problem areas in forming the enterprise corporate culture and to determine the further necessary measures to improve the gender relations at the enterprise.

Three-dimensional vibration of cantilevered fluid-conveying micropipes—Types of periodic motions and small-scale effect

A new theoretical model is developed for the three-dimensional (3D) nonlinear vibration analysis of fluid-conveying cantilevered micropipes. Particular attention is given on the derivation and analysis of the reduced equations, and the small-scale effect on the periodic motions. Based on the modified couple stress theory (MCST), the governing equations are derived by using Hamilton’s principle. The material length scale parameter and large-deflection-induced geometric nonlinearities given by the Lagrangian strain tensor are incorporated into the governing equations. Utilizing the center manifold theory, normal form method and O(2) symmetry, the original governing equations can be rigorously reduced to a two-degree-of-freedom (2DOF) dynamical system. Then two possible types of periodic motions, i.e. planar periodic and spatial periodic motions, together with their stabilities are investigated by means of averaging methods and numerical simulations. Results show that the larger the dimensionless material length scale parameter is, the wider the region of mass ratio for stable planar periodic motion is. Particularly, the presence of small length scale parameter makes micropipes be more likely to oscillate in a plane. It is also shown that for mass ratio corresponding to the hysteresis of the curves of critical flow velocity versus mass ratio, the stabilities for bifurcating periodic motions at lower, moderate and higher critical flow velocities may be different.

Phase structure of NJL model with weak renormalization group

We analyze the chiral phase structure of the Nambu–Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V(σ;t) is given as a partial differential equation, where σ:=ψ¯ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V(σ;t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

Thermal-mechanical-electrical buckling behavior of functionally graded micro-beams based on modified couple stress theory

This paper presents thermal-mechanical-electrical buckling analysis of micro-beams that are made of functionally graded materials(FGMs) with temperature-dependent thermo-elastic properties. The material properties of the micro-beam are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are based on the principle of the minimum total potential energy, von Kármán geometric nonlinearity theory, and modified couple stress theory is employed to consider the size effect. A differential quadrature (DQ) method combined with an iteration process is used to predict the critical buckling external axial force and buckling temperature increment. The effects of the volume fraction profile parameter, dimensionless length scale parameter, initial gap ratio, ground electrode shape parameter, the applied voltage, slenderness ratio and the axial residual stress on the thermal-mechanical-electrical buckling behavior are evaluated in detail through parametric studies.

Non-classical plate model for FGMs

In this work, we developed a non-classical plate model for the analysis of the behavior of microplates prepared from functionally graded materials (FGMs). It was assumed that the material properties of FGM microplates vary along the direction of thickness and could be estimated using Mori–Tanaka homogenization technique. A variational approach based on Hamilton’s principle was employed to achieve motion equations and corresponding boundary conditions simultaneously. Unlike classical plate theory, the proposed plate model contained three material length scale parameters which allowed size effect to be taken into account effectively. Moreover, the proposed non-classical plate model could be divided into classical and modified couple stress plate models when all material length scale parameters were set at zero. To approve the applicability of the proposed size-dependent plate model, analytical solution for free vibration problem of a simply supported FGM microplate was obtained according to the Navier solution, where generalized displacements were stated as multiplication of undetermined functions with known trigonometric functions to identically satisfy simply supported boundary conditions for all edges. The results obtained by the proposed non-classical plate model were compared with those obtained from reduced ones relevant to different values of material property gradient index and dimensionless length scale parameter. It was found that the differences observed between the sets of predicted natural frequencies obtained from different types of plate models were more significant for lower values of dimensionless length scale parameter.

Size-dependent post-buckling behaviors of geometrically imperfect microbeams

In this paper, the size-dependent buckling and post-buckling analysis of the imperfect microbeams is presented. By accounting the mid-plane stretching, the nonlinear integral partial-differential equation governing the transverse motion of the imperfect microbeam is derived employing Hamilton’s principle. The modified couple stress theory is employed to capture the size effects of microbeams. The exact analytical solutions of the critical buckling load and the static response are acquired for the buckling problem of imperfect microbeams with different boundary conditions. Moreover, the dynamic behavior around the static configurations in the preand postbuckling domain is also investigated. It is found that the buckling of imperfect microbeam occurs through a saddlenode bifurcation, and the responses in postbuckling domain are asymmetrical. The numerical results are depicted to illustrate the influence of the dimensionless scale parameter and the imperfection amplitude on the circuital buckling load, static response and the dynamic properties of the imperfect microbeams.

ИМИТАЦИОННОЕ МОДЕЛИРОВАНИЕ ОБЖИГА ЦИНКОВЫХ КОНЦЕНТРАТОВ В ПЕЧАХ КИПЯЩЕГО СЛОЯ

The simulation roasting process of the sulphide zinc concentrates in the fluidized bed furnaces was studied. The charge humidity, oxygen content in the blast, coefficient of charge feeding into the furnace were used as independent variables. As for dependent variable in the model, the temperature of fluidized bed was chosen. All the variables on the basis of which mathematical models were realized were virtual, and the experiment was designed. The independent variables ranging in terms of impact intensity on the fluidized bed was estimated by absolute value of the regression model coefficients. The higher the coefficient (without accounting a free model element), the greater is its affect on the dependent variable temperature. It is established that the greatest influence on the temperature of the fluidized bed (according to the model in a dimensionless scale) is exerted by the oxygen content in the blast, and further, in descending order: coefficient of concentrate loading into the furnace; the coefficient of excess blast and, the least - the moisture content of the concentrate. In this case, it should be taken into account that the data can be either dimensionless or dimensional, if this is proved by other methods, for example, by the method of expert estimation. It is illustrated that to estimate the model adequacy along with Fisher-Snedecor’s statistics it is possible to use the correlation coefficient between the experimental (virtual) and the calculation (modeling) vectors. The proposed method for the development of mathematical models of sulfide concentrate roasting has the following advantages over physical methods: substantial energy savings time, significant savings in materials for design, high quality mathematical model. It is established, that for the ranking of independent variables it is more correct to use a matrix in a dimensionless scale.

Pulsed Laser Heating of a Finite Silver Selenide Slab Using (HHCE) Model

Heat induced in a finite Silver Selenide slab by an external pulsed laser source is studied in dimensionless scale according to hyperbolic heat conduction model (HHCE) using Laplace integral transform technique. The temperature profile, the critical time required to initiate phase transition and that to initiate damage at the front surface are obtained for different pulses and are illustrated graphically.

The influence of abiotic factors on forming grain quality of bread winter wheat in the conditions of the Donetsk region

Purpose. To establish the dependence of grain quality formation of bread winter wheat on the effect of abiotic factors in the conditions of the Donetsk region. Methods. It was field research supplemented by analytical studies, measurements, calculations and observations in accordance with common methods and methodological recommendations in crop production. The research was carried out on experimental plots in field crop rotation of the State Enterprise “Experimental farm “Zaboishchyk” of the DSAES NAAS”. The years of the research were different by agroclimatic conditions during grain formation and filling: 2014 was wet, 2015 was dry, and 2016 was the optimal for the annual rainfall. Results. Weather conditions had the greatest impact on test weight (79.8 %) and 1000 kernel weight (61.8 %). The most of 17 winter wheat varieties studied formed the maximum 1000 kernel weight under increased rainfall and humidity during period of grain filling. The highest 1000 kernel weight (44.6 g) has been recorded in the variety Ihrysta. This index was the most stable in the varieties Yuzovska and Ihrysta (coefficient of variation 2.9 and 2.1, respectively). The degree of influence of variety characteristics on gluten indices (both quantity and quality) was 72.0 % and 67.9 %, respectively. Grain protein content almost similarly depends on the conditions of the year, and on the characteristics of the variety. Under high moisture protein content decreased, but variation of this index was insignificant. The varieties tested were quite stable in protein content and gluten quality. The minimum variability on test weight, gluten content and 1000 kernel weight was in the variety Ihrysta, whereas on protein content in the variety Yuzovska. To evaluate several indices simultaneously it is advisable to use one typical dimensionless scale with binary conversion of response 1 and 0 (meets or does not meet the normative requirements). This makes it possible to determine the abiotic conditions of growing when grain of given variety meets the requirements of regulatory documents established. So, the grain of the varieties Ihrysta and Peremoha corresponded to normative requirements (the value of complex quality index is 1) regardless of agroclimatic growing conditions, and grain of the variety Yuzovska did only under optimal and wet growing conditions. Conclusions. It has been established that gluten indices (quantity and quality) essentially depended on the variety. Weather conditions had the greatest impact on test weight and 1000 kernel weight. The dependence of the grain protein content is almost the same both on the year conditions and on the variety characteristics. The transition to the using complex quality index allows determining under what abiotic conditions the grain of given variety meets normative requirements.

Influence of air change rates on indoor CO2 stratification in terms of Richardson number and vorticity

Above rules-of-thumb ventilation standard based on air change rate per hour (ACH), it is necessary to assess the indoor airflow and indoor air quality (IAQ) with respect to simple dimensionless numbers from the practical point of view. Hence, this work aims at investigating the influence of air change rates on indoor CO2 stratification and removal with dimensionless time scale ratio (proportional to Ri/α, Richardson number Ri, mass flux ratio α) and vorticity by applying experiment and simulation methods. We firstly carried out a series of experiments with different ACHs along with constant CO2 pollutant sources, further for simulation validation. Next, numerical simulation was employed to investigate five different ACHs (ranged from 4 to 28) on indoor CO2 concentration for two different vent-inlet-size cases. It was found that as the increase of ACH, the averaging outlet CO2 concentration was decreased until ACH equal to 16, both cases starting showing asymptotic behavior. When looking at indoor CO2 distribution, the case with larger vent-inlet size showed clear stratification even with higher ACH value (i.e., 28), due to the relatively smaller vorticity value (i.e., 0.47, with 3.14 for small-vent-size case) and larger Ri magnitude (37 times) compared to the small-vent-size case. Specifically, it is beneficial for indoor CO2 removal to keep time scale ratio Ri/α below 10−3 and vorticity above 1 rather than merely following with high ACH values. These findings will be of great importance for practical applications to design and control ventilation systems in the perspective of health and energy efficiency.

Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of molecular clouds ensembles

We have set ourselves the task of obtaining the probability distribution function of the mass density of a self-gravitating isothermal compressible turbulent fluid from its physics. We have done this in the context of a new notion: the molecular clouds ensemble. We have applied a new approach that takes into account the fractal nature of the fluid. Using the medium equations, under the assumption of steady state, we show that the total energy per unit mass is an invariant with respect to the fractal scales. As a next step we obtain a nonlinear integral equation for the dimensionless scale Q which is the third root of the integral of the probability distribution function. It is solved approximately up to the leading-order term in the series expansion. We obtain two solutions. They are power-law distributions with different slopes: the first one is -1.5 at low densities, corresponding to a equilibrium between all energies at a given scale, and the second one is -2 at high densities, corresponding to a free fall at small scales.

Bounds on the polymer scale from gamma ray bursts

The polymer representations, which are partially motivated by loop quantum gravity, have been suggested as alternative schemes to quantize the matter fields. Here we apply a version of the polymer representations to the free electromagnetic field, in a reduced phase space setting, and derive the corresponding effective (i.e., semiclassical) Hamiltonian. We study the propagation of an electromagnetic pulse and we confront our theoretical results with gamma ray burst observations. This comparison reveals that the dimensionless polymer scale must be smaller than $4\times 10^{-35}$, casting doubts on the possibility that the matter fields are quantized with the polymer representation we employed.

Free vibration analysis of functionally graded stiffened micro-cylinder based on the modified couple stress theory

In this paper, free vibration of the micro-cylinder made by functionally graded material that is stiffened in circumferential direction, has been investigated based on the modified couple stress and first order shear deformation theories. Modified couple stress theory (MCST) has been used to catch size effects in micro scales. By using first order shear deformation theory and Hamilton principle, general equations of motion and corresponding boundary conditions have been derived. Free vibration of the structure has been investigated by implementing simply supported boundary condition as a common case. The effects of different parameters such as dimensionless length scale parameter, distribution of FGM properties, number of stiffeners, thickness and length on the natural frequencies were calculated and compared with classical continuum theory. Results show that effects of the size are considerable and also using stiffeners lead to increase in natural frequencies which is because of increase in stiffness of the cylinder.

Swimming of a sphere in a viscous incompressible fluid with inertia

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier–Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two Hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid.

ASSESSMENT OF ECOLOGICAL SAFETY LEVEL OF A MOTOR TRANSPORT ENTERPRISE

The main methods of assessing the level of ecological safety of an enterprise have been considered in the article. The main purpose of the research is to develop methodical bases of assessing the level of ecological safety of a motor transport enterprise (MTE). The methodical bases of assessing the level of ecological safety of MTE, which are based on assessing safety of MTE basic business processes by four components (innovation, technical and technological, sanitary and hygienic, financial and economic) with the use of generalized function of desirability, have been improved. On this basis, an enterprise can compare its desires and capabilities to implement ecological safety in different business processes. The methodical bases being offered allow making comprehensive assessment of the ecological safety of emissions, discharges and wastes in a single dimensionless scale, which will enable comparative analysis of ecological safety by the business processes of one enterprise or different ones. The methodical bases of assessing the level of ecological safety of an enterprise can be used for any enterprises and organizations. The proposed methods allow identifying problem areas in business processes and creating portfolio of necessary innovation projects in the area of reducing environment pollution from the MTE activity in future.

Influence of turbulence intensity and turbulence length scale on the drag, lift and heat transfer of a circular cylinder

Influence of the turbulence intensity and turbulence length scale on the hydrodynamic characteristics and heat transfer of a circular cylinder, streamlined by a viscous fluid flow, is numerically studied. We take the Reynolds number of the oncoming flow equal to 4×104, the turbulence intensity Tu f and the dimensionless turbulence length scale L f varying from 1.0% to 40% and from 0.25 to 4.0, respectively. We confirmed that the increase of Tu f leads to the suppression of the periodic vortex shedding from the cylinder surface, and as a result the stationary mode of streamlining is formed. Consequently, with the increasing turbulence intensity directly in front of the cylinder Tu*, the amplitude of the lift coefficient decreases monotonically. Nevertheless, the time-averaged drag coefficient of the streamlined cylinder decreases at Tu* 9.0%. The dependence of the average Nusselt number on Tu* is near-linear, and with the increasing turbulence intensity, the Nusselt number rises. However, the change of the average Nusselt number depending on L f is non-monotonic and at L f, the value reaches its maximum.

Dimensionless input parameters in discrete element modeling and assessment of scaling techniques

A set of dimensionless input parameters were defined for DEM using a characteristic time which is a function of density and elastic modulus of particles and an arbitrary characteristic length. Dimensionless strain rate and mass damping ratio are inversely proportional to the characteristic time, and stress is normalized by elastic modulus to give dimensionless stress. It was demonstrated that the response of a model in the dimensionless scale is invariant with the choice of density, elastic modulus and the characteristic length if dimensionless strain rate and mass damping ratio are kept constant. Small time step is a prohibitive aspect of DEM. Scaling techniques are widely employed to enlarge the time step. Using the dimensionless scheme, it was learned that density scaling is equivalent to the use of a higher strain rate, and stiffness scaling results in a higher strain rate and an elevated stress state in the dimensionless scale.

Thermo-electro-mechanical buckling analysis of cylindrical nanoshell on the basis of modified couple stress theory

In the present study, the buckling of piezoelectric cylindrical nanoshell subjected to an axial compression, an applied voltage and uniform temperature change resting on Winkler-Pasternak foundation is studied analytically. The modified couple stress theory combined with the geometrical nonlinear shell model is employed to derive the equilibrium equations and boundary conditions. The numerical results are proposed for the buckling of simply supported cylindrical nanoshell using the Navier-type solution. Thus, the effects of different parameters such as dimensionless length scale parameter, length and thickness to radius ratio, temperature change, external electric voltage and Winkler and Pasternak foundation stiffness on critical buckling load are illustrated. It is shown that increase in dimensionless length scale parameter results in increasing critical buckling load and even intensifying the influence of other parameters, such as length and thickness, on critical buckling load.