Journal of Theoretical and Applied Mechanics, Sofia, Accepted Papers

ABSTRACT: This paper uses a quasi-3D shear deformation theory accounting for integral terms and including the stretching effect to study the free vibration of FG plates with simply supported edges. A new function shape is used to show the variation of tangential stresses through the z-direction of the plate. Poisson's ratio is supposed to be constant, but Young's modulus and densities are assumed to be graded in the thickness direction according to the power law function. The present plate theory satisfies the zero tension on the upper and lower surfaces of the FG plate without using shear correction factors. The equations of motion are obtained via Hamilton's principle and solved using Navier's solution type. The present natural frequencies correspond with the ones in many publications; the outcomes of geometrical ratio, side to thickness ratio, and the material index on the natural frequencies of SS-FGP are investigated.

ABSTRACT: The current study computes the modes of frequency of an orthotropic rectangular plate having 2-D (two-dimensional) circular thickness and 1-D (one-dimensional) linear density with variable temperature field at clamped edge condition. Temperature variation on the plate is considered to be parabolic in both the directions. Rayleigh Ritz technique is used to solve the frequency equation of nonhomogeneous orthotropic rectangular plate and frequency values are calculated for first four modes of vibration. The convergence study of modes of frequency of orthotropic rectangle plate is also done at clamped edge condition. The aim of the present study is to present some numerical data in the form of frequency and to demonstrate how different plate parameters variations can be used to control frequency modes. A comparative analysis of the modes of frequency of the current study with the available published results is effectively presented at clamped edge condition, which is also provided in tabular form.

ABSTRACT: Air entrapment in soil-pores during cyclically hydraulic loading requires a physical insight by means of both modelling and experimental works. In the present study, transient drying and wetting tests are performed in a sand column device. The device enables to perform measurements of transient water content and pore water pressure in unsaturated soils. The measurements of water content as well as the pore pressure are directly linked to soil-water retention curve. The experimental results show that it exists an entrapped air together with hysteresis in soil water retention. Based on the experimental results, a new computer model of soil water retention is proposed. Finally, numerical simulation of air-water transport in unsaturated media is implemented using this model. The comparison between measured data and numerical simulation results shows that the proposed model can improve an accuracy in simulation of the water transport in unsaturated media.

ABSTRACT: In this paper, the spatial deformations and transverse vibrations in the cutting mechanisms of big band saw machines are investigated. Functions describing the static deformations in two mutually perpendicular planes are received. Transverse vibrations and dynamic deformations are also studied. Functions describing these vibrations and deformations have been received. Diagrams and surfaces, showing the type of the static and dynamic deformations are built. The proposed theoretical expressions, diagrams and surfaces can be used to design new band saw machines, as well as to study the influence of various dynamic processes that occur in operational mode.

ABSTRACT: Specimens of 40X steel were tested in tension and strain controlled low-cycle fatigue. It was found that the increase of strain amplitude leads to a decrease in the exploitation durability of 40X steel. The microstructure evaluation after cyclic tests with 0.18{\%} and 0.35{\%} deformation amplitude was investigated. The existing in the initial materials state banding in the rolling direction is preserved after cycling loading, but with increase of deformation amplitude, ferrite is refined, cementite lamellae break and spheroidal cementite is aggregated. Dislocation substructure also changes~-- dislocation walls are compacted, dislocation network develops, dislocation tangles appear. New dislocation walls are formed from parallel screw dislocations with the same sign. The state is characteristic of volumes with high level of elastic deformation.

ABSTRACT: The paper outlines a finite elements refined mathematical model of the thermal state of modern single shaft gas turbine engine that can be used in ground or floating power plants. The mathematical model is based on special finite elements of hexagonal type. On the base of the developed mathematical model the turbine rotor temperature field was found and experimentally verified. Using the results of temperature field calculation the rotor thermal deformations and stresses have been found too. The obtained results could be used in further studies of the turbine rotor stress-strain state and fatigue strength.

ABSTRACT: We consider rotationally driven nonlinear viscoelastic jet. In contrast to previous unrealistic planar studies with no gravity effect, we investigate here realistic three-dimensional jet with gravity effect. Using theoretical and computational methods, we develop models for such jet and its stability and determine the solutions. We find three-dimensional jet with gravity effect leads to faster and thinner jet. For jet arc length higher than its exit diameter, our calculation with typical parameter values shows that jet radius is smaller by a factor of more than 1.4 and jet speed is higher by factor of more than 2 as are compared to the exact planar jet counterpart results. Our linear stability of such jet uncovers new instability of the most critical three-dimensional spatiotemporal disturbance that grows in time very close to the three-dimensional jet exit but decays in space and can become stable for sufficiently far away from jet exit.

ABSTRACT: A mathematical model is developed in the present study to investigate the heat and mass transfer phenomena in blood flow under stenotic condition. The non-Newtonian Carreau fluid model is used to characterize the streaming blood. The nonlinear governing equations are solved numerically by employing a finite difference scheme along with suitable initial and boundary conditions under the action of applied magnetic field. Various significant hemodynamic parameters are examined for additional qualitative insight of the flow-field, temperature-field and concentration-field over the entire flow regime with the help of the numerical results obtained in this study. Comparisons are made with available results in open literature and are found in good agreement between these two results.