Journal of Theoretical and Applied Mechanics, Sofia, vol. 49 Issue 2 (2019)

Table of contents



IN MEMORY TO ALEXANDER BORISOFF KAZAKOFF

Editorial Board of the Journal of
Institute of Mechanics, Bulgarian Academy of Sciences


Our dear colleague and friend Dr. Alexander B. Kazakoff passed away on May 13th, 2019. He is well known in the field of applied mathematics and vibrations – structural vibrations; dynamic modelling of single and double mass systems; vibration control, and dynamic systems of spiroid gears – for which computer solutions have been validated by extensive experimental studies. He is an author and co-author of more than 68 journal and conference papers and contributions to national and international scientific publications, including two books...

JTAM, Sofia, vol. 49 Issue 2 pp. 105-106 (2019), [Full Article]




MODIFIED METHOD OF SIMPLEST EQUATION FOR OBTAINING EXACT SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS: HISTORY, RECENT DEVELOPMENTS OF THE METHODOLOGY AND STUDIED CLASSES OF EQUATIONS

Nikolay K. Vitanov
Institute of Mechanics, Bulgarian Academy of Sciences, Akad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria


We present a short review about the story of the methodology of the Method of simplest equation for obtaining exact particular solutions of nonlinear partial differential equations (NPDEs) with emphasis on the recent extension of a version of this methodology called Modified method of simplest equation (MMSE). The extension of MMSE allows the use of more than one simplest equation and makes the methodology capable to lead to solutions of nonlinear partial differential equations that are more complicated than a single solitary wave. We list the classes of equations that have been studied up to now by the MMSE and mention as an example one of the theorem proved in the course of the application of the methodology.

JTAM, Sofia, vol. 49 Issue 2 pp. 107-122 (2019), [Full Article]




EXACT TRAVELING WAVE SOLUTIONS OF A GENERALIZED KAWAHARA EQUATION

Elena V. Nikolova1, Zlatinka I. Dimitrova2
1Institute of Mechanics, Bulgarian Academy of Sciences, 4, Acad. G. Bonchev Str. BG-1113 Sofia, Bulgaria
2Institute of Solid State Physics, Bulgarian Academy of Sciences, 72, Tsarigradsko Chaussee, BG-1784 Sofia, Bulgaria


We apply the modified method of simplest equation for obtaining exact solutions of nonlinear partial differential equations (PDEs) from the kind of the generalized Kawahara equation (gKE). The ordinary differential equation of Abel of first kind is used as the simplest equation and two exact solutions of the studied equation are obtained. These solutions are expressed by the special function discussed in [1]. Particular cases of one of the obtained solutions are visualized. For these cases the special function is reduced to elementary functions and the corresponding solutions describe a kink and a solitary wave.

JTAM, Sofia, vol. 49 Issue 2 pp. 123-135 (2019), [Full Article]




STATISTICAL ANALYSIS OF THE WATER LEVEL OF HUANG HE RIVER (YELLOW RIVER) IN CHINA

Wang Bo1, Zlatinka I. Dimitrova2, Nikolay K. Vitanov3,4
1China-Central and Eastern Europe International Science and Technology Achievement Transfer Center, Ningbo University of Technology, 201 Fenghua Rd., Jiangbei Qu, Ningbo Shi, Zhejiang Sheng 315000, China
2G. Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 72, 1784, Sofia, Bulgaria
3Institute of Mechanics, Bulgarian Academy of Sciences, Akad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
4Institute for Climate, Atmosphere and Water Research, Bulgarian Academy of Sciences, Blvd. Tsarigradsko Chaussee 66, 1784 Sofia, Bulgaria


Very high water levels of the large rivers are extremely dangerous events that can lead to large floods and loss of property and thousands and even tens of thousands human lives. The information from the systematical monitoring of the water levels allows us to obtain probability distributions for the extremely high values of the water levels of the rivers of interest. In this article we study time series containing information from more than 10 years of satellite observation of the water level of the Huang He river (Yellow river) in China. We show that the corresponding extreme values distribution is the Weibull distribution and determine the parameters of the distribution. The obtained results may help for evaluation of risks associated with floods for the population and villages in the corresponding region of the Huang He river.

JTAM, Sofia, vol. 49 Issue 2 pp. 136-148 (2019), [Full Article]




MIXED CONVECTION OF A Cu-Ag/WATER HYBRID NANOFLUID ALONG A VERTICAL POROUS CYLINDER VIA MODIFIED TIWARI–DAS MODEL

Saeed Dinarvand, Mohammadreza Nademi Rostami
Department of Mechanical Engineering, Islamic Azad University, Central Tehran Branch, Tehran, Iran


Herein, a Cu-Ag/water hybrid nanofluid is analytically modeled to develop the problem of the MHD axisymmetric mixed convective stagnation-point flow along a vertical porous cylinder. A new mathematical model has been presented and formulated based on Tiwari–Das nanofluid scheme. Using similarity transformations, the governing PDEs are altered into dimensionless ODEs, which is solved numerically using bvp4c function from MATLAB. The thermal characteristics of hybrid nanofluid are found to be higher relative to mono-nanofluid and base fluid, respectively. Besides, the results indicate that dual solutions exist for hybrid nanofluid flow in both assisting and opposing regimes. We conclude that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluid in various problems.

JTAM, Sofia, vol. 49 Issue 2 pp. 149-169 (2019), [Full Article]




NUMERICAL SOLUTION OF POLLUTION OF GROUNDWATER

Radko Petkov
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 4, Sofia 1113, Bulgaria


The present work describes the obtained mathematical model of non-steady filtration thermal dispersion, taking into account the changes in the fluid density and viscosity depending on temperature and concentration of the contained admixtures.
A method has been developed for evaluating the dispersion coefficients in porous media. An original hybrid numerical method has been developed on the basis of the finite element and finite difference methods for pressure-head and non-pressure filtration for solving the problems of filtration thermal dispersion in porous media.
The "Nonsteady_Termo_Dispersion-RP" software, operated in Windows environment and visualizing the results using MATLAB has been developed. The software has been applied for real conditions with the respective input data. As a result of the numerical experiments, data have been obtained for the effect of density and viscosity of sodium chloride, ammonium nitrate depending on the equations of state in filtration dispersion in porous media. The degree of substantiation and reliability of the scientific achievements is ensured by the use of a complemented hydrodynamic model, based on the fundamental equations of filtration, dispersion and thermal conductivity. The reliability of the results is also ensured by the fact that absolutely stable and convergent numerical schemes are used in the realized numerical experiments [1].

JTAM, Sofia, vol. 49 Issue 2 pp. 170-178 (2019), [Full Article]




FATIGUE BEHAVIOR OF HIGH STRENGTH Al-Cu-Mg AND Al-Cu-Li ALLOYS JOINTS OBTAINED BY FUSION AND SOLID STATE WELDING TECHNOLOGIES

Illia Klochkov, Anatoliy Poklaytsky, Sviatoslav Motrunich
E.O. Paton Electric Welding Institute of the National Academy of Science of Ukraine, 11 Kazymyra Malevycha street, 03150 Kyiv, Ukraine


This paper presents analyses of strength characteristics and fatigue behavior of butt welded joints of 2 mm thickness high strength D16T1 (Al-Cu-Mg) and 1460T1 (Al-Cu-Li) aluminum alloys, produced by tungsten inert gas (TIG) welding and friction stir welding (FSW). It is shown that friction stir welded joints has minimal stress concentrations in places of transition from the weld to the base material and also have no defects in the joint such as oxide film macroinclusions and hot cracks caused by melting and crystallization of the metal in fusion welding. At that, severe plastic deformations of metal under tool shoulder and in weld core results in formation of fine grain (3–4 μm), homogeneous disoriented structure and elongation and deviation of grains in a direction of plasticized metal movement take place in adjacent areas. Consequently, hardness and tensile strength of the joint weld metal are increased. Fatigue behavior under constant amplitude loading of FSW joints exceeds the characteristics of the joints obtained by TIG welding.

JTAM, Sofia, vol. 49 Issue 2 pp. 179-189 (2019), [Full Article]




HYDROLOGY MODELS APPLICATION TO SOLUTION OF THE RIVER DEVIATION PROBLEM DURING DAM CONSTRUCTION

Olga Nitcheva1, Polya Dobreva1, Borislav Milev2, Emil Bournaski3
1Institute of Mechanics, Bulgarian Academy of Sciences, 4, Acad. G. Bonchev Str. BG-1113 Sofia, Bulgaria
2Ss Cyril and Methodious European Politechnical University, 23 Str., Pernik, Bulgaria
3Institute for Climate, Atmosphere and Water Research, Bulgarian Academy of Sciences, 66 Tsarigradsko Shose Blvdл, Sofia, Bulgaria


Building of dams on mountainous rivers in narrow valleys always gives rise to the problem of the river waters deviation during the construction period. It becomes especially important in the periods of flood waves (FW) threatening with floods bringing considerable losses to the builders. Mostly the problem is solved by river deviation structures consisted of a weir, barring the river dam upstream and forming a small lake, a deviation tunnel or canal and sometimes a downstream weir. They have to transfer the river discharge from the upstream to the downstream side rounding the construction area. Qmax p is the river discharge with assumed exceedance probability p, which is expected to minimise the sum of the losses caused by the flood as well as the cost of the deviation structures. As the problem looks serious enough the evaluation of the Qmax p at the dam site with absence of the river flow observations must be done by larger number of methods. The article suggests the job to be performed through employment of more or less sophisticated hydrology models with or without consideration of the weir impounded lake's FW retention. For limited up to 2000 km2 catchments a simple partly based on empirical formulae model is proposed.

JTAM, Sofia, vol. 49 Issue 2 pp. 190-200 (2019), [Full Article]