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Series in Applied Mathematics and Mechanics,

Volume 3

ISSN: 1314-3034


Vassil Kаvardzhikov, Editor-in-chief

Ludmila Parashkevova, Anguel Baltov, Editors


Mechanics of nanomaterials and nanotechnology,

Series in Applied Mathematics and Mechanics, Volume 3, Institute of Mechanics - BAS, Sofia, 2012, 326 pp.

This collection is issued with the financial support of Bulgarian Science Fund, Ministry of Education, Youth, and Science.

The jubilee collection of original works of the authors team presented is aimed to acquaint the scientific community, the doctoral students, and the high-tech industry with the achievements of scientists from the Institute of Mechanics (IMech), BAS, in international research collaboration. The book is dedicated to the 50th anniversary of the organized research in mechanics and the 35th anniversary of IMech.

The purpose of this collection is to demonstrate the research level in IMech in the field of mechanics of nanomaterials (NM) within the context of the recent world achievements and the capabilities of the modern equipment available in IMech and the Open Laboratory of Experimental Mechanics of Micro- and Nanomaterials.

This book is based on the results of 26 autors from different generations with significant contribution from young researchers. It consists of 11 chapters distributed into 4 sections: Nanomaterials based on metals; Nanomaterials based on polymers; Modeling of nanomaterials and nanostructurs; and Experimental nano- and micromechanics. The chapters describe the most recent technologies, theoretical methods, and experimental techniques and their application in NM studies.

Each chapter contains rich overview and analysis in the specific sub-field. Total are cited 624 publications of which 58 belong to the authors. The book is illustrated with 13 tables, 181 photos, charts and diagrams, of them ~ 14% colored.



V. Kamburov, Assoc. Prof., PhD ( Chapters I.1, ІІІ.4 )

M. Popova, Prof., PhD ( Chapters I.2, III.1, III.2 )

A. Topliyska, Assoc. Prof., PhD ( Chapters II.1, IV.3 )

N. K. Vitanov, Prof., DS ( Chapter III.3 )

J. Ivanova, Prof., DS ( Chapter III.5 )

Tz. Babeva, Assoc. Prof., PhD ( Chapter IV.1 )

M. Jordanov, Assoc. Prof., PhD ( Chapter IV.2 )


© 2012, Institute of Mechanics, Bulgarian Academy of Sciences

Alexander Kazakoff




VDM Verlag Dr. Müller e.K., paperback, 140 Pages, 2011

ISBN 978-3-639-34476-9


This book presents an attempt of the author at systematizing the work devoted to multi body vibration system mechanics and to highlight the application of the models in science and technology. Vibrations are considered in two main directions: first, as a technological useful motion in industry, where vibrations are generated and controlled by means of a suitable system adjustment and second, as a harmful vibration shock loading, where active and passive vibration isolation is needed. The book is structured in three main parts dealing with single, double and three mass vibration mechanical models, respectively. The objective of the work presented here is creation, investigation and control in plane and space of mono-frequency and poly-frequency vibrations of multi body system vibration mechanical models and their application in vibration technics, science and technology. Author highlights some of the up-to-date scientific and technical problems, as well as some technically applicable software, widely used in the engineering community worldwide and of course, the author will be very happy if the investigations give some thoughts and are used as a basis for some future research.

Alexander Kazakoff, Yulian Tsankov





VDM Verlag Dr. Müller e.K.
paperback, 100 Pages, 2011

ISBN 978-3-639-36013-4


The objective of this book is an attempt at presenting and solving the known from the classical mechanics two and three dimensional single mass mechanical and mathematical vibration models in a higher order dimensional space. The common algorithm derived here for motion transformation is a geometrical transformation by means of projection of the vectors in the higher order dimensional space. The study can be applied successfully in many engineering fields and in physics and in astronomy, where the motion of the celestial bodies can be described by using the common algorithm. It is known in celestial mechanics that the bodies move usually in a curved surface or in a curved space. That is why the common algorithm can be applied successfully in the description of motion in the curved space and easily transformed into 3D or 4D space for a suitable analysis. These problems can have a philosophical aspect as well in cases when the space is considered as a curved one like around the black holes and the dwarfs in cosmos. Any kind of a trajectory of motion can be transformed successfully in a higher order dimensional space and vice verse by means of applying of the common algorithm.



B. Marinov


VDM-Verlag Dr. Müller GmbH & Co. KG, Saarbrücken, Germany, pp. 96, 2011


ISBN: 978-3-639-32902-5

The presented book analyses the shock loads on the railway vehicles. For this purpose the system state is studied at the end of the shock-wave process. Expressions determining motion kinematical components and the free damped vibrations are derived. Dependences describing energy losses are proposed. An optimization task is also solved. For that purpose the expressions describing the kinetic energy losses are analyzed and different ways to minimize energy losses are proposed. A research connected to running locomotive wheel pair axle is proposed by the last part of this book. Torque is usually transmitted to locomotive wheel pair axle using single-step gear box. In this case dynamic loads are considerable. Reductionless drives of a locomotive wheel axis as well as a research on the undergoing dynamic processes are proposed. This book can be used in engineering design of transmission systems on locomotives and optimization of the transport process so that the loss of energy to be minimal.

Mladenova C., The Rotation Group and its Mechanical Applications, VDM-Verlag Dr. Muller GmbH & Co. KG (2011).(ISBN 978-3-639-36947-2)

The rotations play an extremely decisive role in the description of the Euclidean motions. The rotations are everywhere - in physics and engineering problems, computer simulations and visualizations, computer graphics, and therefore in the whole computerized world. The way of their representation defines the set of the problems which may be solved and the computational eficiency of the procedures. The present book is based on our research activities concerning the problems of modelling and control of rigid body motions and various applications to multibody mechanical systems. Starting with the algebraic aspects of the rigid-body motions, we involve quite naturally the vector-representation of the rotations. The kinematics and dynamics of a rigid body and multibody systems with rigid and fiexible joints as well as the dynamics of rigid spacecrafts are considered in the vector - parameter language. Difierent mechanical applications of the vector - parameter approach are traced: screws and dual vector-parameters, diagonalization of real 3×3 symmetric matrices, computation of the Euclidean motions on the base of the measurement data, vector decomposition of finite rotations and motion planning in the configuration space of vector - parameters. Control problems of a system built by mobile platform and manipulator as well problems of modelling, simulation and motion planning of robot locomotion are considered. The book presents last tendencies in the developing of kinematics and dynamics of rigid-body chains, spacecraft stability and control and celestial mechanics, and in this way may serve as a tool for students, scientists and engineers from academia and industry experienced in these attractive areas.

Abadjieva E., Spatial rack drives. Mathematical modelling for synthesis, VDM Verlag Dr. Müller e.K., 72 p.,( 2011), (ISBN 978-3-639-24045-0)

Series in Applied Mathematics and Mechanics
Volume 2

ISSN: 1314-3034

Nikolay K. Vitanov

Upper bounds on heat transport and energy dissipation in moving fluids

Series in Applied Mathematics and Mechanics, Volume 2, Institute of Mechanics - BAS, Sofia, 2011, 318 pp.

The aim of this book is to present the methods of the optimum theory of turbulence to the reader. The book consists of introductory part (up to chapter 3 inclusive) where the model equations of the hydrodynamics which are the basis for the optimum theory of turbulence are presented. In addition the two methods of the optimum theory of turbulence are discussed. The second part of the book is devoted to the upper bounds on the quantities connected to the thermal convection in a fluid layer without presence of rotation. The influence of rotation on the thermal convection is discussed in the third part of the book. In the same part one of the methods of the optimum theory of turbulence is illustrated on the basis of isothermal flow without presence of thermal convection.
The material presented in the book is based on studies of the author published in renowned international journals.
Acad. Prof. Stojcho Panchev, D. Sc.
Prof. Zapryan Zapryanov, D. Sc.

Series in Applied Mathematics and Mechanics

Volume 1

ISSN: 1314-3034

S. Iliev,N. Pesheva, D. Iliev

Equilibrium and quasi static dynamics of liquid, partially wetting solid surface

Series in Applied Mathematics and Mechanics, Volume 1, Institute of Mechanics - BAS, Sofia, 2011, 234 pp.

The aim of this book is to acquaint the reader with the variational derivation of the equations, describing the statics and dynamics of the three-phase system liquid/fluid/solid, which takes into account the existence of hysteresis of the equilibrium contact angle and the dissipation of energy when the contact line is moving. The effect of different possible realiza-tions of the heterogeneity and roughness of the solid substrate on the equilibrium shapes of a drop placed on it is studied numerically. The asymptotic and numerical solutions for the liq-uid motion are obtained for different three-phase systems taking into consideration the energy dissipation occurring when the contact line moves. A variational numerical method is devel-oped for the realization of the numerical studies which allows to treat real three-dimensional problems.

The material, presented in the book is based on previous studies of the authors pub-lished in renowned international journals.

N. Bontcheva, G. Petzov,

Metal behaviour and predictive simulation in termomechanical processing,

Prof. Marin Drinov Academic Publishing House,pages 174,

ISBN 978-954-322-407-4, Sofia, 2012

J. G. Brankov, D. M. Danchev, N. S. Tonchev

The Theory of Critical Phenomena in Finite-size Systems:

Scaling and Quantum Effects

World Scientific

Modern Condensed Matter Physics, vol.9

ISBN 981-02-3925-4


The aim of this book is to familiarize the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory.

This theory:

• offers an interpretation of experimental results on finite-size effects

in real systems;

• gives the most reliable tool for extrapolation to the thermodynamic

limit of data obtained by computer simulations;

• reveals the intimate mechanism of how the critical singularities build

up in the thermodynamic limit;

• can be fruitfully used to explain the low-temperature behaviour of

quantum critical systems.

The exposition is given in a self-contained form which presumes the reader's knowledge only in the framework of standard courses on the theory of phase transitions and critical phenomena. The instructive role of simple models, both classical and quantum, is demonstrated by putting the accent on the derivation of rigorous and exact analytical results.

P. Dineva, D. Gross, R. Müller, T. Rangelov


Dynamic Fracture of Piezoelectric Materials

Series: Solid Mechanics and Its Applications, Series editor: G.M.L. Gladwell, Elmira, Canada, Vol. 212, 255 pages. 200 illustrations. 2013, Springer, ISBN 978-3-319-03960-2.

Dynamic Fracture of Piezoelectric Materials focuses on the Boundary Integral Equation Method as an efficient computational tool. The presentation of the theoretical basis of piezoelectricity is followed by sections on fundamental solutions and the numerical realization of the boundary value problems. Two major parts of the book are devoted to the solution of problems in homogeneous and inhomogeneous solids. The book includes contributions on coupled electro-mechanical models, computational methods, its validation and the simulation results, which reveal different effects useful for engineering design and practice. The book is self-contained and well-illustrated, and it serves as a graduate-level textbook or as extra reading material for students and researchers.

Keywords » Boundary Integral Equation Method - Cracks in Piezoelectric Materials - Fracture Mechanics - Piezoelectric Materials - Stress Concentration Factors - Stress Intensity Factors

Related subjects » Computational Science & Engineering - Mechanics - Optical & Electronic Materials

  • Step-by-step tutorial for application of Boundary Integral Equation Method in mechanics

  • Includes methodology for numerical modeling of dynamic Fracture Mechanics problems

  • Test and benchmark examples, validated numerical schemes and algorithms for creating scientific software

  • Provides good mathematical basis for derivation of fundamental solutions for coupled problems of modern multifunctional materials

Classic and new approaches


Stefan Radev

Institute of Mechanics - BAS

Stoycho Panchev

Sofia University "St. Kl. Ohridski"

Nikolay K. Vitanov

Institute of Mechanics-BAS

Academic Publishing House Prof. Marin Drinov, 271 pages

ISBN 978-954-322-550-7, Sofia, 2012


Chapter 1: Instability - Cor. Member prof. DSc St. Radev
Chapter 2: Chaos - Acad. Prof. S. Panchev
Chapter 3: Optimum theory of turbulence - Prof. DSc N. K. Vitanov
Chapter 4: Stochastic modeling of turbulence - Prof. DSc N. K. Vitanov

This book contains an introduction to the problems of turbulent motion. Chapter 1 is devoted to selected instabilities of fluid motion. Chapter 2 contains a discussion on the connection between chaos and fluid turbulunce. In Chapter 3 we discuss the Howard-Busse variational theory of turbulence. Chapter 4 is devoted to discussion of the stochastic models of turbulent flow connected to the Lagrangian description of the fluid motion.

Series in Applied Mathematics and Mechanics,

Volume 4

Al. Popov Non-destructive evaluation of mechanical properties of iron-carbon alloys, Series in Applied Mathematics and Mechanics, Volume 4, Institute of Mechanics - BAS, Sofia, 2013, 196 pp.

ISSN: 1314-3034

The monograph look at the existing knowledge in non-destructive evaluation (NDE) in mechanical properties of iron-carbon alloys by means their ultrasonic and magnetic properties. One direction of NDE is measurement of ultrasonic characteristics (ASTM 494) of materials – velocities and attenuation on propagation of longitudinal and transversal waves. Second direction of NDE is measurement of magnetic properties – elements of magnetic lop.

The book is addressed to scientists in solid mechanics, experts in NDE and mechanical engineers.

Series in Applied Mathematics and Mechanics,

Volume 5

ISSN: 1314-3034

V. Kavardzhikov –Editor-in-chief Optical metrology in applied mechanics, Series in Applied Mathematics and Mechanics, Volume 5, Institute of Mechanics - BAS, Sofia, 2015, 247 pp.

This monographic reference book consists of five chapters. Its goal is to inform the readers with the classical and novel directions of optical metrology used in applied mechanics for qualitative and quantitative determination of mechanical characteristics of materials, surfaces, components and constructions. The Bulgarian and European standard documentation legalizing measurement of mechanical, geometrical and physical quantities as well as the eye’s metrology are examined. A special attention is directed to the metrological accuracy and experimental data processing. This monographic reference book is addressed to a wide audience such as metrologists and professionals from the field of applied mechanics, engineering physics and technical sciences.

Modified date:25-02-2018