Assen Shulev, Tihomir Tiankov, Detelina Ignatova,
Kostadin Kostadinov, Ilia Roussev, Dimitar Trifonov
Institute of Mechanics, Bulgarian Academy of Science,
Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria,
e-mails: {assen,tihomir,ignatova,kostadinov,ilia,trifonov}@imbm.bas.bg
Valentin Penchev
Medical Centre – ReproBioMed,
28, Boicho Ognianov St., Ovcha Kupel, Sofia, Bulgaria
e-mail: v.penchev@reprobiomed.eu

OPTOMECHATRONIC SYSTEM FOR AUTOMATED
INTRA CYTOPLASMIC SPERM INJECTION

Abstract.
This paper presents a complex optomechatronic system for In-Vitro Fertilization (IVF), offering almost complete automation of the Intra Cytoplasmic Sperm Injection (ICSI) procedure. The compound parts and sub-systems, as well as some of the computer vision algorithms, are described below. System capabilities for ICSI have been demonstrated on infertile oocyte cells.
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Svetoslav Nikolov
Institute of Mechanics, Bulgarian Academy of Science,
Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria,
University of Transport, 158, G. Milev St., 1574 Sofia, Bulgaria,
e-mail: S.Nikolov@imbm.bas.bg
Nataliya Nedkova
University of Transport, 158, G. Milev St., 1574 Sofia, Bulgaria,
e-mail: Nataliya_Nedkova@abv.bg

GYROSTAT MODEL REGULAR
AND CHAOTIC BEHAVIOR

Abstract. During recent years, the interest in the phenomena of chaos in gyroscopic systems has been increasing. It is well-known, that depending on the speed of rotation, a gyroscopic system may lose or gain stability. Despite the overwhelming number of studies reporting the occurrence of various chaotic structures, little is known yet about the construction details and the generality of the underlying bifurcation scenarios that give rise to such chaotic (complex) behaviour.
In this paper, we report a detailed investigation of the abundance of regular and chaotic behaviour for rigid body (gyrostat) motion. The model contains 6 parameters that may be tuned to produce rich dynamical scenarios. The results confirm that homoclinic and heteroclinic structures with two fixed points from saddle-focus type occur and the emergence of Shilnikov chaos takes place. Finally, we find new results concerning the system’s evolution and bifurcation scenarios for its routes to chaos.
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Anguel Baltov, Ana Yanakieva
Institute of Mechanics, Bulgarian Academy of Science,
Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria,
e-mails: anguelbaltov@gmail.com, aniyanakieva@imbm.bas.bg

LOCAL DEPLANATION OF DOUBLE REINFORCED
BEAM CROSS SECTION UNDER BENDING

Abstract. Bending of beams, double reinforced by means of thin composite layers, is considered in the study. Approximate numerical solution is proposed, considering transitional boundary areas, where smooth quadratic transition of the elasticity modulus and deformations take place.
Deplanation of the cross section is also accounted for in the areas. Their thickness is found equalizing the total stiffness of the cross section and the layer stiffness. Deplanation of the cross section of the transitional area is determined via the longitudinal deformation in the reinforcing layer, accounting for the equilibrium between the internal and the external moment, generated by the longitudinal stresses in the cross section.
A numerical example is given as an illustration demonstrating model’s plausibility. The model allows the design and the calculation of recycled concrete beams double reinforced by means of thin layers. The approach is in agreement with modern design of nearly zero energy buildings (NZEB).
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Mohammad Arefi
Department of Solid Mechanic, Faculty of Mechanical Engineering,
University of Kashan, 87317-51167, Iran,
e-mail: arefi63@gmail.com, arefi@kashanu.ac.ir
Iman Nahas
School of Mechanical Engineering, Iran University of Science and Technology,
Narmak, Tehran, Iran,
e-mail: nahas@mecheng.iust.ac.ir
Majid Abedi
Department of Mechanical Engineering,
Shiraz University, Shiraz, Iran,
e-mail: majidabedi1989@gmail.com

THERMO-ELASTIC ANALYSIS OF A ROTATING
HOLLOW CYLINDER MADE OF ARBITRARY
FUNCTIONALLY GRADED MATERIALS
Abstract. Thermo-mechanical analysis of the functionally graded orthotropic rotating hollow structures, subjected to thermo-mechanical loadings is studied in this paper. The relations were derived for both plane strain and plane stress conditions as a cylinder and disk, respectively. Non homogeneity was considered arbitrary through thickness direction for all mechanical and thermal properties. The responses of the system including temperature distribution, radial displacement and radial and circumferential stresses were derived in the general state. As case study, power law gradation was assumed for functionally graded cylinder and the mentioned results were evaluated in terms of parameters of the system such as non-homogeneous index and angular velocity.

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Indrajit Roy
Department of Mathematics,
Gayeshpur Netaji Vidyamandir, WB, India,
e-mail: mathjit@gmail.com
D. P. Acharya
Principal (Retired), Bangabasi Morning College,
Kolkata – 9, India,
e-mail: acharyadp_05@rediffmail.com
Sourav Acharya
Atomic Energy Regulatory Board,
Mumbai, India,
e-mail: acharyasourav08@gmail.com

RAYLEIGH WAVE IN A ROTATING NONLOCAL
MAGNETOELASTIC HALF-PLANE

Abstract. This paper investigates the propagation of Rayleigh surface waves in a rotating semi-infinite solid medium, permeated by an initial magnetic field in the context of linear nonlocal elasticity. Frequency equations are derived and the combined effect of magnetic field and rotation on Rayleigh wave propagation, based on the linear theory of nonlocal elasticity has been studied. Effects of magnetic field, as well as rotation on Rayleigh wave propagation in a nonlocal medium, have also been analyzed in details as special cases. Numerical calculations, graphs and discussions presented in this paper lead us to some important conclusions. Fourier double integral transform technique has been applied to solve the problem.

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Zlatinka I. Dimitrova
“G. Nadjakov” Insitute of Solid State Physics„
72, Tzarigradsko Chaussee Blvd., 1784 Sofia, Bulgaria,
e-mail: zdim@issp.bas.bg

NUMERICAL INVESTIGATION OF NONLINEAR WAVES
CONNECTED TO BLOOD FLOW IN AN ELASTIC TUBE
WITH VARIABLE RADIUS

Abstract. We investigate flow of incompressible fluid in a cylindrical tube with elastic walls. The radius of the tube may change along its length. The discussed problem is connected to the fluid-structure interaction in large human arteries and especially to nonlinear effects. The long-wave approximation is applied to solve model equations. The obtained model Korteweg-deVries equation possessing a variable coefficient is reduced to a nonlinear dynamical system of three first order differential equations. The low probability of a solitary wave arising is shown. Periodic wave solutions of the model system of equations are studied and it is shown that the waves, that are consequence of the irregular heart pulsations may be modelled by a sequence of parts of such periodic wave solutions.
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