EMILIA A BADJIEVA1,2∗, VALENTIN ABADJIEV2 ,
A KIHIRO NAGANAWA1
1 Graduate School of Engineering Science, Faculty of Engineering Science, Akita University, Tegatagakuen - machi 1-1, Akita, Japan
2 Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev, block 4, 1113 Sofia, Bulgaria
[Received 16 October 2017. Accepted 04 December 2017]

SPATIAL RACK DRIVES PITCH CONFIGURATIONS:
ESSENCE AND CONTENT

ABSTRACT: The practical realization of all types of mechanical motions converters is preceded by solving the task of their kinematic synthesis. In this way, the determination of the optimal values of the constant geometrical parameters of the chosen structure of the created mechanical system is achieved.
The searched result is a guarantee of the preliminary defined kinematic characteristics of the synthesized transmission and in the first place, to guarantee the law of motions transformation. The kinematic synthesis of mechanical transmissions is based on adequate mathematical modelling of the process of motions transformation and on the object, realizing this transformation. Basic primitives of the mathematical models for synthesis upon a pitch contact point are geometric and kinematic pitch configurations. Their dimensions and mutual position in space are the input parameters for the processes of design and elaboration of the synthesized mechanical device. The study presented here is a brief review of the theory of pitch configurations. It is an independent scientific branch of the spatial gearing theory (theory of hyperboloid gears). On this basis, the essence and content of the corresponding primitives, applicable to the synthesis of spatial rack drives, are defined.
KEY WORDS: Hyperboloid gears, spatial rack mechanisms/drives, mathematical modelling, kinematic synthesis, pitch configurations.
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DIMITAR CHAKAROV, IVANKA VENEVA , MIHAIL TSVEOV , PAVEL VENEV
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 4, 1113, Sofia, Bulgaria
[Received 16 October 2017. Accepted 04 December 2017]


POWERED UPPER LIMB ORTHOSIS ACTUATION SYSTEM
BASED ON PNEUMATIC ARTIFICIAL MUSCLES

ABSTRACT: The actuation system of a powered upper limb orthosis is studied in the work. To create natural safety in the mutual “man-robot” interaction, an actuation system based on pneumatic artificial muscles (PAM) is selected. Experimentally obtained force/contraction diagrams for bundles, consisting of different number of muscles are shown in the paper. The pooling force and the stiffness of the pneumatic actuators is assessed as a function of the number of muscles in the bundle and the supply pressure. Joint motion and torque is achieved by antagonistic actions through pulleys, driven by bundles of pneumatic muscles. Joint stiffness and joint torques are determined on condition of a power balance, as a function of the joint position, pressure, number of muscles and muscles
KEY WORDS: Upper limb orthosis, actuation system, pneumatic artificial muscles, experimental diagrams, stiffness, torques.


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V.S. JIVKOV 1, E.V. Z AHARIEV2
1 Mech. and Mach. Theory Dept., Technical University of Sofia, Bulgaria
2 Institute of Mechanics, Bulgarian Academy of Sciences, Bulgaria
[Received 10 October 2017. Accepted 12 March 2018]



CANTILEVER BEAM NATURAL FREQUENCIES IN
CENTRIFUGAL INERTIA FIELD

ABSTRACT: In the advanced mechanical science the well known fact is that the gravity influences on the natural frequencies and modes even for the vertical structures and pillars. But, the condition that should be fulfilled in order for the gravity to be taken into account is connected with the ration between
the gravity value and the geometrical cross section inertia. The gravity is related to the earth acceleration but for moving structures there exist many other acceleration exaggerated forces and such are forces caused by the centrifugal accelerations. Large rotating structures, as wind power generators, chopper wings, large antennas and radars, unfolding space structures and many others are such examples. It is expected, that acceleration based forces influence on the structure modal and frequency properties, which is a subject of the present investigations.
In the paper, rotating beams are subject to investigations and modal and frequency analysis is carried out. Analytical dependences for the natural resonances are derived and their dependences on the angular velocity and centrifugal accelerations are derived. Several examples of large rotating beams with different orientations of the rotating shaft are presented. Numerical experiments are conducted. Time histories of the beam tip deflections, that depict the beam oscillations are presented.
KEY WORDS: Natural frequencies, systems with distributed parameters, differential transformation method (DTM), numerical methods.

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A.A. MARKOU1, G.D. MANOLIS 2
1 Norwegian Geotechnical Institute, Sognsveien 72, Oslo 0806, Norway
2 Department of Civil Engineering, Aristotle University Panepistimioupolis,
Thessaloniki 54124, Greece
[Received 10 October 2017. Accepted 04 December 2017]


NUMERICAL SOLUTIONS FOR NONLINEAR HIGH DAMPING
RUBBER BEARING ISOLATORS: NEWMARK’S METHOD WITH
NETWON-RAPHSON ITERATION REVISITED

ABSTRACT: Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated
with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb
friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark’s time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.
KEY WORDS: High damping rubber bearings; mechanical models; trilinear hysteretic model; shear behaviour; nonlinear response; base isolation; Newmark’s method.
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NIKOLAY K. V ITANOV1∗, ZLATINKA I. DIMITROVA2
1 Institute of Mechanics, Bulgarian Academy of Sciences, Akad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
2 G. Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria
[Received 16 October 2017. Accepted 04 December 2017]


MODIFIED METHOD OF SIMPLEST EQUATION APPLIED TO
THE NONLINEAR SCHRÖDINGER EQUATION
ABSTRACT: We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.
KEY WORDS: Nonlinear partial differential equations, exact solutions, nonlinearSchroedinger equation, method of simplest equation.
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VLADYSLAV KYRYCHOK, VASYL TOROP
The E.O. Paton Electric Welding Institute of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
[Received 16 October 2017. Accepted 12 March 2018]

DETERMINATION OF THE CRACK RESISTANCE PARAMETERS
AT EQUIPMENT NOZZLE ZONES UNDER THE SEISMIC LOADS
VIA FINITE ELEMENT METHOD

ABSTRACT: The present paper is devoted to the problem of the assessment of probable crack growth at pressure vessel nozzles zone under the cyclic seismic loads. The approaches to creating distributed pipeline systems, connected to equipment are being proposed. The possibility of using in common different finite element program packages for accurate estimation of the strength of bonded pipelines and pressure vessels systems is shown and justified. The authors propose checking the danger of defects in nozzle domain, evaluate the residual life of the system, basing on the developed approach.
KEY WORDS: Seismic analysis, crack growth, nozzle, vessel, distributed pipelines, response spectrum.

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SAEED EBRAHIMI1, NADER VAHDATAZAD2 ,
GHOLAMHOSSEIN LIAGHAT3

1 Department of Mechanical Engineering, Yazd University, Yazd, Iran
2  School of Mechanical Engineering, Shahid Sattari University of Aeronautical Engineering, Tehran, Iran
3 Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
[Received 16 October 2017. Accepted 12 March 2018]

EXPERIMENTAL CHARACTERIZATION OF THE ENERGY
ABSORPTION OF FUNCTIONALLY GRADED FOAM FILLED
TUBES UNDER AXIAL CRUSHING LOADS

ABSTRACT: This paper deals with the energy absorption characterization of functionally graded foam (FGF) filled tubes under axial crushing loads by experimental method. The FGF tubes are filled axially by gradient layers of polyurethane foams with different densities. The mechanical properties of thepolyurethane foams are firstly obtained from axial compressive tests. Then, the quasi-static compressive tests are carried out for empty tubes, uniform foam filled tubes and FGF filled tubes. Before to present the experimental test results, a nonlinear FEM simulation of the FGF filled tube is carried out in ABAQUS software to gain more insight into the crush deformation patterns, as well as the energy absorption capability of the FGF filled tube. A good agreement between the experimental and simulation results is observed. Finally, the results of experimental test show that an FGF filled tube has excellent energy absorption capacity compared to the ordinary uniform foam-filled tube with the same weight.
KEY WORDS: Foam-filled tubes, functionally graded foam (FGF), energy absorption, peak crushing force, polyurethane.
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