Valentin Abadjiev , Emilia Abadjieva

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 4, Sofia 1113, Bulgaria,

e-mail: abadjiev@imbm.bas.bg

Haruhisa Kawasaki, Tetsuya Mouri

Mechanical Engineering Department, Faculty of Engineering,

Gifu University, Yanagido 1-1, Gifu, Japan,

e-mails:
h_kawasa@gifu-u.ac.jp, __mouri@gifu-u.ac.jp__

COMPUTER SYNTHESIS APPROACHES
OF

HYPERBOLOID GEAR DRIVES WITH
LINEAR CONTACT

Abstract. The computer design has improved forming different type software for scientific researches in the field of gearing theory as well as performing an adequate scientific support of the gear drives manufacture. Here are attached computer programs that are based on mathematical models as a result of scientific researches. The modern gear transmissions require the construction of new mathematical approaches to their geometric, technological and strength analysis. The process of optimization,synthesis and design is based on adequate iteration procedures to find out an optimal solution by varying definite parameters. The study is dedicated to accepted methodology in the creation of software for the synthesis of a class high reduction hyperboloid gears – Spiroid and Helicon ones (Spiroid and Helicon are trademarks registered by the Illinois Tool Works, Chicago, Ill). The developed basic computer products belong to software, based on original mathematical models. They are based on the two mathematical models for the synthesis: “upon a pitch contact point” and “upon a mesh region”. Computer programs are worked out on the basis of the described mathematical models, and the relations between them are shown. The application of the shown approaches to the synthesis of commented gear drives is illustrated.

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D. Ignatova, E. Abadjieva, V. Abadjiev, Al. Vatzkitchev

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 4, Sofia 1113, Bulgaria,

e-mails: ignatova@imbm.bas.bg, abadjiev@imbm.bas.bg, alex@imbm.bas.bg

**WALKING ROBOT
LOCOMOTION SYSTEM**

**CONCEPTION**

Abstract. This work is a brief analysis on the application and perspective of using the walking robots in different areas in practice. The most common characteristics of walking four legs robots are presented here. The specific features of the applied actuators in walking mechanisms are also shown in the article. The experience of Institute of Mechanics – BAS is illustrated in creation of Spiroid and Helicon1 gears and their assembly in actuation of studied robots. Loading on joints reductors of robot legs is modelled, when the geometrical and the walking parameters of the studied robot are preliminary defined. The obtained results are purposed for designing the control of the loading of reductor type Helicon in the legs of the robot, when it is experimentally tested.

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P. Dineva

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 4, Sofia 1113, Bulgaria,

e-mail: petia@imbm.bas.bg

S. Parvanova, G. Vasilev

Department of Structural Engineering, UACEG,

1, Hristo Smirnenski Blvd, 1046 Sofia, Bulgaria

e-mail: gpekov@gmail.com

F. Wuttke

Marine and Land Geomechanics and Geotechnics,

Christian-Albrechts-University of Kiel,

Institute of Applied Geo-science, Germany

**SEISMIC
SOIL-TUNNELS INTERACTION VIA BEM**

**PART
I. MECHANICAL MODEL**

Abstract. Two-dimensional elastodynamic problem for seismic response of unlined and lined tunnels located in a layered half-plane with free sur face relief is solved. The computation tool uses the idea of the global matrix propagator method which allows derivation of a relation between the wave field quantities along different interfaces in the layered half-plane. The numerical realization of this idea is performed with the help of the sub-structured boundary element method (BEM) well suited when objects with arbitrary geometry are considered. A relation between displacements and tractions along the free surface and arbitrary interface of the soil stratum is derived. It works for arbitrary geometry of the interfaces between soil layers. Finally, in the companion paper, numerical results are presented which show both a validation study of the proposed computational methodology and extensive numerical simulations demonstrating the influence of some important factors as type and characteristics of the incident wave, dynamic tunnels interaction, soil-tunnel interaction, free surface relief, type of the tunnel construction and mechanical properties of the layered half-plane on the complex seismic field near and far-away from the underground structures.

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Li Li

Department of Mathematics, Qiqihar University, Qiqihar, 161006, China

and

Department of Applied Mechanics, University of Sciences and Technology Beijing,

Beijing, 100083, China,

e-mail: lili19762001@163.com

P. J. Wei

Department of Applied Mechanics, University of Sciences and Technology Beijing,

Beijing, 100083, China,

e-mail: weipj@ustb.edu.cn

**SURFACE WAVE
SPEED OF FUNCTIONALLY GRADED**

**MAGNETO-ELECTRO-ELASTIC
MATERIALS WITH**

**INITIAL STRESSES**

Abstract. The shear surface wave at the free traction surface of half infinite functionally graded magneto-electro-elastic material with initial stress is investigated. The material parameters are assumed to vary exponentially along the thickness direction, only. The velocity equations of shear surface wave are derived on the electrically or magnetically open circuit and short circuit boundary conditions, based on the equations of motion of the graded magneto-electro-elastic material with the initial stresses and the free traction boundary conditions. The dispersive curves are obtained numerically and the influences of the initial stresses and the material gradient index on the dispersive curves are discussed. The investigation provides a basis for the development of new functionally graded magneto-electro-elastic surface wave devices.

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T. O. Awodola, B. Omolofe

Department of Mathematical Sciences,

Federal University of Technology, Akure, Nigeria,

e-mail:
__babatope_omolofe@yahoo.com__

**RESPONSE TO
CONCENTRATED MOVING MASSES**

**OF ELASTICALLY
SUPPORTED RECTANGULAR PLATES**

**RESTING ON
WINKLER ELASTIC FOUNDATION**

Abstract.
The dynamic response to moving concentrated masses of elastically
supported rectangular plates resting on Winkler elastic foundation is
investigated in this work. This problem, involving non-classical
boundary conditions, is solved and illustrated with two common
examples often encountered in engineering practice. Analysis of the
closed form solutions shows that, for the same natural frequency (i)
the response amplitude for the moving mass problem is greater than
that one of the moving force problem for fixed Rotatory inertia
correction factor R_{0}
and foundation modulus F_{0},
(ii) The critical speed for the moving mass problem is smaller than
that for the moving force problem and so resonance is reached earlier
in the former. The numerical results in plotted curves show that, for
the elastically supported plate, as the value of R_{0}
increases, the response amplitudes of the plate decrease and that,
for fixed value of R_{0},
the displacements of the plate decrease as F_{0}
increases. The results also show that for fixed R_{0}
and F_{0},
the transverse deflections of the plates under the actions of moving
masses are higher than those when only the force effects of the
moving load are considered. Hence, the moving force solution is not a
save approximation to the moving mass problem. Also, as the mass
ratio Г
approaches zero, the response amplitude of the moving mass problem
approaches that one of the moving force problem of the elastically
supported rectangular plate resting on constant Winkler elastic
foundation.

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Ognyan Y. Kamenov

Department of Applied Mathematics and Informatics,

Technical University of Sofia, P.O. Box 384, 1000 Sofia, Bulgaria,

e-mail: __okam@abv.bg__

**EXACT PERIODIC
SEISMIC WAVES IN THE**

**NIKOLAEVSKII
MODEL**

Abstract. In the present paper three different in their structure families, of exact periodic solutions of the nonlinear evolution equation of Nikolaevskii, have been obtained. The common dynamic structure of these families of periodic solutions has been shown as well as the spatial displacements, typical of the non-integrable evolution equations, for each separate harmonics. These exact solutions are published for the first time.

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