Journal of Theoretical and Applied Mechanics

Volume 41, Number 1, 2011

 

Contents

E. Zahariev

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: evtimvz@bas.bg

J. Cuadrado

University of La Coruna, Ferrol, Spain,

e-mail: javicuad@cdf.udc.es

 

DYNAMICS OF MECHANISMS IN OVER CONSTRAINED

AND SINGULAR CONFIGURATIONS

 

Abstract. The present paper deals with the problems of dynamics simulation of rigid and flexible mechanisms with closed chains falling into singular and self-locking configurations. Dependent constrained equations and singularity of the mass-matrix of the dynamics equations are discussed.

A novel approach to decomposition of the closed chains into open branches is applied. The difference to the conventional methods using such decomposition consists in substitution of the constrained equations by stiff forces. The elasticity of certain mechanism links is taken into account for precise dynamics simulation of the singular configurations. The elasticity is modelled using finite element discretization. Generalized Newton-Euler dynamic equations with respect to the quasi-velocities and acceleration of the rigid bodies and flexible nodes are applied. Damping is considered for eliminating of undesirable high level oscillations of the stiff forces in the elastic links. Friction forces in the bearings for self-locking configurations are taken into account. Examples of dynamic analysis of mechanisms in over-constrained and singular configurations are presented.

Key words: dynamics, over-constrained mechanisms, singular configurations, flexibility.

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Stephan Tasev, Stoyan Grigorov

Institute of Water Problem, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 1, 1113 Sofia, Bulgaria,

e-mails: stefan.g.tasev@gmail.com, s.grigorov@mist-bg.com

Anton Tzenkov

EPFL, Swiss Federal Ins. of Technology, Lausanne, Switzerland,

e-mail: anton.tzenkov@gmail.com

 

AN ENGINEERING APPROACH FOR WAVE NUMBER DETERMINATION

 

Abstract. An engineering approach to radiation damping evaluation for both concrete and embankment dams has been proposed in some recent papers of the authors. The approach employs some elements of the Wave Mechanics to solve the problem of the dynamic dam-foundation interaction, e.g. the velocity of seismic shear wave, the frequency dependent wave number values, etc. The present paper demonstrates the possibilities of obtaining and         estimating these parameters. The wave number values of Santa Felicia earthfill dam are obtained for five different types of excitation. The variations in the wave number value are determined on the recorded field data and recently developed Method of Identification

and Prognostication of dynamic characteristic of dams. A generalization of the obtained results is presented. Possible practical applications of the proposed approach include an estimation of the total and the radiation damping for existing dams, as well as prediction of the dynamic characteristics of dams under construction, and analyzing the dam-water- foundation interaction effects. The proposed approach can be employed in the solution of similar problems for other civil engineering structures as tall buildings, towers, etc.

Key words: dam, damping, dynamic, earthquake, frequency, wave number.

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Mohamed Slim Abbes, Taissir Hentati, Mohamed Maatar,

Tahar Fakhfakh, Mohamed Haddar

Dynamics of Mechanical Systems Research Unit,

Mechanical Engineering Department,

National Engineering School of Sfax, BP 1173, 3038 Sfax, Tunisia University,

e-mails: ms abbes@yahoo.fr, taissirhentati@yahoo.fr

 

DYNAMIC ANALYSIS OF HELICAL GEARS SUPPORTED BY DEFECT ELEMENT BEARINGS

 

Abstract. This paper presents a simulation model for gear and bearing interactions in the presence of faults. A global model predicting dynamical behavior of a gear supported by four angular ball bearing system is developed, based on finite element approach. The implemented model has the capacity of considering gear transmission error and ball bearing waviness as sources of excitation in terms of forces or imposed displacements. The Hertzian contact theory is applied to calculate the elastic deflection and the non linear contact force exerted by the totality bearings balls on the input and output shafts. The nonlinear differential equations

are iteratively resolved using the Newmark integration technique coupled with the Newton Raphson method. The influence of the Ball bearing waviness order on the system transmission dynamic behaviour is studied. The results show the presence of system characteristic frequencies and their harmonics, and also, the frequencies resulting from waviness, which change with order and type of imperfection.

Key words: angular ball bearing, gear mesh, dynamic analysis, waviness.

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Dantchi Koulova

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: dantchi@imbm.bas.bg

Philippe Traor´e, Hubert Romat

Laboratoire d’Etudes A´erodynamiques,

Boulevard Pierre et Marie Curie,

BP 30179, 86962 Futuroscope-Chasseneuil, France,

e-mails: philippe.traore@univ-poitiers.fr,

hubert.romat@lea.univ-poitiers.fr

NUMERICAL STUDY OF THE ELECTRO-THERMO-CONVECTIVE FLOW PATTERNS IN DIELECTRIC LIQUID LAYER SUBJECTED TO UNIPOLAR INJECTION

 

Abstract. In this article we study the electro thermal convection in a dielectric liquid layer placed between two electrodes subjected to the simultaneous action of an electric field and a thermal gradient. The full set of equations describing the electro-thermo-convective phenomena is directly solved using a finite volume method. The electro convective motion

development is analysed in detail in four configurations: 1) strong injection from the upper or lower electrode; 2) when the electric potential and heating are applied simultaneously in the same time and in different time. We also study the heat transfer enhancement due to electro-convection. The evolution of the Nusselt number in terms of various non dimensional electrical parameters is presented and analyzed.

Key words: electro-thermo-convection, heat transfer, dielectric liquid, charge injection.

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Baljeet Singh

Department of Mathematics, Post Graduate Government College,

Sector-11, Chandigarh 160011, India,

e-mail: bsinghgc11@gmail.com

Lakhbir Singh, Sunita Deswal

Department of Mathematics, Guru, Jambheshewar University of Science and

Technology,

Hisar- 125001, Haryana, India

 

PROPAGATION OF WAVES AT AN INTERFACE BETWEEN TWO THERMOELASTIC HALF-SPACES WITH DIFFUSION

Abstract. Theory of generalized thermo-elastic diffusion is applied to study the reflection and the transmission of P and SV waves at an inter face of two dissimilar thermo-elastic solids with diffusion. The boundary conditions at the interface are satisfied by the suitable potentials to obtain a system of eight non-homogeneous equations in amplitude ratios of various reflected and transmitted waves. These amplitude ratios depend on the angle of incidence of P and SV waves, thermo-diffusion parameters and other material constants. The numerical values of these reflection and transmission coefficients are shown graphically against the angle of incidence for a particular model. The graphical results are compared with those without diffusion.

Key words: generalized thermo-elasticity, reflection and transmission, diffusion, amplitude ratios.

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Anguel Baltov

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: anguelbaltov@gmail.com

 

STRUCTURAL SYSTEMS SECURITY ZONES

 

Abstract. This presentation is based on some reviews’ of published papers and some new results. We propose the determination of security zones for structural system or the zones of good quality for structural materials. In the particular case, we verify if our system (or material) under consideration lies in these zones and what is the corresponding stock of security (quality). We introduce the nondimensional parameters characterized by the loading to realize this verification, the dimensions of the system and the mechanical properties of the structural material. These parameters come form the space of events. We apply the different criteria for the carrying capacity loss of the system and on this base we build up the limit surfaces. We introduce the sub zone of admissible parameter values. The zone between the limit surfaces and the corresponding admissible sub zone forms the security zone (or the zone of a good material quality). On this base, we can verify, what the stock of the system security is (or for the quality of the material). We give some examples. The special attention is paid to the seismic security zone and to the calculation of the seismic risk for the multi-storey building under seismic action.

Key words: structural system, security zones.

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