Alexander Borisoff Kazakoff, Boycho Ivanov Marinov
Institute of Mechanics, Bulgarian Academy of Science,
Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria,
e-mails: alex_kazakoff@yahoo.co.uk, boicho_marinoff@yahoo.co.uk,
boicho_marinoff@abv.bg

FIVE MASS POWER TRANSMISSION LINE OF A SHIP
COMPUTER MODELLING


Abstract. The work, presented in this paper, appears to be a natural continuation of the work presented and reported before, on the design of power transmission line of a ship, but with different multi-mass model. Some data from the previous investigations are used as a reference data, mainly from the analytical investigations, for the developed in the previous study, frequency and modal analysis of a five mass model of a power transmission line of a ship. In the paper, a profound dynamic analysis of a concrete five mass dynamic model of the power transmission line of a ship is performed using Finite Element Analysis (FEA), based on the previously recommended model, investigated in the previous research and reported before. Thus, the partially validated by frequency analysis five mass model of a power transmission line of a ship is subjected to dynamic analysis. The objective of the work presented in this paper is dynamic modelling of a five mass transmission line of a ship, partial validation of the model and von Mises stress analysis calculation with the help of Finite Element Analysis (FEA) and comparison of the derived results with the analytically calculated values. The partially validated five mass power transmission line of a ship can be used for definition of many dynamic parameters, particularly amplitude of displacement, velocity and acceleration, respectively in time and frequency domain. The frequency behaviour of the model parameters is investigated in frequency domain and it corresponds to the predicted one.
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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
Valentin Nedev
University of Transport,
158, G. Milev St., 1574 Sofia, Bulgaria,
e-mail: val_nedev@abv.bg

BIFURCATION ANALYSIS AND DYNAMIC BEHAVIOUR
OF AN INVERTED PENDULUM WITH BOUNDED
CONTROL

Abstract. This paper presents an investigation on the behaviour of conventional inverted pendulum with an inertia disk in its free extreme. The system is actuated by means of torques applied to the disk by a DC motor, mounted on the pendulum’s arm. Thus, the system is underactuated since the pendulum can rotate freely around its pivot point. The dynamical model is given with three ordinary nonlinear differential equations. Using Poincare-Andronov-Hopf’s theory, we find a new analytical formula for the first Lyapunov’s value at the boundary of stability. It enables one to study in detail the bifurcation behaviour of the above dynamic system. We check the validity of our analytical results on the first Lyapunov’s value by numerical simulations. Hence, we find some new results.


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Ning Han, Qingjie Cao

Centre for Nonlinear Dynamics Research,
Harbin Institute of Technology,
School of Astronautics, Harbin 150001 China,
e-mails: han_ning@outlook.com, q.j.cao@hit.edu.cn


MULTIPLE BIFURCATIONS OF A CYLINDRICAL
DYNAMICAL SYSTEM

Abstract. This paper focuses on multiple bifurcations of a cylindrical dynamical system, which is evolved from a rotating pendulum with SD oscillator. The rotating pendulum system exhibits the coupling dynamics property of the bistable state and conventional pendulum with the homoclinic orbits of the first and second type. A double Andronov-Hopf bifurcation, two saddle-node bifurcations of periodic orbits and a pair of homoclinic bifurcations are detected by using analytical analysis and numerical calculation. It is found that the homoclinic orbits of the second type can bifurcate into a pair of rotational limit cycles, coexisting with the oscillating limit cycle. Additionally, the results obtained herein, are helpful to explore different types of limit cycles and the complex dynamic bifurcation of cylindrical dynamical system.

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V. Rizov

Department of Technical Mechanics,
University of Architecture, Civil Engineering and Geodesy,
1, Chr. Smirnensky Blvd, 1046 Sofia, Bulgaria,
e-mail: V_RIZOV_FHE@UACG.BG


NON-LINEAR ANALYSIS OF MODE II FRACTURE
IN THE END NOTCHED FLEXURE BEAM

Abstract. Analysis is carried-out of fracture in the End Notched Flexure (ENF) beam configuration, taking into account the material nonlinearity. For this purpose, the J-integral approach is applied. A non-linear model, based on the Classical beam theory is used. The mechanical behaviour of the ENF configuration is described by the Ramberg-Osgood stress-strain curve. It is assumed that the material possesses the same properties in tension and compression. The influence is evaluated of the material constants in the Ramberg-Osgood stress-strain equation on the fracture behaviour. The effect of the crack length on the J-integral value is investigated, too. The analytical approach, developed in the present paper, is very useful for parametric analyses, since the simple formulae obtained capture the essentials of the non-linear fracture in the ENF configuration.
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Albena Doicheva
Technical Mechanics Department,
University of Architecture Civil Engineering and Geodesy,
1, Hristo Smirnenski Blvd, Sofia 1046, Bulgaria,
e-mails: doicheva_fhe@uacg.bg, a_doicheva@abv.bg

T-SHAPED FRAME CRITICAL
AND POST-CRITICAL ANALYSIS

Abstract. The paper shows solution of a T-shaped frame, strengthened with two linear springs, regarding critical and post-critical analysis. The solution is exact using the Euler elastic approach and the frame of reference, originated in the point of column axis inflexion. The derived Numerical results show the effect of the springs strengthening for the critical and the post-critical system behaviour. The influence of the geometry change is analyzed, as well.
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Hao-Peng Song, Kun Song
State Key Laboratory of Mechanics and Control of Mechanical Structures,
Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China,
e-mail: shp305@163.com

ELECTRIC AND HEAT CONDUCTIONS ACROSS A
CRACK IN A THERMOELECTRIC MATERIAL

Abstract. The crack problem in a thermoelectric material is studied in this paper. Two kinds of crack surface conditions are discussed. The closed form solutions are derived, based on the complex variable method. The field intensity factors as well as the conversion efficiency are discussed in detail. The results show that the electric current density and thermal flux density exhibit traditional square-root singularity at the crack tip in case 1, while the electric current density has no singularity at the crack tip in case 2. It is proved due to the electric current flow and thermal flux separation, that the thermoelectric conversion efficiency can be higher than the maximum conversion efficiency of one-dimensional thermoelectric under the same temperature condition. In the numerical example, the conversion efficiency is increased by 29.6% as compared to the maximum conversion efficiency of one-dimensional thermoelectric.

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