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

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

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

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

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

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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