** **

**Journal of Theoretical and Applied Mechanics**

Volume 32, Number 4, 2002

**Contents**

**V. Petrov, N. Georgiev**

Institute of Mechanics, Bulgarian Academy of Sciences,

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

*e-mail*: valko@imbm.bas.bg

**J. Kurths**

Institute of Physics, Potsdam University,

D-14415, Germany,

*e-mail: *juergen@agnld.uni-potsdam.de

**Numerical reconstruction of low-dimensional dynamical system from a time
series**

Abstract.** **On the basis of theorems proved in a previous authors
paper and in view of the well known trajectory type classifications for these cases, an
example for reconstructing unknown ordinary differential equation* *from a given
solution in the form of integral depending on parameter is solved geometrically and
numerically. Moreover, the problems for reconstructing third- and fourth- order
differential equations are illustrated by geometrical and numerical processing the
numerical solutions of Rossler and Duffing equations, respectively. For these purposes a
specific form of interpolation method is applied.

Key words**: **phase space dimension, differential equation,
interpolation procedure.

**Al. B. Kazakoff**

Institute of Mechanics, Bulgarian Academy of Sciences,

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

*e-mail***:** alex_kazakoff@yahoo.co.uk

**CHARACTERISTICS OF MECHANICAL FILTERS INCORPORATING VISCOELASTIC
MATERIALS (PART I)**

Abstract**.** This paper describes investigation of spatial
vibrations of mechanical filters presented as a double mass vibration dynamic system
utilising viscoelastic properties and natural frequency prediction of dynamically scaled
models of the mechanical filters subjected to a half sine wave shock input. The mechanical
and mathematical modelling is performed on the basis of a double mass dynamic model with
twelve degrees of freedom in the spatial variant: six for each mass - three for the linear
and three for the angular motion. A forced response analysis was used to determine the
resonant frequencies of viscoelastically damped structures. Finite Element Analysis (FEA)
is used to predict the vibration characteristics of the viscoelastic systems. The
frequency dependant properties of the Young’s modulus and loss factor are incorporated
in the FEA, in which a commercial code ABAQUS is used. The results of FEA are partially
validated by means of analytical analysis using the energy approach and the classical
Lagrange’s differential equation of second order. Natural frequencies and amplitudes of
displacement are obtained by means of computer experiment in the three dimensional
solution and compared with the results of finite element analysis. In this paper an
optimisation of the double mass dynamic system has been performed in two basic directions:
with respect to material and geometry optimisation of dynamically scaled bodies.

Key words**:** vibrations, mechanical filters, viscoelastic material
properties,

frequency dependence, forced response calculations.

**St. Bachvarov**

Engineering Pedagogical Faculty-Sliven, Technical University–Sofia,

59, Bourgasko shosse Str., 8800 Sliven, Bulgaria

**V. Zlatanov**

Higher Institute of Food and Flavour Industry,

26, Maritza Str., 4000 Plovdiv, Bulgaria,

*e-mail: *vassil60@Hotmail.com

**S. Delcheva**

Engineering Pedagogical Faculty-Sliven, Technical University–Sofia,

59, Bourgasko shosse Str., 8800 Sliven, Bulgaria

**DYNAMICS OF MACHINE AGGREGATES WITH IDEALLY RIGID LINKS AND FRICTION
COUPLING BETWEEN THE POWER MACHINE AND THE GEARING (Part II)**

Abstract. The paper treats the dynamics of a machine aggregate set in motion by an asynchronous electric motor, and a working machine with constant, linear and quadratic characteristics of the resistance forces. A number of devices are mounted between the aggregate and the working machine: a switching friction coupling, a reducer with constant gear ratio, a permanently switched on coupling, and ideally rigid shafts. Motion of the latter is reduced to the electric motor shaft. Transition processes of acceleration, stopping and the loading of the aggregate shaft-conductor are also studied. The results found are illustrated by means of a numerical example, which considers an aggregate with real parameters.

Key words: machine aggregate, reducer (gearing), friction coupling, transitory processes under acceleration and stopping, dynamic loads.

**V, Valeva, J. Ivanova ^{ }**

Institute of Mechanics, Bulgarian Academy of Sciences,

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

*e-mail :*

**Z. Mroz**

AMAS Center, Institute of Fundamental Technological Research,

Polish Academy of Sciences,

21. Swietokrzyska, 00-048 Warsaw, Poland,

*e-mail: *zmroz@ippt.gov.pl

Parametric analysis of the decay rate of End effects in heat conduction for multi-layered semi-infinite SANDWICH structures

Abstract. This article is concerned with the effect of imperfect interfaces on the decay of end effect for heat conduction in non-symmetric sandwich strip with - layers. The constituent layers are isotropic and the interface conditions between the layers are assumed to be either LC-type or HC-type at vanishing temperature at the bottom and top side of the strip. The characteristic decay length in all considered cases for three-layered sandwich strip is numerically calculated and represented by the smallest real and positive root of a corresponding transcendental equation. The results of parametric analysis of decay rate depending on volume fraction and heat conductivity of constituents provided for three-layered sandwich strip are illustrated in figures and discussed. Some optimal parameters for the considered structure at which the maximal value of the decay rate is reached are proposed.

Key words: decay rate of end effects, heat condition, semi-infinite sandwich structure.

**V. A. Dzhupanov, D. V. Dzhupanova**

Institute of Mechanics, Bulgarian Academy of Sciences,

*Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,*

e-mail: dzhupan@imbm.bas.bg

**Statement ruses of the problem on the dynamic stability of cantilevered
pipe conveying liquid and lying on elastic foundation (Part I)**

Abstract. Following the hypothesis of *Winkler* the *Foundation
response* = - *cw*, where *w *is current vertical
displacement of the points of the pipe neutral axis, and *c* is constant
proportionality coefficient. The sense of *c* is "*a* *local foundation
response force due to local unit displacement of the pipe*". The use of this
hypothesis in some special dynamical problems generated paradoxical results. The matter is
that in the process of the analytical solution of the problem the local force of the
foundation response naturally has to be associated with the inertial forces, although they
are not permanently cophasal in the time of one period of the vibration. In contrast this
force is permanently cophasal with the force of the internal pipe stiffness *Kw*,_{xxxx},
where *K* ? *EI* and *w*,_{xxxx} ? ¶ ^{4}*w*/¶ *x*^{4}. So it is more natural to use the expression
of the foundation response like *Foundation response* = - D *Kw*,_{xxxx},. The proposal introduces a set of ruses,
which permit to avoid the paradoxical results mentioned above.

Key words: beam-like pipe, dynamic stability, flutter, elastic resisting foundation, joined stiffness.

**D. Kisliakov**

University of Architecture, Civil Engineering and Geodesy,

1, Chr. Smirnenski Blvd., 1421 Sofia, Bulgaria,

*e-mail: *kiss_fhe@uacg.bg

**Coupled 3-D Analysis of the Axial and Transversal Earthquake-Induced
Vibrations of a Pressure Pipeline on Frictional Support Columns**

Abstract. In this work, the spatial seismic response of a multiple-supported pressure pipeline on frictional columns is analysed. The governing equations of motion of an arbitrary pipeline span in terms of the unknown component of the dynamic transversal displacement are presented. The dynamic interaction between the pipe and the flowing liquid inside is also accounted for. Here, the support columns are regarded as stiff in axial direction. The necessity of this assumption is argued, and it is shown by a comparative non-linear FE study that the discrepancy of the results caused by this assumption is on the safety side in the engineering practice. The developed computational procedure for the coupled 3-D response analysis of the pipeline is presented in detail. Numerical example with a real structural data set is solved as well.

Key words**:** multiple-supported pressure pipeline, Coriolis
theorem, Coulomb friction, kinematic support excitation, pipe-liquid interaction,
comparative non-linear dynamic FEA.

**G. Tzvetkova, D. Petrova, H. Hristov, A. Cheremensky**

Institute of Mechanics, Bulgarian Academy of Sciences,

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

*e-mail*: ana@bgcict.acad.bg

**Identification of linear parameters in dynamical systems**

Abstract. The optimal LQ approximation is proposed for identification of linear parameters in dynamical systems when their integral curves are known in some special sense. Mechanical examples of such systems are given.

Key words: LQ-approximation, identification, star tracker.