### Contents of Journal of Mechanical Engineering *52,* 4 (2001)

R. VODICKA: Boundary integral equation systems for some kinds
of contact problems 193
M. SAGA: Numerical study of random vibration of nonlinear truss
structures (in Slovak) 208
V. M. VIHAK, Y. Z. POVSTENKO, A. V. RYCHAHIVSKYY: Integration
of elasticity and thermoelasticity equations in terms of stresses 221
E. MALENOVSKY, F. POCHYLY: Some results of computational modelling
of dynamic behaviour of journal bearings using the Bezier body 235

# Abstracts

###
Boundary integral equation systems for some kinds of contact problems

R. VODICKA

A boundary integral equation (BIE) solution of a contact problem is presented.
Two kinds of BIE systems are shown (the first-kind BIE and the second-kind
BIE), using both displacement strongly singular BIE and traction
hyper-singular BIE. Boundary element approaches are used to solve these
systems. The paper also presents some of the numerical results of both types
of BIE systems.

###
Numerical study of random vibration of nonlinear truss structures

M. SAGA

This study considers the solution of elastic-plastic trusses under random
excitation. The hysteretic constitutive laws will be derived from Bouc-Wen's
smooth differential equations model. The stochastic linearization method, the
Hurtado-Barbat's linearization approach and the Monte Carlo approach are
presented. Monte Carlo simulation is used to check the accuracy of the
results. Results of simple truss structures under Gaussian white-noise
excitation indicate that the proposed methods are adequate for the first and
second statistical moments but inadequate for estimating spectral properties.

###
Integration of elasticity and thermoelasticity equations in terms of stresses

V. M. VIHAK, Y. Z. POVSTENKO, A. V. RYCHAHIVSKYY

Formulation and a method of integration of differential elasticity and
thermoelasticity equations in terms of stresses are proposed. The existence of
only three compatibility equations in terms of strains is proved, which makes
it possible to formulate correctly three-dimensional elasticity or
thermoelasticity problems in terms of stresses. The single-valued
relationships between tractions and displacements at the body boundary are
obtained. Integral equilibrium conditions for stresses as well as integral
compatibility conditions for strains and displacements are found. They are
pointed out to play an important part when solving direct and inverse
elasticity or thermoelasticity problems.

###
Some results of computational modelling of dynamic behaviour of journal
bearings using the Bezier body

E. MALENOVSKY, F. POCHYLY

A new theoretical approach to the modelling of dynamic behaviour of the rigid
rotating shaft in real liquid is presented in this contribution. The approach
is based on application of the Navier-Stokes equation. It is possible to
separate the motion of a rigid body and liquid using suitable transformation
relations as well as the stationary and nonstationary motions from each other.
Method of control volumes is used for the analysis, and a solution is obtained
in a curvilinear co-ordinate system. The Bezier body is used for description
of the geometrical configuration and also for approximation of velocity and
pressure functions. The combined ALE (Arbitrary Lagrange-Euler) method is
used, as it is necessary to generate a new net (perform new meshing) for
change of the shaft position. Some results of numerical solution of the model
task using both theories are presented.