## Contents of the Journal of Mechanical Engineering 49, 4 (1998)



ADAMCZAK, S.: Development of mathematical modelling of reference
methods to measure roundness deviations of machine parts
(Review Paper)                                                           229

MAZUCH, T.: The use of finite element method
in axisymmetric-stress-wave dispersion analysis (in Slovak)              243

MORAVKA, S.: Elastic waves propagation in  thick cylindrical
semiinfinite elastic bars subjected to longitudinal impact
solved by an exact three-dimensional theory. Part II (in Czech)          253

WISZT, E.,  WISZTOVA, E.: Power balance of mechanical oscillators
coupled with acoustical fluid                                            268

RUZICKA, M., VALENTA, J., SOCHOR, M., VALERIAN, D.: Biomechanics
of age-related remodelling of vertebral trabecular bone structure        281

ZIGO, M.: Minimization of vibration amplitudes  of a resiliently
supported source of vibration in space (in Slovak)                       291



## Abstracts

### Review paper Development of mathematical modelling of reference methods to measure roundness deviations of machine parts

The development of mathematical modelling applied to the reference measuring of roundness deviations of machine parts discussed in the paper includes five stages: modelling symmetrical and asymmetrical methods (stages 1 and 2), adapting the mathematical model to computer calculations (stage 3), reanalysing the developed models after introducing simplifications (stage 4), and, finally, developing a universal model of measuring methods with regard to the concept of transformation of the profile measured with a reference method F(\phi) into the real profile R(\phi) (stage 5). Positive results of the mathematical mo-delling enable elimination or minimisation of all disadvantages and shortcomings of the measuring methods used hitherto.

### The use of finite element method in axisymmetric-stress-wave dispersion analysis

T. MAZUCH

In the study of stress-wave propagation in elastic bodies of infinite length the greatest attention in the literature is paid to the dispersion of axisymmetric waves. A modification of the author's recently published general FE approach for this special case is presented in this paper.

The proposed approach and the developed PC codes were tested on the case of torsionless axisymmetric wave dispersion in the isotropic hollow cylinder of infinite length. Comparison of the FE solution of the problem with the exact solution of the problem showed an unexpectedly good agreement. The highest relative error among 40 lowest phase velocities was less than 3.5 x 10-3%.

### Elastic waves propagation in thick cylindrical semiinfinite elastic bars subjected to longitudinal impact solved by an exact three-dimensional theory. Part II

S. MORAVKA

The results of analytical solution of a longitudinal impact of thick cylindrical bars obtained by using an exact three-dimensional theory are presented. The convergence of the results obtained by the exact 3D theory to the results performed in terms of a 1D elementary bar theory has been thoroughly investigated. The obtained dependences of displacements and stresses have been compared with the thin bar theory, Rayleigh-Love theory, with Skalak's asymptotic expansion for a long time, and with experiments realized by Miklowitz and Nisewanger.

### Power balance of mechanical oscillators coupled with acoustical fluid

E. WISZT, E. WISZTOVA

In the paper the problem of quantitative determination of particular power quantities (mean power of exciting force, mean power flow from the first oscillator to the second one, mean dissipated powers at the individual oscillators) of two harmonically excited mechanical oscillators is solved. The oscillators are coupled with acoustical fluid. The power quantities are determined as functions of parameters of the system and of the excitation frequency utilizing the results of previous works of the authors. The analytically derived general relations are complemented by numerical calculations for two particular cases of the acoustical coupling.

### Biomechanics of age-related remodelling of vertebral trabecular bone structure

M. RUZICKA, J. VALENTA, M. SOCHOR, D. VALERIAN

The submitted paper deals with the possibility of a mathematical age-related modelling of the constitution equation of the vertebral trabecular bone. We utilized an extensive set of experimental data obtained from cadavers (both male and female) concerning the third lumbar vertebra. For the aim, parametric regression analysis was applied while paying attention to the functions of ageing and trabecular bone softening. The coefficient of osteoporosis was introduced characterising not only the degenerative influence of the ageing process occurring in the vertebral trabecular bone but, also to a certain extent, the alteration taking place in the trabecular bone structure, i.e., in the spacing and thickness of the horizontal and vertical trabeculae as well as in its volume taken up, in dependence on the ageing process.

### Minimization of vibration amplitudes of a resiliently supported source of vibration in space

M. ZIGO

In previous paper [1] we derived basic equations for calculation of properties of springs created from two mutually symmetrically inclined rubber prisms. In [2] we determined limiting values of stiffness and bearing capacity which can be attained by the springs of this type.

In this study we utilize this knowledge for determination of properties and position of the described springs so that the amplitudes of vibration of the resiliently supported source of vibration in space are minimal. 