Contents of the Journal of Mechanical Engineering 49, 2 (1998)

DANEK, O., KOZANEK, J.: Mathematical models of dynamic systems 
with general structure (Review paper) (in Czech)                           81


JILEK, M.: Stress transients propagation in a viscoelastic conical bar. 
II. Dynamic analysis and results (in Czech)                                97 


HOMISIN, J., JURCO, M.: Application of  differential pneumatic  clutch 
with an additional regulating system (in Slovak)                          106


AWAD, A. S. Kh., MOLNAR, V.: Computational model of gas turbine combustor
                                                                          112


DOVICA, M., GMITERKO, A., HOMISIN, J., JURCO, M.: Basic study of a mobile 
minimechanism for movement in pipes of small diameter (in Slovak)         124


BEKES, J., VELISEK, K.: Analytical approach to tool-machine design 
(in Slovak)                                                               141

This paper deals with modal analysis and inverse problem of mathematical models of general dynamic systems, i.e. systems with simple and Jordan-type structure. It is concerned with dynamic systems with dominant appearance of multiple eigenvalues, e.g. systems with kinematic degrees of freedom, evolutive dynamic systems, or overdamped systems.

The type of considered mathematical models, identified in m-dimensional space with the system of m linear differential equations of order r >= 2 with respect to time t and with time independent coefficient matrices, is described in the first chapter. The model is transformed into the state space with one coefficient matrix A of order n = m x r to resolve the above-mentioned problem.

The general solution, derived from the canonical transformation of the coefficient matrix A, is given in the second chapter. General formulas explain the different behaviour of simple and Jordan-type dynamic systems for free and forced vibration, in resonance and in non-resonance regime.

The third chapter is devoted to the inverse problem, and the formulas for coefficient matrices of the mathematical model of the dynamic system with prescribed spectral and modal properties are deduced.

The solution in the case of the singular coefficient matrix determining the order r of differential equations is suggested in the fourth chapter.

Finally, the last chapter is devoted to the modification of the mathematical model with additional small non-linearities and with parametric coupling in the case of a possible defective structure. Regarding technical applications, only the formula for the first approximation of this iterative solution is given.

The paper is the second part of an analysis dealing with the axial impact of a slender viscoelastic conical bar upon a rigid half-space. An analytical approach for two parallelly coupled string-piston groups reveals two different motion components - oscillatory-wave and exponential. Numerical evaluation was carried out for materials differing quantitatively in viscous effects. The results are represented by stress-time and stress-position curves. They show interesting features as a consequence of both conical geometry and viscoelastic behaviour, e.g., tensile stresses in the bar and filtering properties of the bar.

Mechanical systems with piston engines can be characterized as torsionally oscillating mechanical systems. Intensive torsional oscillations cause an excessive dynamic load imposed upon the systems. For this reason, it is inevitable to control their dangerous torsional oscillations. The most suitable way to eliminate this is a use of a flexible shaft clutch.

The results of the theoretical research are pointing to the fact that the differential pneumatic clutch with an added regulatory system satisfies all requirements for the use in mechanical systems with a broad range of revolutions.

The objective of this paper is to show a computational method for determination of the effect of secondary air on the flow and pollutant emissions inside and at the exit from the combustor of a gas turbine, and to compare the results at different positions of the inlet of the secondary air along the combustor. The computational model is applicable to two dimensional, turbulent, swirling, and recirculating flows with actual combustion inside the combustor of a gas turbine. The fundamental conservation laws of mass, momentum, and energy provide differential equations. With the aid of auxiliary and thermodynamic relations and taking into account the boundary conditions, we make the mathematical problem complete. All that is needed is to solve the equations and to deduce from their solution information of practical interest. From the equation of actual combustion we obtain many species in the products of combustion. From the investigation of the products of combustion, we find that NO is the predominant oxide of nitrogen produced inside the combustor of gas turbine. NO forms via the extended Zeldovich mechanism.

The paper deals with a mobile minimechanism which exploits the principle of impact of two masses for a movement inside a thin tube. The mobile minimechanism consists of the driving and the driven body which is propelled by magnetic force and elastic hairs. In the theoretical analysis of minimechanism movement its mean velocity on the base of two-elastic-masses impact model is examined and the distance of the damping spring from the active surface is optimized. In the experimental part dependences of the attractive and repulsive force on the distance are examined.

The procedure of tool-machine design is derived from mathematical description of workpiece surfaces by logical surface models which are transformed to the logical machining models. In nodal points the solution splits into branches with different design conceptions.