OSCILLATIONS OF A PULSE LOADED OSCILLATOR WITH A SQUARE RESISTANCE IN THE COMPOSITION OF THE DISSIPATIVE FORCE

The unsteady oscillations of a dissipative oscillator caused by an instantaneous impulse of the force are described. The case is considered when the dissipative force consists of quadratic viscous resistance and dry friction, and the theoretical results are generalized to the case of the sum of three forces. The third is the force of positional friction. Formulas for calculating the ranges of oscillations have been constructed In this case, the Lambert function of negative and positive arguments is used. It is a tabulated special function. Its value can also be calculated using its known approximations in elementary functions. It is shown that, due to the action of the dissipative force, the process of post-pulse oscillations consists of a finite number of cycles and is limited in time. This is due to the presence of dry friction among the resistance components. Examples of calculations that illustrate the possibilities of the stated theory are given. In order to check the reliability of the derived calculation formulas, numerical computer integration of the differential equation of motion was also carried out. The convergence of the numerical results obtained by two different methods is shown. Thus, it has been confirmed that with the help of analytical solutions it is possible to find the extreme displacements of the oscillator without numerically solving its nonlinear differential equation of motion. Using Lambert function and the first integral of the equation of motion made it possible to derive precise calculation formulas for determining the range of oscillations caused by the pulsed load of the oscillator. The derived formulas are suitable for calculating the value of the instantaneous impulse applied to the oscillator, which refers to the inverse problems of mechanics. Thus, by measuring the maximum displacement of the oscillator, it is possible to identify the initial velocity or instantaneous impulse applied to the oscillator. The performed numerical computer integration of the output differential equation confirmed the adequacy of the obtained analytical solutions, which concern not only direct, but also inverse problems of dynamics.

NUMERICAL COMPUTER SIMULATION OF THE OPERATION OF CULVERTS OF A HYDRO-RECLAMATION SYSTEM

The aim of this research was to study the operating modes of water-passing structures that are part of the irrigation and drainage system using numerical computer modeling in the HEC-RAS environment. The paper describes the main stages of processing the source data, preparing a model, performing modeling and analyzing the results. The problem of the program description of the rules for managing a water-passing structure – a controlled gate located on a trapezoidal channel and performing the function of regulating water levels is investigated. The created rules for the operation of the structure imply a change in the position of the gate depending on the water levels in the upper and lower reaches, which ensures regulation. For the resulting model of a channel with a controlled gate, calculations were carried out for a non-steady fl ow of water, the response of the structure to a change in the fl ow rate of water was investigated, and the obtained values of water levels in the upper and lower reaches was analyzed. Based on the simulation results, conclusions were drawn about the applicability of this research method for solving problems related to the optimization of operating modes of irrigation and drainage systems.

Equivalent Analytical Functions of Sums of Sigmoid like Transcendental Functions

There is no mathematical solution to adding up transcendental functions other than numerical process. This paper put forward analytical method to model the sum of sigmoid like functions with an equivalent function. The Brillouin and Langevin as well as the error function, the tanh, sigmoid and the tan-1 functions are investigated, their equivalent functions are calculated for four components and the error between the numerical (computer assisted) result and the equivalent function is tested for accuracy. The best modelling function, the most useful to include into mathematical operations, is pointed out finally, based on its performance and convenience. The paper intends to help people involved mostly in modelling hysteresis in Magnetism and other field of research in physics.

WATERTUBE SMOKE TUBE BOILER: NUMERICAL COMPUTER SIMULATION AND EXPERIMENT

The improvement of natural gas use technologies in water-heating boilers is considered. The concept of a new watertube smoke tube boiler, created on the basis of the screen radial tube bundle placement in the space of a cylindrical heat pipe-furnace. The results of numerical computer simulation of the furnace process in the 630 kW watertube smoke tube boiler are compared with the corresponding data obtained during the experiment. The analysis of the results of numerical computer simulation reveals the efficiency of the installed tube radial bundle: the total heat perception in the furnace increased by 56 %, while the growth of the part of the heat transferred by convective heat exchange occurred by 22 %; the temperature level in the furnace volume has decreased, while the concentration of nitrogen oxides has decreased by 45–51 %. It is experimentally established that the presence of the cooled screen tube radial bundle in the furnace of the watertube smoke tube boiler makes it possible: to increase heat release rate in the furnace volume by 10 %; to reduce the concentration of nitrogen oxides and carbon monoxide in flue gases by 24–40 % and 25–67 % respectively (resulting in a compliance of the level of pollutant emission to the requirements of the Ukrainian national regulations, viz. GOST 30735–2001); reduce the excess air in the furnace by 3 % and increase the efficiency of the boiler by 0.5 %. The pre-production prototype of the water-heating smoke tube boiler (KVVD-0.63 Gn) has passed the certification tests, state registration; the boiler has been adopted in permanent operation. The boiler is not complicated in manufacturing, and producible in the conditions of municipal heating network companies. The reliability of the boiler's design has been confirmed by the experience of many years of functioning.

Application of Numerical Simulation for the Verification of Design of Clamping a Workpiece in Jaws

This paper deals with the use of the numerical computer oriented method for the analysis and verification of the design of workpiece clamping. The inaccuracies of the positioning in clamping locating points were simulated using the FEM software ANSYS. The influence of inaccuracies in the positions of contact locating points on the displacements of the workpiece characteristic points and their position in clamped removable jaws was examined. The reaction forces in the contact locating points were also computed and analyzed.