asymptotic methods

A numerical evaluation of the temperature of a solidification point in ingot casting processes

An analysis for the numerical computing of the temperature around a solidification point of liquid steel or melt contained in a mould is performed via the interaction of the conservation equations of mass, momentum and heat transfer.  A cooling process of liquid steel due to the extraction of heat through the walls of the mould is analyzed using asymptotic methods and an ordinary differential equation that describes the temperature of interface melt-air is obtained.  Also, the temperature of the melt in the mould around the solidification point is computed numerically u

On the external and internal resonance phenomena of the elastic bodies with the complex oscillations

Complex nonlinear oscillations in the elastic bodies are studied using a priori information about the oscillations form and taking into account a refined mathematical model of the second (other) form of oscillations.  Application of existing methods or development of the new ones for the analysis of received non-autonomous boundary value problems is proposed.  The effectiveness of the practical implementation of the discussed methodology significantly increases in cases where the magnitude of the elastic body displacements due to the one form of oscillations is much higher than the other on

Research of Dynamics of the Vibrating Machine's Downloading With the Vertical Movement

The purpose of research. The main purpose of the work is to develop mathematical software for studying the dynamics of vibration machines of volumetric processing, and calculate the influence of various factors on the efficiency of the process based on applied systems of automated mathematical calculations, including MathCad and MatLab. Method. The research was carried out on the basis of a class of vibrating machines with unbalanced drive type and spring suspension.