Математична модель руху сипкого матеріалу у вібраційному сепараторі

Мета. Побудова математичної моделі руху сипкого матеріалу у вібраційному сепараторі. Методика. Побудовано розрахункову схему вібраційного сепаратора з двома ексцентричними вібраторами з незалежним приводом. На основі схеми прийнято вважати, що вібросепаратор здійснює тільки вертикальні коливання в площині обертання ексцентрикових вібраторів. Розглянуто циліндричний вібраційний сепаратор, завдяки можливості передачі вібрацій більшої сили на сито та значно ефективнішому використанню всієї поверхні просіву.

Asymptotic method and wave theory of motion in studying the effect of periodic impulse forces on systems characterized by longitudinal motion velocity

A methodology for researching dynamic processes of one-dimensional systems with distributed parameters that are characterized by longitudinal component of motion velocity and are under the effect of periodic impulse forces has been developed.   The boundary problem for the generalized non-linear differential Klein–Gordon equation is the mathematical model of dynamics of the systems under study in Euler variables.  Its specific feature is that the unexcited analogue does not allow applying the known classical Fourier and D'Alembert methods for building a solution.  Non-r

Nonlinear mathematical model of the five-container vibration system

The construction of a non-linear mathematical model of movement and interaction of  the commanding and executive components of vibration systems is an important task. It implements vibration technologies of separation, grinding, mixing, compaction, transportation, surface  product  processing  and  technology for regulating the vibration effect on systems and mechanisms for their further research to increase the efficiency of vibrating machines, devices, and mechanisms and relevant technological processes.

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

Modeling of partially regular microreliefs formed on the end faces of rotation bodies by a vibration method

The scheme of formation of a set of variants of grooves of partially regular microreliefs formed on the end faces of rotation bodies by a vibration method has been developed, and the conditions of their existence have been determined. Using a block approach, mathematical models of partially regular microreliefs have been constructed, which described a set of their variants, taking into account such characteristics as the shape of axial lines of continuous regular microroughness, type, and location of axial symmetry lines of grooves, and groove shape.

Advanced asymptotic approaches and perturbation theory methods in the study of the mathematical model of single-frequency oscillations of a nonlinear elastic body

A combination of asymptotic methods in nonlinear mechanics with basic techniques of perturbation theory to study a mathematical model of the nonlinear oscillation system is proposed in the paper.  The system under consideration describes the torsional vibrations of an elastic body, where its elastic properties are under the nonlinear law.  The relationships presented as the ordinary differential equations are obtained due to the proposed procedure.  Therefore, the main parameters of the single-frequency oscillations and the resonance conditions can be determined.  There are proposed applica

Wave concept of motion in mathematical models of the dynamics of two-dimensional media studying

The methodology of the studying of dynamic processes in two-dimensional systems by mathematical models containing nonlinear equation of Klein-Gordon was developed. The methodology contains such underlying: the concept of the motion wave theory; the single - frequency fluctuations principle in nonlinear systems; the asymptotic methods of nonlinear mechanics. The aggregate content allowed describing the dynamic process for the undisturbed (linear) analogue of the mathematical model of movement.

Substantiation of parameters and modelling the operation of three-mass vibratory conveyer with directed oscillations of the working element

У статті проаналізовано конструктивні і функціональні особливості тримасового вібротранспортера з напрямленими коливаннями та розглянуто можливі сфери його використання.

Використання акустичного каротажу для визначення густини гірських порід

Розглядається спосіб визначення густини гірських порід за даними обробки хвильового поля акустичного каротажу. Наводяться результати обробки свердловинних даних.