# frequency

## Mathematical Model of Movement of Bulk Material in a Vibratory Separator

Aim. The aim is to construct the mathematical model of the movement of loose material in a vibrating separator. Method. The calculation scheme of the vibration separator with two eccentric vibrators with an independent drive was built. Based on the scheme, it is assumed that the vibration separator performs only vertical oscillations in the plane of rotation of the eccentric vibrators.

## 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

## 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.

## Modeling of Steady-state Modes of the Electrical Network From the Synchronous Electric Drive of Hydraulic Loading

Pumping stations that provide fluid transportation by pipeline are significant consumers of electricity. Energy overruns due to sub-optimal modes of operation of individual high-power units or sub-optimal number of simultaneously operating less powerful units are quite significant and can have a significant impact on overall energy consumption. Energy overruns at pumping stations also lead to significant overruns in electricity grid elements.

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

The purpose of research. The main goal of the presented research consists in substantiation of inertial, stiffness and force (excitation) parameters of mechanical oscillatory system of three-mass vibratory conveyer with directed oscillations of the working element in order to provide the highly efficient (high-performance) resonant operation mode. Methodology. The technique of the research is based on fundamental concepts of engineering mechanics and theory of mechanical vibrations.

Operation of radio communication systems for special purposes (FSA SP) in practice is random in terms of various factors, some of which are codified in standards, and some — previously known. Specificity of modern shipyard JV determines the need to manage their operations in terms of parametric uncertainty as facility management and signaling uncertainty of external influences. So the challenge is the analysis and consideration of uncertainty arising from the operation of such a complex hierarchical system as the FSA SP.

## Temperature Dependence Estimation of the Vibration and Frequency Sensor Resonator Mechanical State

The complex of technological and metrological researches concerning development of filamentous monocrystals application and fixing methods on various materials of substrate (elastic elements) is considered. The ways of uncontrolled distortions avoiding of the initial monocrystal defect-free structure that can occur at the nodes of its mounting and reduce the Q-value of the resonator oscillations, which is the main characteristic of the tensotransducer quality, is shown.

## High-speed Frequency Divider With Variable Division Ratio

Overviewed conceptual basis for development frequency dividers and disadvantages of standard decisions were analyzed. A high-speed with variable division ratio and minimum phase shift of output signal against input signal, which forms output square waves, is presented in the article.

## Two-mass Vibratory Conveyor-manipulator with Three-Component Electromagnetic Drive

Vibratory conveyor with three-component oscillations provides the opportunity to move the piece goods and details for any trajectory on a plane. Phase difference between independent horizontal (longitudinal or transverse) and vertical (normal) oscillations releases elliptical vibration of conveyor in plane perpendicular to the conveyor’s track. Elliptical vibrations allow increasing conveying velocity and inclination angle of conveyor’s track in comparison with the simplest linear vibrations.