# amplitude

## Method of normal oscillations and substantiation of the choice of parameters for certain nonlinear systems with two degrees of freedom

On the example of the plane model of wheeled vehicle oscillations with adaptive power characteristic of the suspension system, the methodology for selecting its main parameters that would maximize the movement smoothness is developed.  To solve this problem, the mathematical model of relative oscillations of the sprung part is constructed, provided that they are carried out in the vertical plane.  The latter represents the system of two nonlinear differential equations describing the relative displacement of the center of mass of the sprung part and the angle of rotatio

## 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

## 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

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.

## Asymptotic method in investigation of complex nonlinear oscillations of elastic bodies

The main provisions of the methodology of the study of complex oscillations of elastic bodies are outlined.