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
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.
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.
The main provisions of the methodology of the study of complex oscillations of elastic bodies are outlined.
There has been considered a method of determination rocks density on the basis of the processing of the wave field of the acoustic log. The results of the borehole data processing are demonstrated.