Browsing by Author "Gursky, Volodymyr"

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    Nonlinear analysis in synthesis of the resonant vibro-impact systems
    (Publishing House of Lviv Polytechnic National University, 2015) Gursky, Volodymyr; Kuzio, Ihor
    The paper considers differential equation of the vibro-impact resonance system with an asymmetric piecewise linear elastic characteristic. The time-instant of switching of elastic characteristic is determined on the basis of equality of oscillation period to average value of the corresponding eigenfrequencies. Then, expansion of the asymmetric piecewise linear elastic characteristic into Fourier series was made. The initial differential equation was reduced to a kind of parametric equations of Hill’s andMathieu’s type with taking into account the time of elastic characteristic change. Stability analysis of parametric Mathieu equation is shown for the analysis of natural oscillations. For stability analysis of the synthesized by various stiffness coefficients of vibro-impact system, dependencies of Mathieu equations coefficients on the parameter of synthesis are used. The solution of the initial equation with forced oscillations in the form of asymmetric two-frequency vibrations has been obtained by means of Bubnov-Galerkin and Levenberg-Marquardt methods for nonlinear algebraic systems of equations, also amplitude and phase frequency dependence was graphically drawn. The basic equation with an asymmetric elastic response characteristic feature is determined by the fixed natural frequency of oscillations independently of amplitude. Numerical solution of differential equations by means of Runge–Kutta method are presented for comparison. Comparison of the vibro-impact resonance system kinematics characteristics, synthesized by the elastic parameters and solved by the listed methods, is conducted. The feasibility of using nonlinear analysis presented in two harmonics in Fourier series asymmetric elastic characteristic is justified in the article. The suggested approach with Bubnov-Galerkin method for general Hill’s equation and correlation analysis of time kinematic characteristics was used. Acceleration frequency spectrum and harmonics are obtained on the basis of Runge–Kutta numerical method simulation of the initial nonlinear differential equation.
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    Numerical solution of parametric optimization of the resonant vibro-impact system with technological limitations
    (Lviv Polytechnic Publishing House, 2015) Gursky, Volodymyr; Lviv Polytechnic National University
    The purpose of research: development of method of optimization of the resonance vibro-impact system stiffness parameters with technological limitations of kinematic and dynamic characteristics. The synthesis is based on a numerical dynamic analysis which uses methods of tackling nonlinear differential system of equations. The discrete algorithm of choice-based optimization of synthesized coefficients of asymmetric lump linear stiffness characteristic with limitations imposed on technological parameters and system frequency characteristics is proposed. Optimal parameters of a vibroimpact machine are determined by the maximum of power criteria, which is the ratio of maximum acceleration of the working mass to the current value of the power consumption of a mechanical system.
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    Optimal synthesis of the impulsive resonant two-mass vibro-impact systems
    (Видавництво Львівської політехніки, 2013) Gursky, Volodymyr; Murashev, Sergiy; Gogol, Rostyslav
    The article solves the applied problem of the technological efficiency increase of resonant two-mass vibrating machines with an impulsive electromagnetic drive based on optimization synthesis and frequency analysis of asymmetric piece-linear elastic description. The value of speed of working mass is accepted for an objective function. Synthesis is based by frequency coefficient and relation of eigenfrequencies. The rational resilient parameters of asymmetric piece-linear elastic description settle accounts after the optimum values of the proper coefficients. The availability of the poly-frequency spectrum in the resonant mode of machine, operated by impulsive electromagnetic perturbation, is confirmed by the dynamic analysis and numerical system modeling.