Browsing by Author "Minárik, Ján"

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    Model nelineárneho oscilátora
    (University of Žilina, 2024) Minárik, Ján; Ftorek, Branislav; Chupáč, Radoslav
    This article deals with a simple nonlinear model of mechanical system. Nonlinear mechanical model described by a nonlinear system of differential equations can lead to interesting phenomena. The linearized analytical solution is compared with the numerical solution obtained by the Runge-Kutta method in the MATLAB environment.
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    Parametricky modulovaný oscilátor v asymptotickom prípade
    (University of Žilina, 2024) Minárik, Ján; Ftorek, Branislav; Chupáč, Radoslav
    This article deals with the asymptotic solution in analytical form of some second-order linear differential equation with time-dependent parameters. Time-periodic modulation of the parameters of the oscillatory system can lead to interesting phenomena. The analytical solution is compared with the numerical solution obtained by the Runge-Kutta method in the MATLAB environment. The convergence conditions of this analytical method are discussed.
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    Porovnanie optimalizačných algoritmov pri spektrálnom ladení mechanickej sústavy
    (University of Žilina, 2025) Majko, Jaroslav; Deganová, Lucia; Piroh, Ondrej; Minárik, Ján
    This article deals with a comparison of various, gradient-based optimisation algorithms in terms of their accuracy and effectivity. The compared algorithms are the steepest descent method (SDM) and the most well-know quasi-Newton methods. The presented methods were applied to the spectral tuning of a simple two degree of freedom (DOF) mechanism, in order to evaluate their performance. The obtained results were statistically processed and utilised to compare the algorithms, based on their accuracy and overall effectivity. The results show that the quasi-Newton methods are superior to the SDM in terms of both the accuracy and computing time. Moreover, the overall performance of these methods is also significantly less influenced by the selection of starting point. Thus, the obtained results render the quasi-Newton methods as a significantly better choice, compared to the standard SDM.