Research of stochastic stability of constructions parametric vibrations by the Monte-Carlo method
DOI:
https://doi.org/10.32347/2410-2547.2024.112.327-331Keywords:
random parametric loading, stochastic stability, Monte Carlo method, finite element method, Runge-Kutta method, elastic systems, I-beam with corrugated wallAbstract
The stochastic parametric vibrations of the elastic systems behave to the statistical dynamics section of the nonlinear systems. Under stochastic parametric influence the vibrations of the elastic systems, which is a random process more frequent are not stabilized, but their amplitudes are fading or unlimited are growing. Therefore important is stability of stochastic vibrations, which can be examined as stability by probability, on average or by the moment functions of different orders. The mathematical models which describe the stochastic parametric vibrations of the elastic systems are building by analytical or numeral approaches. Researches of stochastic stability of parametric vibrations are executing by probabilistic methods. Stability of parametric vibrations of modern constructions under the action of operating random loads are not enough investigated.
In the article the numeral method of research of dynamic stability of the elastic systems under stochastic parametric influence was presented. The mathematical model of stochastic parametric vibrations of construction in the form of a reduсed finite element model was formed. Matrixes of the reduced model were obtained using calculated procedures of finite element analysis software NASTRAN. The dynamic loading as stationary ergodic random process with the spectral density was presented in the form of a finite amount of harmonic functions. Stochastic stability of the constructions was investigated using the Monte Carlo method and the Runge Kutta method of direct numeral integration of the equations of reduсed model. Stochastic stability as stability by probability of appearance of tendency to fading or unlimited growth of amplitude of parametric vibrations was examined during the time interval in space of the random parameters of loading. Dynamic stability of a I-beam with corrugated wall under narrow-band parametric influence was investigated using the numeral method.
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