Statistical characteristics of the damped vibrations of a string excited by stochastic forces

• Autorzy: Jabłoński M. , Ozga A.
• Języki publikacji: EN

Abstrakty

EN

Our theoretical study aims at finding some statistic parameters characterizing the damped vibrations of a string excited by stochastic impulses. We derive the dependence of these parameters on the parameters of the string as well as on the stochastic distributions of the impulse magnitude, and on the place of the action. We also carry out a numerical simulation verifying the derived mathematical model and interpret the differences between the results obtained in simulation and the mathematical calculations. This study is the fourth stage of a research aimed at designing a probe that facilitates the process of measuring of the parameters, determining the quality of a technological process.

Słowa kluczowe

EN

string; stochastic impulses; statistic parameters characterizing the vibrations

• Wydawca: Instytut Podstawowych Problemów Techniki PAN ; Komitet Akustyki PAN ; Polskie Towarzystwo Akustyczne
• Czasopismo: Archives of Acoustics
• Rocznik: 2009
• Tom: Vol. 34, No. 4
• Strony: 601--612
• Opis fizyczny: Bibliogr. 11 poz., wykr.

Twórcy

autor

Jabłoński M.

autor

Ozga A.

• Jagiellonian University Faculty of Mathematics and Computer Science Gołebia 24, 31-007 Kraków,

Bibliografia

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• [2] Iwankiewicz R., Dynamic response of non-linear systems to random trains of nonoverlapping pulses, Meccanica, 37, 1, 1-12 (2002).
• [3] Jabłonski M., Ozga A., On statistical parameters characterizing vibrations of oscillators without damping and forced by stochastic impulses, Mechanics, 25, 4, 156-163 (2006).
• [4] Jabłonski M., Ozga A., Parameters characterizing vibrations of oscillators with damping forced by stochastic impulses, Archives of Acoustics, 31, 3, 373 (2006).
• [5] Jabłonski M., Ozga A., Statistical characteristics of vibrations of a string forced by stochastic forces, Mechanics, AGH University of Science and Technology, 27, 1, 1-7 (2008).
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• [7] Roberts J. B., Distribution of the Response of Linear Systems to Piosson Distributed Random Pulses, Journal of Sound and Vibration, 28, 1, 93-103 (1973).
• [8] Roberts J. B., Spanos P. D., Stochastic Averaging: an Approximate Method for Solving Random Vibration Problems, International Journal of Non-Linear Mechanics, 21, 2, 111-134 (1986).
• [9] Rowland E. N., The theory of mean square variation of a function formed by adding; known functions with random phases and applications to the theories of shot effect and of light, Mathematical Proceedings of the Cambridge Philosophical Society, 32, 04, p. 580 (1936).
• [10] Takác L., On secondary processes generated by a Poisson process and their applications in physics, Acta Mathematica Hungarica, 5, 3-4, 203-236 (1954).
• [11] Tylikowski A., Stochastic stability of continuous systems [in Polish:] Stochastyczna stateczność układów ciągłych, PWN, Warszawa, 1991, p. 230.