Abstract
An approach combining the method of moment equations and the statistical linearization technique is proposed for analysis of the response of non-linear mechanical systems to random excitation. The adaptive statistical linearization procedure is developed for obtaining a more accurate mean square of responses. For these, a Duffing oscillator and an oscillator with cubic non-linear damping subject to white noise excitation are considered. It is shown that the adaptive statistical linearization proposed yields good accurate results for both weak and strong non-linear stochastic systems.
Sommario
Si propone un procedimento per l'analisi della risposta di sistemi meccanici non lineari ad eccitazioni stocastiche, che combina il metodo delle equazioni dei momenti e la tecnica di linearizzazione statistica. Si sviluppa un procedimento di linearizzazione statistica adattativa, che permette di ottenere più accurati valori medi quadratici della risposta. Per illustrazione, si prende in esame un oscillatore di Duffing e un oscillatore con smorzamento cubico, soggetti a un'eccitazione tipo “rumore bianco”; e si mostra che la proposta linearizzazione statistica adattativa fornisce buoni risultati per sistemi sia debolmente che fortemente non lineari.
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Anh, N.D., Schiehlen, W. An approach to the problem of closure in non-linear stochastic mechanics. Meccanica 29, 109–123 (1994). https://doi.org/10.1007/BF01007496
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DOI: https://doi.org/10.1007/BF01007496