Субгармонический отклик третьего порядка гармоническим и случайным воздействием для осциллятора Дуффинга, возмущенного

осциллятор Дюффинга субгармоника метод усреднения эквивалентная линеаризация вспомогательная функция гармонические возбуждения случайные возбуждения.

О методике представления нечётких экспертных знаний, Техническое сравнение соединений с помощью новых муфт с коническими манжетами и традиционного соединения цилиндрической муфтой для полиэтиленовых труб номинальным диаметром более 1000 мм, ...

In this paper, we are concerned with the Duffing oscillator, which has been applied to model many mechanical systems and has attracted much attention as a typical nonlinear system. <...> When the system is under only a harmonic excitation or random one, two popular tools used to study such a nonlinear system are the averaging method and equivalent linearization method, respectively. <...> The former was originally given by Krylov and Bogolyubov [1] and then it was developed by Bogolyubov and Mitropolskiy [2-4] and was extended to systems under a random excitation with the works of Stratonovich [5], Khasminskii [6], and others, which were reviewed in survey paper by Mitropolskiy [3], Robert and Spanos [7] and Manohar [8]. <...> The later, the stochastic equivalent linearization method, which has attracted many researchers due to its originality and capability for various applications in engineering, was first studies by Kazakov [9], who extended Krylov and Bogolyubov’s linearization technique [1] of deterministic problems to random problems. <...> Recently, some approaches to the stochastic linearization have been proposed in Refs. [12-14]. <...> In [13-14], for example, Anh have proposed a dual criterion of stochastic linearization method for single and multi-degree-of-freedom nonlinear systems under white noise random excitations. <...> In a Duffing oscillator under periodic excitation, the phenomenon of subharmonic response has been known for years and has been described in many textbooks (see e.g. [15-18]) and works (see e.g. [19-21]). <...> When the system is subjected to a combination of harmonic and random excitations, however, to the authors’ knowledge, although the response of this oscillator has received a flurry of research effort for years (see e.g. [22-25]), there is no work on its subharmonic response. <...> Thus, in this research, we present a technique to treat a one third order subharmonic response of a Duffing oscillator subjected to periodic and random excitations. <...> The technique is a combination of the stochastic averaging method, the equivalent linearization method, and the technique of auxiliary function which yields the exact joint stationary probability density function (PDF) * The paper is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED), by Vietnam National University HoChiMinh City (VNU-HCM), and RFFI grant no. 14-08-00206 <...>

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