Summary
In order to enhance our ability to predict and detect the behaviour characteristics of a parametrically excited vibratory system, one has to grasp the fundamental features concerning the mode interactions between self-excitation and parametric excitation. In this regard, two types of nonlinear models are proposed, and the correlation and the interaction between both excitations are discussed. These models differ from those obtained earlier. Taking into account the effect of exciting terms y n cos (2ωt) and y n−1y × cos (2ωt) (n=1, 3) where y represents a deflection and ω is the frequency, the features of these models are considered in comparison with those in previous works. Resonance phenomena of orders 1 and 1/2 and the behaviour in the neighborhood of resonances are mainly investigated by the averaging method.
Übersicht
Zur Vorhersage und Charakterisierung des Verhaltens parametererregter Schwingungssysteme ist es hilfreich, die Wechselwirkungen zwischen Selbsterregung und Parametererregung zu untersuchen. Zu diesem Zweck werden am Beispiel zweier nichtlinearer Modelle diese Wechselwirkungen studiert. Dabei werden Erregerterme der Form y n cos (2ωt) und y n−1y cos (2ωt) (n=1, 3) betrachtet, wobei ω die Erregerfrequenz ist. Die typischen Eigenschaften der untersuchten nichtlinearen Systeme werden mit Resultaten früherer Arbeiten verglichen. Die Resonanzen der Ordnungen 1 und 1/2 und das Verhalten der Systeme in der Nachbarschaft dieser Resonanzen werden untersucht, wobei die Mittelwertmethode Anwendung findet.
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Yano, S. Considerations on self- and parametrically excited vibrational systems. Ing. arch 59, 285–295 (1989). https://doi.org/10.1007/BF00534368
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DOI: https://doi.org/10.1007/BF00534368