Summary
Fundamental behaviors in parametrically and self-excited mechanical systems are discussed through the analysis of a category of nonlinear models described by typical excitation mechanisms. In the present paper the self-excitation and parametric excitation are idealized by a nonlinear resistance of van der Pol type and some kinds of restoring forces consisting of nonlinear functions of deflection y and a periodic one of time τ. The effects of nth-power exciting terms y n cos 2ητ (η: exciting frequency) and self-excitation on resonance phenomena and amplitude-modulated motions are considered in comparison with the stability analysis of linear modelling.
Übersicht
In Abhängigkeit von typischen Erregermechanismen wird das grundsätzliche Verhalten von parameter- und selbsterregten mechanischen Schwingern untersucht. Die Selbsterregung und die Parameter-erregung werden idealisiert angenommen als ein nichtlinearer Widerstand vom Van-der-Pol-Typ sowie als Rückstellkräfte, die nichtlineare Funktionen der Auslenkung y mit periodischen Koeffizienten sind. Es werden die Resonanzerscheinungen und die amplitudenmodulierten Bewegungen infolge der Selbsterregung und der Erregerterme der Form y n cos 2ητ (mit der Erregerfrequenz η) diskutiert sowie deren Stabilitätsverhalten analysiert.
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Yano, S. Analytic research on dynamic phenomena of parametrically and self-exited mechanical systems. Ing. arch 57, 51–60 (1987). https://doi.org/10.1007/BF00536811
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DOI: https://doi.org/10.1007/BF00536811