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Autoparametric resonance by coupling of linear and nonlinear systems. (English) Zbl 0794.70014

Summary: A pendulum is attached to one mass of a chain of \(n\) masses, connected by \(n\) linear springs. One of the masses is harmonically excited. The stability of the semi-trivial solutions, representing vibration of \(n\) masses without pendulum oscillation, is investigated in general. Using this approach, the occurrence of all autoparametric resonances can be determined. As an illustration, a two-mass subsystem with two degrees of freedom, where the pendulum is attached to the upper mass, is analysed.

MSC:

70K28 Parametric resonances for nonlinear problems in mechanics
70J40 Parametric resonances in linear vibration theory
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