Svoboda, R.; Tondl, A.; Verhulst, F. Autoparametric resonance by coupling of linear and nonlinear systems. (English) Zbl 0794.70014 Int. J. Non-Linear Mech. 29, No. 2, 225-232 (1994). 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. Cited in 2 Documents MSC: 70K28 Parametric resonances for nonlinear problems in mechanics 70J40 Parametric resonances in linear vibration theory Keywords:pendulum; linear springs; stability; autoparametric resonances; two-mass subsystem PDFBibTeX XMLCite \textit{R. Svoboda} et al., Int. J. Non-Linear Mech. 29, No. 2, 225--232 (1994; Zbl 0794.70014) Full Text: DOI