Starossek, UweUweStarossek2020-03-242020-03-242015-11-12Nonlinear Dynamics 4 (83): 2349-2359 (2016-03-01)http://hdl.handle.net/11420/5463A strongly nonlinear oscillator is considered in which the restoring force is a purely cubic function of the displacement variable. Its forced undamped oscillation response to non-harmonic periodic loading is studied. The loading function is derived from the free oscillation response whose time course follows a Jacobi elliptic function. It is chosen such that exact analytical solutions are obtained for the steady-state response and the amplitude–frequency relation. The equation describing the amplitude–frequency relation is a cubic polynomial equation. Its solutions are presented and further discussed by means of diagrams that illustrate the equilibrium of dynamic forces. Furthermore, results of a numerical study are presented concerning the stability of the identified analytical steady-state solutions. The numerical study also reveals the existence of a subharmonic steady-state response with a period three times the period of the loading function. The general approach of using non-harmonic loading functions is transferable to other types of nonlinear oscillators.en1573-269X2015423492359Springer Science + Business Media B.VAmplitude–frequency relationJacobi elliptic functionsNon-harmonic periodic loadingNonlinear oscillatorTechnikIngenieurwissenschaftenHausbau, BauhandwerkJournal Article10.1007/s11071-015-2486-2Other