Starossek, UweUweStarossek2020-02-052020-02-052016-05-01Mechanism and Machine Theory (99): 207-216 (2016-05-01)http://hdl.handle.net/11420/4737A strongly nonlinear pendulum mechanism is considered in which the restoring force is approximately a cubic function of the displacement variable. Its free oscillation frequency is approximately proportional to the amplitude of oscillation and distinctly lower than that of a simple pendulum. The mechanism has therefore been named infra-pendulum. The forced undamped oscillation response of the mechanism to non-harmonic periodic loading is studied under the assumption of small displacements. 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. The general approach of using non-harmonic periodic loading functions is transferable to other types of nonlinear oscillators.en0094-114X2016207216Amplitude-frequency relationExact analytical solutionsJacobi elliptic functionNon-harmonic periodic loadingNonlinear oscillatorPassive mass damperJournal Article10.1016/j.mechmachtheory.2016.01.004Other