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# Forced response of low-frequency pendulum mechanism

Publikationstyp

Journal Article

Publikationsdatum

2016-05-01

Sprache

English

Author

Starossek, Uwe

Institut

TORE-URI

Enthalten in

Volume

99

Start Page

207

End Page

216

Citation

Mechanism and Machine Theory (99): 207-216 (2016-05-01)

Publisher DOI

Scopus ID

A 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.