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Forced response of low-frequency pendulum mechanism
Publikationstyp
Journal Article
Date Issued
2016-05-01
Sprache
English
Author(s)
Institut
TORE-URI
Journal
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.
Subjects
Amplitude-frequency relation
Exact analytical solutions
Jacobi elliptic function
Non-harmonic periodic loading
Nonlinear oscillator
Passive mass damper