Forced response of low-frequency pendulum mechanism

Publikationstyp
Journal Article
Publikationsdatum
2016-05-01
Sprache
English
Author
Starossek, Uwe 
Institut
Baustatik B-4 
TORE-URI
http://hdl.handle.net/11420/4737
Enthalten in
Mechanism and machine theory 
Volume
99
Start Page
207
End Page
216
Citation
Mechanism and Machine Theory (99): 207-216 (2016-05-01)
Publisher DOI
10.1016/j.mechmachtheory.2016.01.004
Scopus ID
2-s2.0-84957586763
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.
Schlagworte
Amplitude-frequency relation
Exact analytical solutions
Jacobi elliptic function
Non-harmonic periodic loading
Nonlinear oscillator
Passive mass damper