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A low-frequency pendulum mechanism
Publikationstyp
Journal Article
Date Issued
2014-09-30
Sprache
English
Author(s)
Starossek, Uwe
Institut
Journal
Volume
83
Start Page
81
End Page
90
Citation
Mechanism and Machine Theory 83 (): 81-90 (2015)
Publisher DOI
Scopus ID
Publisher
Elsevier Science
A pendulum mechanism is presented whose natural frequency of oscillation is distinctly lower than that of a conventional pendulum of comparable size. Furthermore, its natural frequency is approximately proportional to its amplitude of oscillation. The mechanism can thus be tuned to extremely low frequencies by using small amplitudes. The undamped free oscillation response of the mechanism is studied. The derivation of the equation of motion is outlined for both large and, after neglecting higher order terms, small displacements. In both cases, a second-order nonlinear differential equation results. When higher order terms are neglected, the equation of motion is of simple form and can be solved symbolically in terms of a Jacobi elliptic function. Based on this solution, a closed-form expression for the natural frequency is derived and the characteristics of the free oscillation response are discussed.
Subjects
Elliptic function
Free oscillation response
Low frequency
Mechanism
Pendulum
Tuned mass damper
DDC Class
620: Ingenieurwissenschaften
690: Hausbau, Bauhandwerk