Research Papers

Nonlinear Dynamics of Stockbridge Dampers

[+] Author and Article Information
O. Barry

Department of Mechanical
and Industrial Engineering,
University of Toronto,
Toronto, ON M5S 3G8, Canada
e-mail: oumar.barry@utoronto.ca

J. W. Zu

Department of Mechanical
and Industrial Engineering,
University of Toronto,
Toronto, ON M5S 3G8, Canada

D. C. D. Oguamanam

Department of Mechanical
and Industrial Engineering,
Ryerson University,
Toronto, ON M5B 2K3, Canada

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 7, 2013; final manuscript received December 29, 2014; published online February 9, 2015. Assoc. Editor: Jiong Tang.

J. Dyn. Sys., Meas., Control 137(6), 061017 (Jun 01, 2015) (7 pages) Paper No: DS-13-1346; doi: 10.1115/1.4029526 History: Received September 07, 2013; Revised December 29, 2014; Online February 09, 2015

The present paper deals with the nonlinear dynamics of a Stockbridge damper. The nonlinearity is from damping and the geometric stretching of the messenger. The Stockbridge damper is modeled as two cantilevered beams with tip masses. The equations of motion and boundary conditions are derived using Hamilton’s principle. The model is valid for both symmetric and asymmetric Stockbridge dampers. Explicit expressions are presented for the frequency equation, mode shapes, nonlinear frequency, and modulation equations. Experiments are conducted to validate the proposed model.

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Fig. 1

Photograph of Stockbridge damper

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Fig. 2

Schematic of two cantilevered beams with tip masses

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Fig. 3

Schematic of experimental setup

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Fig. 4

Damper 1 mode shapes

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Fig. 5

Damper 2 mode shapes

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Fig. 6

Damper 3 mode shapes

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Fig. 7

Variation of fundamental nonlinear frequency with vibration amplitude

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Fig. 8

Frequency-response curve for varying f0 and constant damping

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Fig. 9

Frequency-response curve for varying μ1 and constant force

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Fig. 10

Effect of the counterweight mass and rotational inertia




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