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Technical Brief

Partial Stochastic Linearization of a Spherical Pendulum With Coriolis Damping Produced by Radial Spring and Damper

[+] Author and Article Information
L. D. Viet

Institute of Mechanics,
Vietnam Academy of Science and Technology,
264 Doi Can,
Hanoi 10000, Vietnam
e-mails: laviet80@yahoo.com; ldviet@imech.ac.vn

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 12, 2014; final manuscript received May 16, 2015; published online June 15, 2015. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 137(5), 054504 (Oct 01, 2015) (6 pages) Paper No: VIB-14-1388; doi: 10.1115/1.4030663 History: Received October 12, 2014; Revised May 16, 2015; Online June 15, 2015

This study considers the stochastic analysis of a spherical pendulum, whose bidirectional vibration is reduced by spring and damper installed in the radial direction between the point mass and the cable. Under sway motion, the centrifugal force results in the radial motion, which in its turn produces the Coriolis force to reduce sway motion. In stochastic analysis and design, the problem is that the Monte Carlo simulation is time-consuming, while the full stochastic linearization totally fails to describe the effectiveness of the spring and damper. We propose the partial linearization applied to the Coriolis damping to overcome the disadvantages of two mentioned methods. Moreover, the proposed technique can give the analytical solution of partial linearized system. A numerical simulation is performed to verify the proposed approach.

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Figures

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Fig. 1

Spherical pendulum attached with radial spring–damper

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Fig. 2

Geometrical description of the axisymmetric spherical pendulum attached with the spring–damper and two swing angles

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Fig. 3

Performance index versus frequency ratio, in the case ϕ0 = θ0 = 10 deg

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Fig. 4

Performance index versus frequency ratio, in the case ϕ0 = 2θ0 = 20 deg

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Fig. 5

Damping error versus effective damping ratio in the case ϕ0 = 2θ0 = 20 deg, α = 2. Markers denote the effective damping obtained analytically.

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