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Research Papers

Stability Analysis of an Articulated Loading Platform in Regular Sea

[+] Author and Article Information
A. K. Banik1

Department of Civil Engineering, National Institute of Technology, Silchar, Silchar 788010, Indiaakbanik@gmail.com

T. K. Datta

Department of Civil Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India

1

Corresponding author.

J. Comput. Nonlinear Dynam 3(1), 011013 (Dec 12, 2007) (9 pages) doi:10.1115/1.2815332 History: Received October 31, 2006; Revised June 12, 2007; Published December 12, 2007

Stability of the response of an articulated loading platform under regular wave, modeled as a SDOF nonlinear oscillator, is investigated. Relative velocity square drag force for harmonic wave appearing in the right hand side of the equation of motion is mathematically treated to bring the velocity dependent nonlinear hydrodynamic damping term to the left hand side of the equation of motion. Use of these two techniques makes the equation of motion amenable to the application of method IHBC. In order to trace different branches of the response curve and investigate different instability phenomena that may exist, the commonly used incremental harmonic balance method (IHB) is modified and integrated with an arc-length continuation technique to develop into incremental harmonic balance continuation (IHBC) method. Further, a technique for treating the nonlinear hydrodynamic damping term using a concept of distribution theory has been developed. The stability of the solution is investigated by the Floquet theory using Hsu’s scheme. The stable solutions obtained by the IHBC method are compared with those obtained by the numerical integration of equation of motion wherever applicable.

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Figures

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Figure 1

Articulated loading platform (all dimensions are in meters)

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Figure 2

Mathematical model of loading platform

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Figure 3

Variation of amplitude with forcing frequency (1T solution; backward sweep)

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Figure 4

Variation of amplitude with forcing frequency (1T solution; backward sweep; no hydrodynamic damping due to drag)

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Figure 5

Phase plot at ω=0.1842rad∕s (1T solution; no hydrodynamic damping due to drag)

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Figure 6

Variation of amplitude with forcing frequency (1T solution; backward sweep; θ̇∣θ̇∣ removed)

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Figure 7

Variation of amplitude with forcing frequency (2T solution; backward sweep)

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Figure 8

Phase plot at ω=0.64rad∕s (stable 2T solution)

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Figure 9

Variation of amplitude with forcing frequency (3T solution; backward sweep)

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Figure 10

Phase plot at ω=0.64rad∕s (stable 3T solution)

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Figure 11

Variation of amplitude with forcing frequency (2T solution; backward sweep; θ̇∣θ̇∣ removed)

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Figure 12

Variation of amplitude with forcing frequency (3T solution; backward sweep; θ̇∣θ̇∣ removed)

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