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Research Papers

Uncertain Dynamic Responses of Fuzzy Arbitrary-Order Damped Beam

[+] Author and Article Information
Diptiranjan Behera

Department of Mathematics,
National Institute of Technology Rourkela,
Odisha 769 008, India
e-mail: diptiranjanb@gmail.com

S. Chakraverty

Department of Mathematics,
National Institute of Technology Rourkela,
Odisha 769 008, India
e-mail: sne_chak@yahoo.com

Smita Tapaswini

Department of Mathematics,
National Institute of Technology Rourkela,
Odisha 769 008, India
e-mail: smitatapaswini@gmail.com

1Corresponding author.

Manuscript received August 26, 2014; final manuscript received January 14, 2015; published online October 2, 2015. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 1(4), 041007 (Oct 02, 2015) (9 pages) Paper No: RISK-14-1042; doi: 10.1115/1.4030440 History: Received August 26, 2014; Accepted April 27, 2015; Online October 02, 2015

Uncertain dynamic responses of fuzzy fractionally damped beams have been studied using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads. Uncertainties are assumed to be present in the initial conditions, and these are modeled through triangular convex normalized fuzzy sets. Using the alpha-cut form, the corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying a double-parametric form of fuzzy numbers. Finally, homotopy perturbation method (HPM) has been used to solve the same for obtaining the general fuzzy responses. Various numerical examples are taken into consideration. The results are plotted.

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Figures

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Fig. 1

Fuzzy unit step response for ω=5  rad/s, η=0.5, and λ=0.2

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Fig. 2

Fuzzy unit step response for ω=10  rad/s, η=0.05, and λ=0.5

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Fig. 3

Interval unit step response for (a) α=0.4 and (b) α=0.8 with ω=5  rad/s, η=0.5, λ=0.2, and α=1

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Fig. 4

Interval unit step response for (a) α=0.4 and (b) α=0.8 with ω=10  rad/s, η=0.05, λ=0.5, and α=1

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Fig. 5

Interval unit step response for (a) α=0.4 and (b) α=0.8 with ω=5  rad/s, η=0.5, λ=0.5, and α=1

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Fig. 6

Interval unit step response for (a) α=0.4 and (b) α=0.8 with ω=5  rad/s, η=0.5, λ=0.8, and α=1

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Fig. 7

Fuzzy unit impulse response for ω=5  rad/s, η=0.5, and λ=0.2

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Fig. 8

Fuzzy unit impulse response for ω=10  rad/s, η=0.5, and λ=0.5

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Fig. 9

Fuzzy unit impulse response for ω=5  rad/s, η=0.05, and λ=0.8

Grahic Jump Location
Fig. 10

Fuzzy unit impulse response for ω=10  rad/s, η=0.05, and λ=0.2

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