Analytical Solution of a Fractionally Damped Beam by Using Adomian Decomposition Method

LIANG Zu-feng; TANG Xiao-yan

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(2): 200-208

LIANG Zu-feng, TANG Xiao-yan. Analytical Solution of a Fractionally Damped Beam by Using Adomian Decomposition Method[J]. Applied Mathematics and Mechanics, 2007, 28(2): 200-208.

Citation:

LIANG Zu-feng, TANG Xiao-yan. Analytical Solution of a Fractionally Damped Beam by Using Adomian Decomposition Method[J]. Applied Mathematics and Mechanics, 2007, 28(2): 200-208.

Citation:

LIANG Zu-feng, TANG Xiao-yan. Analytical Solution of a Fractionally Damped Beam by Using Adomian Decomposition Method[J]. Applied Mathematics and Mechanics, 2007, 28(2): 200-208.

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Analytical Solution of a Fractionally Damped Beam by Using Adomian Decomposition Method

LIANG Zu-feng¹,
TANG Xiao-yan²

1.
Power Engineering College, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;

Received Date: 2006-03-13
Rev Recd Date: 2006-10-24
Publish Date: 2007-02-15

Abstract

Abstract

The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the Adomian decomposition method.The solution contains arbitrary initial conditions and zero input.For specific analysis,the initial conditions were assumed homogeneous,and the input force was treated as a special process with a particular beam.Two simple cases,step and impulse function responses,were considered respectively.Subsequently,some figures were plotted to show the displacement of the beam under different sets of parameters including different orders of the fractional derivatives.
- viscoelastic beam,
- fractional derivative,
- Adomian decomposition method,
- vibration

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References(21)

References

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