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.
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Communicated by GUO Xing-ming
Project supported by the National Natural Science Foundation of China (Nos.10547124 and 10475055)
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Liang, Zf., Tang, Xy. Analytical solution of fractionally damped beam by Adomian decomposition method. Appl Math Mech 28, 219–228 (2007). https://doi.org/10.1007/s10483-007-0210-z
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DOI: https://doi.org/10.1007/s10483-007-0210-z