137 粘弾性体のフラクタル構造と分数階微分(粘弾性体の減衰のモデル化, OS-11 ダンピング(2))

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概要

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• The dynamical behavior of an viscoelastic body is known to be well described by fractional derivatives of the amount of deformation. The physical reason of this fact is the underlying fractal nature of the molecular structure of such materials. By using the Schiessel-Blumen ladder of mechanical system, it has been shown that the fractal structure would produce the asymptotic power law decay of the deformation, which is the most distinguished characteristics of fractional derivatives. So far, this has been shown by asymptotic behavior of the Laplace transform of the impulse response of the relaxation. Here, we generalize this result, and show that the exact solution of the impulse response function is obtained for a large class of parameter values in terms of confluent hypergeometric functions. The asymptotic expression is then readily obtained which shows the power law decay.

• 一般社団法人日本機械学会の論文
• 2004-09-27

著者

• 榊原 進

  東京電機大情報環境

• 榊原 進

  東京電機大

関連論文

• G. Baumann, Mathematica for Theoretical Physics, 2nd ed.; Classical Mechanics and Nonlinear Dynamics, Springer Science-Business Media, Inc., New York, 2005, xvi+544p, 24×18cm, \14,470, [学部・大学院向] / G. Baumann, Mathematica for Theoretical Physics, 2nd ed.;
• Fractional Derivative Models of Damped Oscillations (Partial Differential Equations and Time-Frequency Analysis)
• Continued Fractions and Fractional Derivative Viscoelasticity (Feasibility of Theoretical Arguments of Mathematical Analysis on Computer)
• ウェーブレット解析入門
• 137 粘弾性体のフラクタル構造と分数階微分(粘弾性体の減衰のモデル化, OS-11 ダンピング(2))

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