著者

那須野 洋 清水 信行

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 C編 (ISSN:03875024)

巻号頁・発行日

vol.72, no.724, pp.3728-3735, 2006-12-25 (Released:2011-08-16)

参考文献数

21

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This paper is concerned with the development of an efficient algorithm for the numerical solution of the fractional differential equation (FDE). The numerical integration of the FDE requires significant computational cost, because the fractional convolution integral included in the fractional derivative, requires O(N2) operations for N points calculation. The kernel of the fractional integral has singularity and consequently excessive small time-step near the singularity is needed to secure the high precision in the numerical calculation. This difficulty is solved by means of a new computational procedure for fractional derivative by introducing the variable trasformation from the physical time to the power time which is newly defined in this paper. The proposed algorithm is used to solved the nonlinear FDE. Computational results are compared with those by the former method (Nasuno and Shimizu, JSME (C), 2006). The proposed method shows remarkably higher performance than the former one.

著者

那須野 洋 清水 信行 安野 拓也

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 C編 (ISSN:03875024)

巻号頁・発行日

vol.72, no.716, pp.1041-1048, 2006-04-25 (Released:2011-03-04)

参考文献数

9

被引用文献数

3 2

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The experimantal study has been conducted for several years to investigate the nonlinear psudo-statical and dynamical behaviors of a viscoelastic body described by the fractional derivative law. Pre-stress due to pre-displacement induces higer damping capacity during sinusoidal excitation. In order to understand this behavior, nonlinear statical and dynamical models are considered. The authors establish and propose the appropriate models to describe the behavior of the fractional derivative viscoelastic body. The nonlinearity having second order term with respect to pre-displacement for pseudo-statical compressive displacement and the nonlinearity having exponential term with respect to pre-displacement for sinusoidal excitation are found to be appropriate to describe the viscoelastic damping coefficients. Some discussions on the values of the viscoelastic damping coefficients and how to model a unified force-displacement relation covering from lower to higher wide frequency range are given.