Comparison of Fractional Derivative Models for Finite Deforamtion with Experiments of Impulse Response
In constructing fractional derivative models for viscoelastic materials based the Maxwell model, or the Boltzmanns superposition principle, difference of interpretation of (∈) results in many types of nonlinear models. In this paper we compare nonlinear fractional derivative models for viscoelastic materials with experimental results of a polymer gel. In the experiment a weight was collided on a cylindrically shaped gel in the vertical direction with the other side fixed. Then, the acceleration and the displacement of the contact surface between the weight and the gel are observed. Deformation of the gel is approximated by the uniaxial compression of incompressible material. Every model considered in this paper reproduces well the acceleration data in the early stage when the change in the velocity of contact surface is small compared with the velocity. Difference of the behaviors among the models is prominent around the maximum of the acceleration when the compression speed is clearly slowed down. It is shown that the models based on the weakly compressible approximation give best fits.
Fractional differentiation fractional integration fractional order constitutive model nonlinear response viscoelastic materials.
Masataka Fukunaga Nobuyuki Shimizu
College of Engineering, Nihon University (P.T. Lecturer),(home)1-2-35-405, Katahira, Aoba-ku, Sendai Department of Mechanical Systems and Design Engineering, Iwaki Meisei University, Iwaki, 970-8551, J
国际会议
The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)
南京
英文
1-6
2012-05-14（万方平台首次上网日期，不代表论文的发表时间）