Effect of the initial ramps of creep and relaxation tests on models with fractional derivatives
Maolin Du, Yi Wang, Zaihua Wang
Abstract: We analyze the influences of the initial ramps of relaxation and creep tests on the determination of the parameters of the Scott-Blair’s model, the simplest model with a fractional derivative. The true input of a test is a constant with an initial ramp. The error resulted from neglecting the initial ramp increases with the increasing of the fractional order, and the closer the data are to the beginning, the larger the errors are. Based on the error analysis, an n-times rule is generalized from the ten-times rule. For illustration, the Scott-Blair’s model is fitted with the experimental data in literature. The data are of two polymer samples, PMMA and PTFE (methylmethacrylate and polytetrafluorethylene), and self-healing and thermoreversible rubbers.
原文链接: https://link.springer.com/article/10.1007/s11012-017-0678-1
