Geometrical Nonlinear Statical and Dynamical Models of Fractional Derivative Viscoelastic Body

Abstract

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.