Nonlinear Statical and Dynamical Models of Fractional Derivative Viscoelastic Body

Abstract

The authors have been conducting experiments on the investigation of nonlinear quasi-statical and dynamical behaviors of a viscoelastic body described by the fractional derivative law. Pre-stress due to pre-displacement induces high damping performance during sinusoidal excitation. To understand this behavior, nonlinear statical and dynamical models are investigated by theoretical consideration. The authors establish and propose appropriate models to describe the nonlinear behavior of the fractional derivative viscoelastic body. The nonlinearity of the viscoelastic coefficient for quasi-statical compressive displacement may be described by the power function with respect to pre-displacement and the nonlinearity of the viscoelastic coefficient for sinusoidal excitation may be described by the exponential function with respect to pre-displacement. Some discussions on the values of the viscoelastic coefficients.