Impact response of a nonlinear viscoelastic auxetic plate

Impact induced geometrically non-linear vibrations of a viscoelastic plate are investigated for the case when the shear operator is governed by the fractional derivative Kelvin-Voigt model in conjunction with the time-independent coefficient of volume extension-compression. Such a model could describe the behavior of so-called auxetic materials with negative Poisson's ratios. The modified method of multiple time scales involving the expansion of the fractional derivative in terms of a small parameter has been utilized for solving nonlinear governing equations of motion. The asymptotic behavior of the roots of the characteristic equation for determining the frequencies of the system as a function of the retardation time is studied and three modes of vibration in the process of impact interaction are described.