A fractional viscoelastic model for vibrational analysis of thin plate excited by supports movement

Abstract

In this paper, a fractional viscoelastic model is presented for vibration analysis of a fully simply supported plate excited by the supports movement. To govern the steady-state condition for the plate vibration, the lower limit of the integral in Riemann-Liouville fractional derivative is assumed in minus infinity. The Voigt viscoelastic model is employed for describing the damping effects. Considering the Kirchhoff hypothesis the governing equation of the viscoelastic plate is derived. An analytical solution for the dynamic response of the fractional viscoelastic plate under the support excitation is proposed. The effect of fractional derivative order and damping coefficient on the amplitude-frequency characteristic of the plate is investigated. Also, the obtained natural frequencies for elastic plate (by setting the fractional derivative order to zero) and classical viscoelastic plate (by setting the fractional derivative order to one) are compared with existing results in the literature.