Dynamic Analysis of an Elastic Plate Resting on a Nonlinear Fractional-Order Viscoelastic Pasternak Foundation and Subjected to Moving Load

Abstract

AbstractThe problem of the nonlinear vibrations of an elastic plate resting on a viscoelastic foundation subjected to moving load is becoming increasingly widespread nowadays. In the present paper, the damping features of the nonlinear viscoelastic foundation are described by the fractional derivative Pasternak-type standard linear solid model. Assuming that only two natural modes of vibrations strongly coupled by the internal resonance are excited, the method of multiple time scales in conjunction with the expansion of the fractional derivative in terms of a small parameter has been utilized for solving nonlinear governing equations of motion. The governing set of equations is obtained for determining nonlinear amplitudes and phases in the case of forced vibrations of the plate under concentrated load moving along the edge of the plate, when the internal resonance 1:1 is combined with the external resonance. The expressions for defining coefficients depending on the vibration mode numbers are presented for simply supported case of boundary conditions of the plate.KeywordsNonlinear vibrationsViscoelastic foundationPasternak modelFractional derivativeMoving load