Analysis of Forced Vibrations of a Nonlinear Elastic Plate on a Viscoelastic Foundation Subjected to Hard Excitation from Harmonic Load

In the present chapter, the dynamic response of a nonlinear Kirchhoff-Love plate resting on a viscoelastic foundation in a viscoelastic medium, damping features of which are described by the Kelvin-Voigt fractional derivative model, is studied for the case of forced vibrations excited by a harmonic load. The damping properties of the viscoelastic Fuss-Winkler-type foundation are described by the fractional derivative, standard linear solid model. Supposing that only two natural modes of vibrations strongly coupled by the internal resonance 1:1 are excited, the generalized 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. Assuming the amplitude of external load to be hard, resolving equations are obtained for determining nonlinear amplitudes and phases for various types of external resonances that may occur in systems with cubic nonlinearities.