Nonlinear Dynamic Response of a Thin Plate Embedded in a Fractional Viscoelastic Medium under Combinational Internal Resonances

Abstract

Dynamic behaviour of a nonlinear plate embedded in a fractional derivative viscoelastic medium and subjected to the conditions of the combinational internal resonances of the additive and difference types has been studied by Rossikhin and Shitikova in [1]. Nonlinear equations, the linear parts of which occur to be coupled, were solved by the method of multiple time scales. A new approach proposed in [2] allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The new approach enables one to find an additional combinational resonance of the additive-difference type, as well as to solve the problems of vibrations of thin bodies more efficiently.