On nonlinear integro-differential equations connected with the von Kármán system (Q2715513)

Using Galerkin method, the author derives a nonlinear integro-differential equation from the system of four differential strain-displacement relations and from integral stress-strain relations for a thin isotropic plate of Boltzmann type. This equation characterizes the time behaviour of viscoelastic von Kármán plates subjected to plane oscillatory loading. The author discusses the stability of unperturbed motion. The relaxation function is selected in an exponential form, and Runge-Kutta method is used to solve numerically the nonlinear system of four differential equations and their linearization.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00021].