Mathematical model of dissipative parametric vibrations of flexible plates with nonhomogeneous boundary conditions

In this work, parametric vibrations of flexible squared plates with changeable boundary conditions along their contours are studied. The known T. von Kármán equations serve as a mathematical model. This continuous system is reduced to a discrete one through the method of finite approximations of O(h4) order, which is solved further by the fourth-order Runge-Kutta technique. New scenarios of transition from harmonic to chaotic vibrations are reported.