Mathematical model of dissipative parametric vibrations of flexible plates with nonhomogeneous boundary conditions (Q610078)

Summary: 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 \(O(h^{4})\) order, which is solved further by the fourth-order Runge-Kutta technique. New scenarios of transition from harmonic to chaotic vibrations are reported.