A mathematical model for non-linear dynamics of conservative systems with non-homogeneous boundary conditions

In this work a transition into a chaotic dynamics of plates with unmovable boundary conditions along a plate contour and subjected to a longitudinal impact action modeled as a rectangular type loading of infinite length in time is studied. The well-known T. von Kármán equations governing behaviour of flexible isotropic plates have been applied. Finite-difference approximation of order O(h⁴) allowed to transform the problem from PDEs to ODEs. We have shown and discussed how the investigated plate vibrations are transmitted into chaotic dynamics through a period doubling bifurcation. Furthermore, essential influence of boundary conditions on bifurcations number is illustrated, and for all investigated problems the Feigenbaum constant estimation is reported.