Bifurcations of the von Kármán equations with Robin boundary conditions (Q1963109)

The authors present a numerical bifurcation analysis of the von Kármán plate equation with Robin boundary conditions. At first, the linear stability of the plane state of the plate is discussed (by using spectral theory of linearized operator). Bifurcation analysis is given for simple and double bifurcation points. Then a central difference approximation of the problem allows to obtain numerical results. Of special interest is the phenomenon of mode jumping in plate deformation. Numerical results show that the mode jumping depends on the length of the plate and on the stiffness of the elastic support.