The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity

The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of the plate thickness, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von Kármán plate equation.