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

Abstract

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