  The asymptotic behaviour of solutions of three-dimensional nonlinear
elastodynamics in a thin shell is considered, as the thickness $h$ of the shell
tends to zero. Given the appropriate scalings of the applied force and of the
initial data in terms of $h,$ it's verified that three-dimensional solutions of
the nonlinear elastodynamic equations converge to solutions of the
time-dependent von K\'arm\'an equations or dynamic linear equations for shell
of arbitrary geometry.
