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The asymptotic behaviour of the solutions of three-dimensional nonlinearelastodynamics in a thin plate is studied, as the thickness $h$ of the platetends to zero. Under appropriate scalings of the applied force and of theinitial values in terms of $h$, it is shown that three-dimensional solutions ofthe nonlinear elastodynamic equation converge to solutions of thetime-dependent von K\'arm\'an plate equation.

The time-dependent von K\'arm\'an plate equation as a limit of 3d nonlinear elasticity