The time-dependent vibration of forced floating elastic plates by eigenfunction matching in two and three dimensions

The time-dependent vibration of a floating elastic plate subject to a transient force is determined. The solution is found in the frequency-domain by the eigenfunction matching method for a plate of finite length in two dimensions and for a circular plate in three dimensions. The symmetry in the two-dimensional case is exploited to write the solution as the sum of symmetric and anti-symmetric solutions. It is shown that the eigenfunction matching solution in two and three dimensions is almost identical when this symmetry is exploited, and the ease of implementation of this method is demonstrated. The time domain solution is calculated for the case of a Gaussian forcing applied at various points on the plate. The subsequent motion of the plate and its decay due to wave radiation is shown.