The theory of scattering frequencies is applied to a simple hydroelastic problem, the wave forcing of a floating thin plate on shallow water. The scattering frequencies are the complex frequencies for which the system has an infinite response. They are calculated by finding the complex frequencies for which the scattering matrix is singular. These singularities are found by using a complex singularity search for a crude estimate. This method allows us to be certain that we have found all the singularities. We then use Newton's method to determine them very accurately. The scattering frequencies allow us to find the real frequencies at which the response of the system peaks. They also give the real frequencies at which the transmission coefficient is unity. Furthermore we can predict the response near the peak frequencies by using the response at the scattering frequency. Introduction Hydroelasticity is the study of elastic bodies in water, in particular problems in which the equations of motion of the water and elastic body must be solved simultaneously. There has been much recent interest in hydroelasticity because of the construction of very large floating structures (VLFS) such as a floating runway. Because of their large size but small thickness, the elastic response of such structures is significant. The major difficulty in solving hydroelastic problems is coupling the equations of motion of the water and the equations of motion of the elastic body. Also, since the discretisation of the problem often requires many points, it is generally important to find efficient methods to calculate the response. One of the major problems in hydroelasticity is to calculate the response of an elastic body to linear wave forcing. A solution method to this problem was developed by Bishop (1986) for wave forcing of a single frequency.

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