Stokes wave traveling along a thin elastic plate floating at water surface

Abstract

This paper addresses nonlinear deflection waves traveling along a thin elastic plate floating at the water surface. The investigations are based on both the analytical and experimental aspects. A finite amplitude wave theory for the waves traveling on the plate developed by the present authors, in which, the nonlinear wave is formulated by a perturbation with respect to the wave height/wavelength ratio, is used. The behavior of the nonlinear wave traveling on the plate is like what the Stokes wave theory predicts for the free surface. However, for the waves traveling on the plate, there is an instability frequency at which the second order wave component grows considerably. The sign of the second order wave component is inverted at the instability frequency when the incident wave frequency is changed from low to high regions. These predictions are verified in a tank test in the two-dimensional flume using a long flexural plate that was newly designed. The spatio-temporal distribution of the deflection and bending strain on the plate was measured directly using the stereo Digital Image Correlation (DIC) technique with two high-speed CCD cameras. The measured results are compared with the predictions by analytical theory. The instability frequency is found in the tank test and the nonlinear wave properties are discussed.