Flexural motion of a semi-infinite floating plate under localised edge loading

摘要

Numerical computation of flexural motion of a floating elastic plate is often complicated. The linear approximation of the motion makes the computation tractable for simple harmonic waves in a plate. I will introduce a few examples of the linear solution methods from various researchers. This talk will show how the Wiener-Hopf technique gives solutions for a semi-infinite plate with a sinusoidal edge loading. The solution is nearly explicit, which lets us analyze the dynamics of the plate for many frequencies in time and space along the edge. Certain distributions of edge loading can approximate 7a localized forcing on the edge. Then, the Wiener-Hopf technique can be used to find the response to a localised force at the edge of the plate. The resulting solutions may be used to find the relationship between the deflection and velocity near the location of forcing.