Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

On the forced dynamics of floating plates

K.M. Dempsey*, I.V. Vasileva
Department of Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699–5815, USA

  Full Text
The uplift of an infinite plate floating on a fluid of finite depth is studied with a view to inverting the forcing required to produce prescribed dynamics. The problem is ill posed and the potential of the forcing is the solution of a Volterra integral equation of the first kind and of convolution type. Analysis shows that the degree of ill-posedness is moderate and reveals that the initial rate of forcing is proportional to the initial acceleration of the plate. For error-free data, this analytical result, and a nonuniform mesh, are used to numerically compute the forcing to three decimal places.

Keywords:  Volterra integral equation of the first kind; Ill-posed; Canonical problems

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