Difference between revisions of "Floating Elastic Plate"

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= Introduction =
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This page has moved to [[:Category:Floating Elastic Plate|Floating Elastic Plate]].
  
The floating elastic plate is one of the best studied problems in hydroelasticity. It can be used to model a range of
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physical structures such as a floating break water, an ice floe or a [[VLFS]]). The equations of motion were formulated
 
more than 100 years ago and a discussion of the problem appears in [[Stoker_1957a|Stoker 1957]]. The problem can
 
be divided into the two and three dimensional formulations which are closely related.
 
 
 
= Two Dimensional Problem =
 
 
 
= Equations of Motion =
 
 
 
The equation for a elastic plate which is governed by Kirkoffs equation is given
 
by the following
 
 
 
<math>D\frac{\partial^4 \eta}{\partial x^4} + \rho_i h \frac{\partial^2 \eta}{\partial t^2} = p</math>
 
 
 
where <math>D</math> is the flexural rigidity, <math>\rho_i</math> is the density of the plate,
 
<math>h</math> is the thickness of the plate (assumed constant), <math> p</math> is the pressure
 
and <math>\eta</math> is the plate displacement.
 
 
 
The pressure is given by the linearised Bernouilli equation at the wetted surface (assuming zero
 
pressure at the surface), i.e.
 
 
 
<math>p = \rho g \phi + \rho \frac{\partial \phi}{\partial t}</math>
 
 
 
where <math>\rho</math> is the water density and <math>g</math> is gravity, and <math>\phi</math>
 
is the velocity potential. The velocity potential is governed by Laplace's equation through out
 
the fluid domain subject to the free surface condition and the condition of no flow through the
 
bottom surface. If we denote the region of the fluid surface covered in the plate (or possible
 
multiple plates) by <math>P</math> and the free surface by <math>F</math> the equations of motion for the
 
[[Frequency Domain Problem]] with frequency <math>\omega</math> is
 
 
 
<math>Insert formula here</math>
 

Latest revision as of 23:56, 15 June 2006

This page has moved to Floating Elastic Plate.

Please change the link to the new page