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
 
 
 
[[Frequency Domain Problem]]
 

Latest revision as of 23:56, 15 June 2006

This page has moved to Floating Elastic Plate.

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