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