Mass matrix
The kinetic energy, T of the element is given as
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(19.1) |
M is the mass matrix,  the density of the plate and V is the volume of the element. Expressing (u,v) and w in terms of nodal variables  and  and using Equation (18.12), the expression for kinetic energy may be written as
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(19.2) |
Hence, for any composite laminate, the mass matrix can be written as
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(19.3) |
 = thickness of the kth layer,  density per unit area of the kth layer.
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(19.4) |
The shape functions used to find mass matrix are the same as that for the field displacement. Such mass matrix is termed as ‘consistent mass matrix’. The consistent mass matrix is computationally more intensive, but more accurate for dynamic analysis and hence it is chosen for this problem.
The expression for mass matrix on transformation to area coordinates is
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(19.5) |
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