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$        RIGID FORMAT No. 15, Normal Modes Analysis Using Cyclic Symmetry
$        Modal Analysis of a Circular Plate Using Cyclic Symmetry (15-1-1)
$ 
$ A. Description
$ 
$ The natural frequencies of a constant thickness circular plate with six radial
$ stiffeners and a central hole are obtained using the rotational symmetry
$ option. The structure is simply supported at the outer circumference.
$ 
$ The finite element model represents only sixty degrees of the plate. Note that
$ since the stiffeners are on the symmetry boundary, only 1/2 of the actual
$ properties are used. The bulk data cards demonstrated are the CYJOIN and
$ PARAM.
$ 
$ B. Input
$ 
$ 1. Parameters:
$ 
$    R  =  1.0          (outside radius)
$     o
$ 
$    R  =   .14         (inside radius)
$     i
$ 
$    t  =   .01         (plate thickness)
$ 
$    a  =   .06         (height and width of stiffeners)
$                  6
$    E  = 10.6 x 10     (modulus of elasticity)
$ 
$    v  =   .325        (Poisson's ratio)
$                   -4
$    p  =  2.59 x 10    (mass density of plate and stiffeners)
$ 
$ 2. Boundary conditions:
$ 
$    u  = u      = theta  = 0    (all points)
$     r    theta        z
$ 
$    u  = theta  = 0              (along r = 1.0)
$     z        r
$ 
$ 3. Eigenvalue extraction data:
$ 
$    Method: Inverse power
$ 
$    Region of interest: 0.0 <= f <= 8000
$ 
$    Number of desired roots: 3
$ 
$    Normalization: maximum
$ 
$ 4. Cyclic symmetry parameters:
$ 
$    CTYPE ROT
$ 
$    KINDEX 2
$ 
$    NSEGS 6
$ 
$ C. Results
$ 
$ Solutions can be obtained using the dihedral symmetry or rotational symmetry
$ described here.
$ 
$ Results are accurate to approximately six significant figures.
$ 
$                           Table 1. Natural Frequencies
$                               ---------------------
$                               Mode   Frequency (Hz)
$                               ---------------------
$                                1        4288.2
$ 
$                                2        4288.2
$ 
$                                3        6844.3
$ 
$                                4        6844.3
$ 
$                                5       11524.3
$ 
$                                6       11524.3
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