$-------------------------------------------------------------------------------
$                  RIGID FORMAT No. 3, Real Eigenvalue Analysis
$                        Acoustic Cavity Analysis (3-4-1)
$ 
$ A. Description
$ 
$ This problem illustrates the use of NASTRAN to determine the acoustic modes in
$ a cavity containing both axisymmetric regions and evenly spaced radial slots.
$ The motor cavity of Stage IlI of the Minuteman III missile is selected for
$ analysis. The finite element model consists of six slots and a long, slender
$ central cavity of irregular shape. The model consists of AXIF2, AXIF3, and
$ AXIF4 finite elements in the central cavity, and SLOT3 and SLOT4 finite
$ elements in the slotted region.
$ 
$ The axisymmetric radial and longitudinal acoustic modes are desired (N = 0)
$ for this problem. The harmonic index N specifies the Fourier Series terms to
$ be analyzed. For example, N = 1 defines the lateral motion where the velocity
$ is normal to the center axis. Repeated runs with N = 0, 1, ...M/2 may be
$ necessary to extract all possible modes, where M is the number of radial slots
$ specified.
$ 
$ B. Input
$ 
$ Parameters:
$                     -7
$ p     =   1.143 x 10   (Fluid density)
$ 
$ beta  =   20.58        (Fluid bulk modulus)
$ 
$ N     =    0           (Harmonic index)
$ 
$ WD    =    4.0         (Slot width)
$ 
$ MD    =    6           (Number of slots)
$ 
$ C. Results
$ 
$ The vibration mode frequencies for harmonic n = 0 as determined with NASTRAN
$ are shown in Table 1. Also shown are the vibration mode frequencies as
$ determined with an acoustic model and reported in Reference 19.
$ 
$ Table 1. Natural Frequencies for the Third Stage, Minuteman III, Motor Cavity
$ 
$                                     Frequency, Hz
$                                 ----------------------
$                                   NASTRAN    Experi-
$                           Mode               mental
$                           ----------------------------
$                            1        0.0         0.0
$ 
$                            2       90.1        93.0
$ 
$                            3      199.5       200.0
$ 
$                            4      310.4       312.0
$ 
$                            5      388.0       388.0
$ 
$                            6      449.1       466.0
$ 
$                            7      512.8       518.0
$                           ----------------------------
$ 
$ APPLICABLE REFERENCES
$ 
$ 19. Herting, David N.; Joseph, Jerrard A.; Kuusinen, Loren R.; and MacNeal,
$     Richard H.: Acoustic Analysis of Solid Rocket Motor Cavities by a Finite
$     Element Method. NASA TN X-2378, September, 1971, pp. 285-324.
$-------------------------------------------------------------------------------
