16.5 Computer Program for the Free Vibration Analysis of Ships …
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changes from mode to mode. As such in the computer program, the complete eigenvalue problem is to be solved each time we need to determine a particular natural
frequency.
16.6 Computer Program for Finite Element Free Vibration
Analysis of Plates
The computer program for the free vibration analysis of plate flexure is given in Table
16.9. The problem has been solved by the finite element method using isoparametric
quadratic bending element. The element used being isoparametric, plate of any shape
can be analysed with it.
Table 16.9 Computer program for free vibration analysis of orthotropic plates using isoparametric
quadratic element
c***********************************************************************
c
c
FREE VIBRATION ANALYSIS OF ORTHOTROPIC PLATES USING ISOPARAMETRIC
C
QUADRATIC ELEMENT
c
c***********************************************************************
dimension gstif(3300000),stifo(24,24),asat(24,24),rgd(5,5)
* , sfd(8),sfde(8),sfdz(8),sfder(8),sfdzr(8),xg(8),yg(8),zx(8),
* zy(8),stiff(24,24),amaso(3300000),elmas(24),nod(40,8)
dimension kind(6000),mind(6000),bb(5,24)
c
sin(y)=dsin(y)
c
cos(y)=dcos(y)
c
abs(yy)=dabs(yy)
c
sqrt(zz)=dsqrt(zz)
c***********************************************************************
c
a
length along x-axis
c
b
length along y-axis
c
t
thickness of the plate
c
dx,dy,
c
d1,dxy
flexural properties of the plate
c
sx,sy
shear rigidities of the plate
c
pr
Poisson's ratio
c
exl,eyl sizes of the finite element in the x and y-directions
c
phai
angle between sides in degrees (=90 for rectangle)
c
nx,ny
mesh divisions in the x and y-directions
c
nbon
a code given for typical boundary conditions
c
nq
no. of Gauss points in the evaluation of stiff
c
nn
no. of nodes in the element
c
nfree
degrees of freedom per node
c
nt
total degrees of freedom of the entire plate
c
nelm
total number of elements
c
nbh
half-band width of the overall stiffness matrix
c
nenp
total degrees of freedom per element
c
dxz
partial derivative of x with respect to zi
c
dyz
partial derivative of y with respect to zi
c
dxe
partial derivative of x with respect to eta
c
dye
partial derivative of y with respect to eta
c
zac
the value of the jacobian
c
dnx
derivative of the shape function with respect to x
c
dny
derivative of the shape function with respect to y
c
sfd
shape function
c
sfdz
partial derivative of the shape function with respect to zi
c
sfde
partial derivative of sfd with respect to eta
(continued)