*heading
TRANSVERSE VIBRATION OF "SIMPLY-SUPPORTED" BEAM			
WITH AND WITHOUT ADDED MASS
*******************************************************************
***		RESULTS/ANALYTICAL SOLUTION
***
*** Analytical solution:
***	f_n = n^2 * (pi/4) * (r/L^2) * sqrt (E/(rho + rho_w))
*** where
***	f	is the frequency in cycles/time
***	n	is the number of the mode
***     r	is the radius of circular cross-section
***     L	is the length of the structure
***     E	is the Young's modulus of the material (of the structure)
***     rho	is the density of material
***     rho_w   is the density of fluid (or water)
***
***	F R E Q U E N C Y    T A B L E
*** Mode  Analytical ABAQUS  Analytical  ABAQUS
***	    No Added Mass        Added Mass
***  1    0.04011   0.04011   0.03766   0.03766
***  2    0.16043   0.16041   0.15064   0.15064
***  3    0.36096   0.3609    0.33894   0.33892
***  4    0.6417    0.64152   0.60256   0.60249
***  5    1.0027    1.0022    0.9415    0.94134
*******************************************************************
**************MODEL********
*node
1,   0.0,    0.0
101, 1000.0, 0.0
*ngen, nset=nall
1,101
*element, type=b21
1, 1,2
*elgen, elset=eall
1, 100, 1, 1
*************AQUA**********
*aqua
-100.0, 100.0, 32.2, 2.0
0., 0., 0., 0.
*WIND
1.987E-2,    10.,    30.0,   0.0,   1.,  0.,  0.0
**   rho,     Z0,    c_x,    c_y,   dx,  dy,  alpha 
*************MATERIAL/SECTION*******
*beam section, elset=eall, section=circ , material=mat1
3.0, 
*material, name=mat1
*elastic
4.32e9, 
*density
14.91, 
**************BOUNDARY***********
*boundary
1,  1,2, 0.0
101,2,2, 0.0
**************HISTORY/LOADING*******
*restart,write,f=100
********
*step,perturbation
Without added mass
*frequency, eigensolver=lanczos, SIM=NO
5, , 
*OUTPUT,FIELD
*MODAL OUTPUT
*endstep
********
*step,perturbation
With added mass
*frequency, eigensolver=lanczos, SIM=NO
5, , 
*d added mass
eall, fi, 6.0, 1.0
*endstep