*heading
TRANSVER VIBRATION OF "CLAMPED-FREE" (CANTILEVER) BEAM		
WITH AND WITHOUT ADDED MASS
*******************************************************************
***		RESULTS/ANALYTICAL SOLUTION
***
*** Analytical solution:
***	f_n = (an/(4 pi)) * (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)
***	a_n	is a constant for the "n"th mode [only for ANALYTICAL soln]
***
***	F R E Q U E N C Y    T A B L E
*** Mode  a_n  Analytical ABAQUS Analytical ABAQUS
***	         No Added Mass        Added Mass
***  1  (3.516)  0.01429  0.01429  0.01342  0.01342
***  2  (22.03)  0.08952  0.08952  0.08406  0.08406
***  3  (61.7)   0.25071  0.2506   0.2354   0.2354
***  4  (120.9)  0.4913   0.491    0.4613   0.4611
***  5  (199.9)  0.8122   0.8114   0.7626   0.7621
*******************************************************************
**************MODEL********
*node
1,   0.0,    0.0
1001, 1000.0, 0.0
*ngen, nset=nall
1,1001,10
*element, type=b21
1, 1,11
*elgen, elset=eb21
1, 100, 10, 10
*************AQUA**********
*aqua
-100.0, 100.0, 32.2, 2.0
0., 0., 0., 0.
*************MATERIAL/SECTION*******
*beam section, elset=eb21, section=circ, material=mat1
3.0, 
*material, name=mat1
*elastic
4.32e9, 
*density
14.91, 
**************BOUNDARY***********
*boundary
1,  1,2, 0.0
1,  6,6, 0.0
**************HISTORY/LOADING*******
*restart,write,f=100
****
*step,perturbation,unsymm=no
Without added mass
*frequency, eigensolver=lanczos, SIM=NO
5, , 
*OUTPUT,FIELD
*MODAL OUTPUT
*endstep
****
*step,perturbation,unsymm=no
With added mass
*frequency, eigensolver=lanczos, SIM=NO
5, , 
*d added mass
eb21, fi, 6.0, 1.0
*endstep