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Example 3: Effect of Tank Width on the Response to Sinusoidal Ground Excitations

In order to study the effect of tank width on the nonlinear liquid response to a sinusoidal ground excitation, a group of four tanks, as shown in Table (4.1), that have the same H/R ratio, but vary in width, are subjected to two groups of sinusoidal ground excitations; the first group of excitation is given by

$\displaystyle \ddot{G}_x$=$\displaystyle 0.1 g \cos(1.1\omega_1 t)$ 

while the second group of excitation is given by
$\displaystyle \ddot{G}_x$=$\displaystyle 0.1 g \cos(1.2\omega_1 t)$ 

where $\omega_1$ is the first sloshing mode frequency of the liquid free surface.
 
Table 4.1: Example 3, Fundamental Frequencies the Four Tanks
2R=H ft.$\omega_1$ rad/sec.T1 sec.
54.491.40
103.171.98
152.592.42
202.252.78
 

It is found that the normalized time history responses of the four tanks are very close. This means that the rigid tank width has no effect on the normalized response time history of the liquid. The same finite element mesh which consists of $20\times20$ elements is used in all cases. Figures (4.10) and (4.11) show the results for the first group of excitation while Figures (4.12) and (4.13) show the results for the second group of excitations.
  
Figure 4.10: Example 3, First Excitation Group, Wave Heights at Left and Right Corners


  
Figure 4.11: Example 3, First Excitation Group, Base Shear and Base Overturning Moment


  
Figure 4.12: Example 3, Second Excitation Group, Wave Heights at Left and Right Corners


  
Figure 4.13: Example 3, Second Excitation Group, Base Shear and Base Overturning Moment

next up previous contents
Next: Example 4: Nonlinear Response Up: Two-Dimensional Examples Previous: Example 2: Nonlinear Response
A. Zeiny
2000-09-06