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W (t ) 0 0.01 0.01 F(t ) 0 0.01 0.05 Z0 0 0.05 0.8 0 in .NET Printer 3 of 9 barcode in .NET W (t ) 0 0.01 0.01 F(t ) 0 0.01 0.05 Z0 0 0.05 0.8 0

0.01 W (t ) 0 0.01 0.01 F(t ) 0 0.01 0.05 Z0 0 0.05 0.8 0 generate, create none none for none projects QR Code Safty Interaction with structures and tuned absorbers 0.01 W (t) 0 0.01 0.

01 F(t) 0 0.01 F(t) 0 0.01 0.

05 Z0 0 0.05 0.8 0 0.

8 0.8 c11 0 0.8 0.

8 d11 0 0.8 180 1425 1475 t 0 180 d11 c11 0.05 Z0 0 0.

05 0.8 0 0.8 0.

8 0 0.8 0.8 0 0.

8 180 0 180 0.01 0.01 W (t) 0 0.

01. 0.8 0.8 c11 0 0.8 0.8 d11 0 0.8 180 0 180 1375 d11 0.8. 0.08 d11 c11 0.08 0.08 0.8. 0.8 c11. 0.08. c11 0.08. 0.8. 0.08. 0.08. (a) 1375 t 1500 (b) 4500 t 4625 (b) 5000 t 5125 Figure 10.3 4 Magnifications of time histories of Figure 10.49 for different time intervals and the corresponding trajectories of (c11, d11).

(Ikeda and Ibrahim, 2002). t 1000 to none for none t 6000 in order to eliminate the transient responses. Figures 35(a) (c) shows the dependence of the mean square responses on the center frequency O of a narrow-band random excitation for three different values of bandwidth. 0.1, 0.2, and 0.

3, respectively, and for the same parameters of Figure 10.33. Comparing these results with those of the uncoupled system reveals that the mean square response, E z2 , in the coupled system drops over a finite range 0 of O, where the liquid-free-surface motion interacts with the structure through nonlinear coupling.

As the filter bandwidth,. , increases none for none , the peak of E z2 , shown by solid circles, 0 decreases and is associated with a shrinking in the range of O, over which the interaction with liquid motion takes place. Figure 10.36 shows the dependence of the normalized mean square of the structure E z2 c /E z2 f on the center frequency for various values of bandwidth,.

, where the subscript 0 0 c denotes coupling, and f denotes frozen. This normalized representation provides direct information regarding the degree of nonlinear coupling and the energy transfer between the structure and liquid surface motions. It can be seen that the amount of the energy transfer from the structure motion to the liquid surface motion becomes predominant as.

decreases. 10.5 Random excitation 10 1 Simu none none lation E[z2 ] 0 10 1 Simulation E[z2 ] 0. 2 E[z0 ]. 6.0 E[z2 ] 0 3.0.

0 1.8 6.0.

2 E[c11 ]. 1.9 2.0 2.1 Center frequency 0 1.8 6.0.

2 E[c11 ]. 10 2. 1.9 2.0 2.1 Center frequency Simulation 2 E[c11 ]. 2 E[d11 ]. Simulation 2 E[c11 ]. 2 E[d11]. 2 E[d11]. 2 E[d11]. 0 1.8 1.9 2.0 2.1 2.2 Center frequency (a) = 0.1 10 1 6.0 Simulation 2] E[z2 ] E[z 0 0 1.8 1.9 2 .

0 2.1 Center frequency (b) = 0.2 2.

2. 1.9 2.0 2.

1 none none 10 2 Center frequency 6.0 Simulation 2 E[c11] 2 E[c11] E[d 2 ] 3.0.

2 E[d11] 11. 0 1.8. 0 1.8. 1.9 2.0 2.

1 none for none Center frequency (c) = 0.3. Figure 10.3 5 Dependence of mean square responses of the structure E [z2 ] and fluid elevation compo0 2 2 nents E [c11 ] and E [d11] on the center frequency O for three different values of the bandwidth. and the sam none none e parameters as Figure 10.49. (Ikeda and Ibrahim, 2002).

Figure 10.3 7(a) shows the dependence of the mean square response of the liquid amplitudes c11 and d11 on the excitation spectral density S0. This figure is magnified in Figure 10.

37(b) and both figures reveal that the mean square value of the liquid elevation gradually increases as the intensity 2 2 S0 increases, and that E [c11 ] is nearly equal to E [d11 ]. The stability boundary of liquid sloshing is defined in this analysis by taking the value of the mean square level Ams 2.0 10 4 that corresponds to S0 % 0.

15 10 7. This threshold mean square level refers to either mode c11 or d11..

1.0 0.8.

2 2 E[z0 ]c / E[z0 ] f Interaction with structures and tuned absorbers 0.6 0.4 0.

2 0 1.8. = 0.1 = 0.2 = 0.

3. 1.9 2.0 Center frequency 2.1 2.2 Figure 10.3 none none 6 Normalized of the structure mean square response with response to its mean square with frozen liquid for different values of bandwidth. , h/R 1.2 ,  1 0.87,  2 0.

034, k 4.0, c 0.03,  01  11  21 0.

01. (Ikeda and Ibrahim, 2002). 2 E[c11] 2 E[c11] 2 E[d11]. 2 E[d11]. 0 0 0.010. 2 E[c11] 2 E[c11] 2 E[d11]. 1 S0. 3 10 7. 2 E[d11].
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