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4:108e in .NET Encode Code-39 in .NET 4:108e

4:108e generate, create barcode code39 none for .net projects iOS (4:108f). where higher-order terms have been neglected. Equations (4.101), and (4.

106) through (4.108) form a closed set of first-order differential equations, which can be solved numerically. The mean and variance responses of the liquid freesurface displacement are determined using equation (4.

89) as follows  E  E a0 J0 0 r E a2 J2 2 r cos 2 2 2 E 2 E  E a2 J2 1 r cos2  1 1 E a2 J2 0 r E a2 J2 2 r cos2 2 2 2 0 0 2E a0 a2 J0 0 r J2 2 r cos 2 2 (4:109b) (4:109a). Note that this non Code 3 of 9 for .NET linear analysis predicts nonzero mean for the free-surface wave height when the excitation has a zero mean. Recall that the linear theory yields zero mean and variance 2 E a2 J2 1 r cos2 .

1 1 Sakata, et al. (1984a) considered an exponential decaying harmonic correlation function of the random process, n(), given in the form Rn  R0 e . j  j cos   The power spectral density of this process is !2  2 2 n o Sn ! R0 p !2  2 2 2 4. 2 !2 (4:110a). (4:110b). where is the exponential VS .NET ANSI/AIM Code 39 decay constant and  is the dominant frequency. These parameters are expressed by the following ratios .

q 2 A . =1 ; B  1 1 ( 4:111) The relationship between the nondimensional root-mean-square (rms) of R0 and the dimen sional value, R0, is. 4.3 Random excitation 10 1 10 2 Sn( ) 10 3 10 4 10 5. * B = 2, R0 = 100 Gal B = 1,. * R0 = 50 Gal Figure 4.16 Power Code 39 Full ASCII for .NET spectra of excitation for damping factor  1 0.

01, A 10, and two different values of center frequency parameter B. (Sakata, et al., 1984a).

, 0.25. 0 (a). , 0.05 . 0 0 10 20 t (b) nonlinear linear 30 40 Figure 4.17 Time h istory records of response mean, , and standard deviation, , of liquid surface p p displacement to unit step envelope for A 10, h 0.4.

(a) R 50 gal, B=1, (b) R 100 gal, B=2. 0 0 (Sakata, et al., 1984a).

Weakly nonlinear lateral sloshing , . 0 (a) 0.1. , 0.05. 0 0 10 20 t (b) nonlinear linear 30 40 Figure 4.18 Time h istory records of response mean, , and standard deviation, , of p p liquid surface displacement to exponential envelope for A 10, h 0.4.

(a) R 50 Gal, B=1, (b) R 100 Gal, 0 0 B 2. (Sakata, et al., 1984a).

p p p R0 R = R!2 R = gy1 1 0 0 (4:112). Recall that R is t Code 39 for .NET he tank radius and g is the gravitational acceleration. Figure 4.

16 shows the power spectra of excitation for two different values of dominant frequency parameter B 1 and 2. The value of B 1 corresponds to the resonance case and B 2 corresponds to the case of an actual earthquake-liquid storage tank system where the dominant frequency is considerably higher than the damped natural frequency of the linear liquid motion. A unit step function, U(), or an exponential function is used as an envelope function, that is, a e e b e  U  ; e  (4.

113a, b) max e a e b Figures 4.17 and 4.18 show the transient mean and standard deviation of liquid surface displacement response to the unit step envelope function and the exponential envelope function, respectively.

The dash curves refer to response statistics obtained by using linear analysis, for the case of small liquid surface amplitudes. Note that the mean response vanishes according p to the linear theory. The rms values of the input noise are R 50 Gal for B 1, 0 p 100 Gal for B 2, where gal refers to a unit of acceleration, 1 Gal 1 cm/s2.

and R0 Figures 4.17(a) and 4.18(a) reveal that a small earthquake excitation may result in a significant.

4.4 Nonlinear phenomena in rectangular tanks response variance visual .net barcode 39 if resonance occurs. The variance predicted by the linear theory is relatively higher than the one estimated by the nonlinear analysis.

. 4.4 Nonlinear phen omena in rectangular tanks 4.4.

1 Background Nonlinear theories of forced sloshing in a rectangular tank were developed by Bauer (1965b, Verhagen and WijnGaarden (1965), Faltinsen (1974), Khosropour, et al. (1995), Young-Sun and Chung-Bang (1996), Lukovskii and Timokha (1999, 2000a), and Faltinsen and Timokha (2001). These studies pertain to lateral excitation of the whole tank and the nonlinear effects were manifested as a soft spring characteristic.

Another group of studies were carried out on rectangular tanks with a wave maker fitted at one or two ends of the tank. The generated surface waves in these studies belonged to standing waves. Two-dimensional standing waves of finite amplitude may be shown to occur in rectangular tanks with flap wave generators.

Depending on the length and width of the tank and the forcing frequency of the wave generator, two classes of resonant standing waves may occur. The first class is the wellknown synchronous, resonant forced longitudinal standing wave whose crest is parallel to the wave maker. The second type is the subharmonic, parametrically excited transverse crosswave whose crest is at right angles to the wave maker.

Cross-waves generally possess half the frequency of the wave maker and reach a steady state at finite amplitude. Penney and Price (1952) developed a Fourier series expansion carried up to fifth-order to determine the wave shape. They indicated that the maximum wave was a sharp-crested form with a 908 angle in contrast to Stokes (1880) result of a 1208 angle for the maximum progressive wave.

The finding of Stokes was a correction of Rankine s (1865) erroneous deduction of a 908 angle. Penney and Price indicated that the finite amplitude affects the frequency of the wave in such a manner as to decrease the frequency. This is in contrast to the frequency increase found by Stokes for finite-amplitude progressive waves.

Later, Sir G. Taylor (1954) conducted an experiment on a rectangular tank with wave generator flaps at the two ends of a rectangular tank. He observed that extremely small synchronous motions of the generator flaps were able to generate high amplitude waves when they were sufficiently close to resonance.

For high amplitudes of water motion, he found that the frequency decreases with the amplitude as predicted by Penney and Price with fair precision of the 908 angle. Beyond the 908-angle maximum form, he observed the occurrence of spontaneous instabilities and transverse wave motions of the free surface. Cross-waves may be generated by applying parametric excitation using a plane wave maker at subharmonic frequency (Miles, 1985b).

Lin and Howard (1960), Garrett (1970), Bernard and Pritchard (1972), Bernard, et al. (1977), and Lichter and Shemer (1986) conducted experimental and analytical investigations on cross-waves generated in a tank with a rigid wall opposite to a wave maker. Standing surface waves of finite amplitude were studied by Mack (1960, 1962), Verma and Keller (1962), Mack, et al.

(1967), and Rajappa (1970a), and Vanden Broeck (1984). Other standing waves were reported by Amick and Tolland (1987) and Agon and Golzman (1996). For certain discrete fluid depths, Mack (1962) reported the occurrence of a coupled motion between higher modes at a frequency equal to an integral multiple of the primary frequency.

Parametric instability in this case is interpreted in terms of the work done by the wave maker against transverse stresses associated with cross-waves..
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