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Linear interaction with elastic containers in .NET Generating ANSI/AIM Code 39 in .NET Linear interaction with elastic containers




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Linear interaction with elastic containers use .net vs 2010 barcode 3/9 implement toget code-39 on .net .NET CF where Cn J0 n R I1 R = ,. En J0 n R J1 R = ,. n i !An 1 Bn D  4 4 n (8:67). J0 R I1 R I0 R barcode 3/9 for .NET J1 R ;. On the other hand, the solu tion of equation (8.65b) that satisfies the boundary conditions (8.64) may be written in the form.

0 W0 r 0 C0 J0 r E0 I0 r 1 (8:68). where C0 I1 R = ; E0 J1 R = ; and 0 i. !A0 B0 D4 (8:69). Equating the velocities of the plate and of the liquid in contact with it, as required by condition (8.34c), gives. 0 i!. 0 C0 J0 r E0 I0 r 1 ei!t 1 X n 1 0 i!. n Cn J0 r En I0 r J0 n r ei!t 1 X n 1 (8:70). A0 ei!t n An Bn 1 J0 n r ei!t Following the same procedur VS .NET barcode code39 e for the case of membrane, the Bessel function J0(r) is replaced by the expansion (8.42) and I0(r) is expanded in series in terms of J0(nr) as follows I0 r .

1 J0 p r 2 2I1 R X I1 R 2 2 J0 p R R R p p 1 (8:71). Substituting (8.42) and (8. 71) into equation (8.

70) gives " # 1 X J0 p r J1 R 1  2! A0 0 C0 2 2 J0 p R R  p p 1. " # 1 X J0 p r I1 R 1  2! A0 0 E0 0 2 2 J0 p R R  p p 1 " # 1 X J0 p r J1 R 1  2! An n Cn R  2 2 J0 p R p n 1 p 1 1 X 2. " # 1 X J0 p r I1 R 1  2! An n En 2 2 J0 p R R  p n 1 p 1 1 X 2. 1 X n 1 !2 An n J0 n r A0 1 X n 1 n An Bn 1 J0 n r (8:72). 8.3 Interaction with tank bottom where 0 B0 =D4 ; and n  1 Bn =D 4 4 n (8:73). Equating the coefficients o 39 barcode for .NET f J0(nr) gives a set of coupled equations. Setting the determinant of the coefficients A0, A1, .

. . to zero gives a frequency equation similar in form to equation (8.

44) where the elements of the determinant are defined by the following expressions 11 12 13 21 2!2 0 C0 J1 R E0 I1 R !2 0 1 R 2!2 1 C1 J1 R E1 I1 R R. 2!2 2 C2 J1 R E2 I1 R R " # 2!2 0 C0 J1 R E0 I1 R RJ0 1 R 2 2 2 2 1 1 " # 2!2 1 C1 J1 R E1 I1 R 1 !2 1 B1 1 RJ0 1 R 2 2 2 2 1 1 " # 2!2 2 C2 J1 R E2 I1 R RJ0 1 R 2 2 2 2 1 1 " # 2!2 0 C0 J1 R E0 I1 R RJ0 2 R 2 2 2 2 2 2 " # 2!2 1 C1 J1 R E1 I1 R RJ0 2 R 2 2 2 2 2 2 " # 2!2 2 C2 J1 R E2 I1 R !2 2 2 B2 1 RJ0 2 R 2 2 2 2 2 2. (8:74). The frequency equation (8.4 4), with coefficients (8.74), has two limiting cases.

If one sets the flexural rigidity of the plate D ! 1, or the density of the liquid  ! 0, one obtains after some manipulations. n Bn 1 0 (8:75). Equation (8.75) implies tha Code 39 for .NET t J0 R I1 R I0 R J1 R 0 or Bn 1; that is !2 gn tanh n h n (8:77) (8:76).

Linear interaction with elastic containers Table 8.1 Coupled frequencies h/R 0.1, D 279 981 lb inch, hp 0.467 inch n 1 2 3 4 5 2 2 3.280 8 8 3.280 5.

724 7.766 9.459 10.

865 Rigid tank 3.288 5.726 7.

770 9.459 10.865.

Source: Bhuta and Koval, 1964b. Table 8.2 Coupled frequencies h/R 0.05, D 16 021 lb inch, hp 0.26 inch n 1 2 3 4 5 2 2 2.299 .NET bar code 39 8 8 2.

299 4.262 6.066 7.

7339 9.278 Rigid tank 2.366 4.

273 6.069 7.740 9.

278. Source: Bhuta and Koval, 1964b. Table 8.3 Coupled frequencies h/R 0.1, D 93 326 lb inch, hp 0.467 inch n 1 2 3 4 5 2 2 3.271 8 8 3.271 5.

723 7.767 9.459 10.

865 Rigid tank 3.288 5.726 7.

770 9.459 10.865.

Source: Bhuta and Koval, 1964b. Table 8.4 Coupled frequencies h/R 0.05, D 48 063 lb inch, hp 0.26 inch n 1 2 3 4 5 2 2 2.342 .net vs 2010 bar code 39 8 8 2.

342 4.269 6.068 7.

740 9.278 Rigid tank 2.366 4.

272 6.068 7.740 9.

278. Source: Bhuta and Koval, 1964b. 8.4 Interaction with tank walls Equation (8.76) gives the f requency equation of axisymmetric vibrations of a clamped elastic circular plate in a vacuum. On the other hand, equation (8.

77) gives the frequencies of the liquid free surface in a rigid circular upright cylindrical tank. Bhuta and Koval (1964b) truncated the frequency equation (8.76), with coefficients (8.

74), in stages at 2nd-, 3rd-, . . .

and 8th-order determinant and estimated the lower values of the coupled frequencies. The results of the numerical results are given in Tables 8.1 4 for different values of liquid depth ratio h/R, and different values of plate flexural rigidity, D.

The effect of the elastic bottom is observed only for smaller values of liquid depth ratio and the plate flexural rigidity is decreased.. 8.4 Interaction with tank w barcode 3 of 9 for .NET alls The interaction of liquid sloshing dynamics with the tank walls may take place between sloshing modes and bending modes; or breathing elastic modes.

Bending deformation of the tanks does not involve stretching of the tank walls and the longitudinal axis of the tank experiences some type of deformation. On the other hand, breathing deformation involves flexure and stretching of the wall in the radial direction and the tank longitudinal axis remains straight. The two types of interaction are considered in the next two sections.

. 8.4.1 Interaction with bend ing modes The modal analysis of liquid sloshing interaction with tank bending deformation involves the estimation of the system coupled natural frequencies.

Within the framework of the linear theory of small oscillations, the liquid elastic container coupling was studied by Merten and Stephenson (1952), Reissner (1956), Rabinovich (1956, 1959, 1964, 1980), Bauer (1958e, h, 1969b), Miles (1958a), Abramson, et al. (1962c), Lindholm, et al. (1963), and Bauer, Hsu, and Wang (1968).

Reissner (1956) formulated the problem as an integral equation describing the tank wall displacement. He also outlined another approach based on a variational treatment. Miles (1958a) analyzed the coupled bending liquid sloshing problem using Lagrangian formulation for potential sloshing in a bending cylindrical tank.

He found that if the mass of the empty tank is small compared to that of the liquid, and the depth of the liquid is equal to the tank diameter, the presence of the free surface increases the bending frequency. Beal, et al. (1965) and Yangyi and Jingliang (1985) determined the effect of elastic tank inertia and bending stiffness on the axisymmetric modes of a partially filled cylindrical container.

Chiba, et al. (1984a, b, 1985) analytically, numerically, and experimentally determined the natural frequencies of a clamped-free circular cylindrical shell partially filled with liquid. The case of free-free tanks filled with liquid was considered by Kreis and Klein (1991).

Koleshov and Shveiko (1971) determined the asymmetric oscillations of cylindrical shells partially filled with liquid. Ohayon and Felippa (1990) and Genevaux and Lu (2000) examined the influence of container wall deformation on the liquid equations of motion. Symmetric flow A Lagrangian formulation for estimating the coupled natural frequencies of liquid in an elastic wall container is presented based on the work of Miles (1958a).

Figure 8.5 shows a uniform.
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