Issue 49

S.A. Bochkarev et alii, Frattura ed Integrità Strutturale, 49 (2019) 814-830; DOI: 10.3221/IGF-ESIS.49.15

performed at different values of the dimensionless annular gap k , filling level  and displacement (eccentricity) of the inner shell           (2) (1) (1) (2) (1) , , k R R R H L a R R   . (32)

(2) ( ) R is fixed, and the radius of the inner shell

(1) ( ) R varies and depends on the

Note that the radius of the outer shell

parameter k .

Geometric data

Fluid properties

Parameter

Value

Parameter

Value 1000 1500

f  , kg/m 3

L , m

1

c , m/s

0.1

(2) R , m



  (1) (2) h h h , m  4 5 10 Table 1 : Geometrical parameters of the shells and physical properties of the fluid. Parameter Value Parameter Value c 11 , GPa 126 e 15 , C/m 2 17 c 12 , GPa 79.5 e 24 , C/m 2 17 c 13 , GPa 84.1 e 31 , C/m 2 -6.5 c 22 , GPa 126 e 32 , C/m 2 -6.5 c 23 , GPa 84.1 e 33 , C/m 2 23.3 c 33 , GPa 117 d 11   10 10 , F/m 150.3 c 44 , GPa 23 d 22   10 10 , F/m 150.3 c 55 , GPa 23 d 33   10 10 , F/m 130 c 66 , GPa 23.3 s  , kg/m 3 7500 Table 2 : Properties of piezoceramics PZT-5H.

Verification of the numerical model The assessment of reliability of the constructed algorithm for the numerical investigation of an electroelastic thin-walled body was made by comparing its performance with the results of work [21]. Here the simply supported at both ends   ( 0) v w shell made of PZT-5H piezoceramics was investigated (Tab. 3). The boundary conditions for the fluid were specified as follows: 0   at  0 x and  . x L

Geometric data

Fluid properties

Parameter

Value

Parameter

Value 1000 1500

f  , kg/m 3

L , m R , m h , m

5 1

c , m/s

0.02 Table 3 : Geometrical parameters of electroelastic shells and physical properties of the fluid [21].

A comparison between the natural frequencies of the empty shell and the shell filled with an ideal compressible fluid is given in Tab. 4. The number of half-waves in the circumferential and meridional directions is denoted by j and m , respectively. According to the data presented in the table, there is good agreement between the results obtained by analytical and numerical solution of the problem. The assessment of the reliability of the results obtained for coaxial shells   ( 0) made of isotropic elastic material and containing fluid in the gap between them was carried out by comparison with the results of analytical solution presented in [36]. In this case, the matrices ( ) i  K and ( ) i s  K in Eqn. (27) are excluded from the calculation, and the stiffness matrices

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