Issue 49

S.A. Bochkarev et alii, Frattura ed Integrità Strutturale, 49 (2019) 814-830; DOI: 10.3221/IGF-ESIS.49.15 825 k     Clamped-Clamped shells Clamped-Free shells Short circuited Open circuited   , % Short circuited Open circuited   , % 1/2 1.00 0.00 32.7722 36.6289 11.7682 8.58148 9.65366 12.4942 0.50 28.0167 30.9768 10.5657 7.78148 8.71879 12.0455 0.95 15.9592 17.8405 11.7885 5.22212 5.88609 12.7145 0.50 0.00 44.0368 49.0209 11.3179 28.3814 31.4965 10.9758 0.50 38.5264 42.7049 10.8459 26.7499 29.7033 11.0407 0.95 21.5175 24.0634 11.8313 17.2344 19.2967 11.9662 0.25 0.00 89.2623 98.0454 9.83972 39.1212 43.3674 10.8539 0.50 81.4270 90.0862 10.6343 39.0705 43.3060 10.8407 0.95 45.0888 49.9111 10.6952 37.8442 41.8567 10.6027 1/10 1.00 0.00 15.4716 17.2113 11.2443 3.81831 4.25959 11.5569 0.50 13.3385 14.7800 10.8069 3.47482 3.87567 11.5359 0.95 7.13355 7.97309 11.7689 2.24936 2.52362 12.1930 0.50 0.00 21.7425 24.0692 10.7013 15.8505 17.4368 10.0074 0.50 18.7429 20.7607 10.7661 14.1066 15.5642 10.3326 0.95 9.70433 10.8434 11.7380 7.85436 8.76154 11.5500 0.25 0.00 53.0114 57.4618 8.39530 36.5821 40.5511 10.8496 0.50 43.6699 47.9169 9.72512 35.7320 39.4371 10.3692 0.95 20.7597 22.9591 10.5944 20.0218 22.0848 10.3036 1/100 1.00 0.00 4.97846 5.50687 10.6138 1.22342 1.35737 10.9483 0.50 4.27499 4.72525 10.5323 1.11144 1.23392 11.0193 0.95 2.25033 2.51305 11.6749 0.71178 0.79643 11.8917 0.50 0.00 7.08603 7.80343 10.1242 5.42042 5.92045 9.22498 0.50 6.04697 6.68328 10.5228 4.69234 5.15888 9.94261 0.95 3.06832 3.42595 11.6555 2.50227 2.78760 11.4030 Table 7 : Natural vibration frequencies  (Hz) of the system of coaxial shells at different values of the annular gap k , eccentricity  , and filling level  and varying electrical and kinematic boundary conditions. (a) (b) Figure 3 : The relative difference in the frequencies   as a function the eccentricity  at different levels of the fluid in the annular gap  for clamped-clamped (a) and cantilevered shells (b),  1 100. k 0.0 0.2 0.4 0.6 0.8  8.0 8.8 9.6 10.4 11.2   , %  = 1.00  = 0.50  = 0.25 0.0 0.2 0.4 0.6 0.8  7.5 8.4 9.3 10.2 11.1   , %  = 1.00  = 0.50  = 0.25