NON-LINEAR DYNAMICS AND STABILITY OF CIRCULAR CYLINDRICAL SHELLS CONTAINING FLOWING FLUID. PART III: TRUNCATION EFFECT WITHOUT FLOW AND EXPERIMENTS

✍ Scribed by M. AMABILI; F. PELLICANO; M.P. PAÏDOUSSIS

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 349 KB
• Volume: 237
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2000.3071

✦ Synopsis

The response of simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of one of the lowest natural frequencies is investigated by using improved mode expansions with respect to those assumed in Parts I and II of the present study. Two cases are studied: (1) shells in vacuo; and (2) shells "lled with stagnant water. The improved expansions allow checking the accuracy of the solutions previously obtained and giving de"nitive results within the limits of Donnell's non-linear shallow-shell theory. The improved mode expansions include: (1) harmonics of the circumferential mode number n under consideration, and (2) only the principal n, but with harmonics of the longitudinal mode included. The e!ect of additional longitudinal modes is absolutely insigni"cant in both the driven and companion mode responses. The e!ect of modes with 2n circumferential waves is very limited on the trend of non-linearity, but is signi"cant in the response with companion mode participation in the case of lightly damped shells (empty shells). In particular, the travelling wave response appears for much lower vibration amplitudes and presents a frequency range without stable responses, corresponding to a beating phenomenon. A liquid (water) contained in the shell generates a much stronger softening behaviour of the system. Experiments with a water-"lled circular cylindrical shell made of steel are in very good agreement with the present theory.

2000 Academic Press

where D"Eh/[12(1! )] is the #exural rigidity, E is Young's modulus, the Poisson ratio, h the shell thickness, R the mean shell radius, the mass density of the shell, c (kg/m/s) the damping coe$cient, and f and p are the radial pressures applied to the surface of the shell as a consequence of external forces and the contained #owing #uid