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

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 filled with stagnant water. The improved expansions allow checking the accuracy of the solutions previously obtained and giving definitive results within the limits of Donnellʹs 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 effect of additional longitudinal modes is absolutely insignificant in both the driven and companion mode responses. The effect of modes with 2 n circumferential waves is very limited on the trend of non-linearity, but is significant 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-filled circular cylindrical shell made of steel are in very good agreement with the present theory.