TABLE OF CONTENTS Calculations have been performed for circular cylindrical shells made of stainless steel with the following dimensions and material properties: L=520 mm, R=149.4 mm, h=0.519 mm, E=1.98 10 11 Pa, ?=7800 kg/m 3, ? F=1000 kg/m 3 and ?=0.3. These data coincide with those used in Section 5.6.2 and with those of an experimentally tested shell, as reported in Section 5.8. An harmonic point excitation at x=251 mm, that is, close to the middle of the shell, is applied in the spectral neighborhood of the fundamental frequency.
Numerical calculations have been performed for the fundamental mode ( n=5, m=1) of the empty shell tested in the experiments in order to investigate the effect of geometric imperfections of a given shape on the natural frequency and nonlinear response.
Figure 5.15 shows the natural frequency of the fundamental mode of the empty shell versus the amplitude of three different geometric imperfections: (i) axisymmetric imperfection 1,0 , (ii) asymmetric imperfection 1,5 having the same shape of the fundamental mode and (iii) asymmetric imperfection 1, 10 having twice the number of circumferential waves of the fundamental mode. It is important to observe that modes with 3 n circumferential waves must be included in equation (5.51) in order to study the effect of imperfection 1,10. The axisymmetric imperfection does not divide the double eigenvalue associated with the fundamental...
