TABLE OF CONTENTS The same shell described at the beginning of Section 5.7 is considered. The shell is assumed to be perfect, simply supported and water-filled with open ends. The 16 dofs model has been used.
Poincar maps have been computed by direct integration of the equations of motion. The excitation frequency ? has been kept constant, ?=0.92 ? 1,5 (the shell displays softening-type response; therefore, for large excitation, the resonance is obtained for ?< ? 1,5), and the excitation amplitude has been varied between 0 and 600 N. The force range has been divided into 500 steps, so that the force is varied in steps of 1.2 N. Each time the force is changed by a step, 500 periods have been allowed to elapse in order to eliminate the transient motion. The initial condition at the first step is zero displacement and velocity for all the variables. In the following steps, the solution at the previous step, with addition of a small perturbation in order to find a stable solution, is used as the initial condition. The bifurcation diagrams obtained by all these Poincar maps by using the conventional Galerkin model are shown in Figures 5.35 and 5.36. In particular, in Figure 5.35 the load is increased from 0 to 600 N; in Figure 5.36 the load is decreased from 600 N to 0. Simple periodic motion, a period-doubling bifurcation, subharmonic response, amplitude modulations and chaotic response have been detected,...
