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In the present work a low dimensional Galerkin model which retains the essential nonlinear terms is used to study the effect of an internal fluid on the nonlinear oscillations and instabilities of an axially loaded thin-walled cylindrical shell. Recently Gonçalves and Del Prado [1] studied the dynamic instability of empty simply supported circular cylindrical shells subjected to harmonic axial loads. Several issues, such as parametric instability, snap-through buckling, truncation of modal solutions, fractal stability boundaries, were studied in detail. The theoretical basis of this low-dimensional model is presented and discussed by the authors in [2].