Introduction

Flutter instability is due to Hopf bifurcation (see Chapter 3) of static equilibrium solution and is observed as an harmonic (or quasi-periodic) oscillation in the absence of excitation. Plates and shells in airflow present flutter instability for high speed, so that the design of wing panels of aircraft must be verified for panel flutter. The natural modes of plates and shells become complex modes in the presence of flow, as discussed in Chapter 14, and their natural frequencies are changed. In particular, the frequency of the mode with one longitudinal half-wave can be raised by increasing the flow speed, whereas the frequency of the mode with two longitudinal half-waves is lowered. At a point, the frequencies of these two modes coincide with a coalescence of the two modes; this gives rise to coupled-mode flutter.

The first reported occurrence of flutter instability for circular cylindrical shells appears to have been on the V-2 rocket (see Figure 15.1). Since that time, the study of the aeroelastic stability of cylindrical shells in axial flow is fundamental in the skin panel design of aerospace vehicles, high-performance aircrafts and missiles. A fundamental contribution to the studies on this topic was due to the introduction of the piston theory by Ashley and Zartarian (1956).

The nonlinear stability of simply supported, circular cylindrical shells in supersonic axial external flow is investigated in this chapter by using an improved model with respect to the one developed by Amabili and Pellicano (2002).