The instability and nonlinear dynamics of planar motions of a cylinder array subjected to crossflow have been studied via a five-mode discretization of the governing partial differential equation, focusing on the effect of initial axial load externally imposed on the cylinder. Theoretical results based on a stability analysis have indicated that, with increasing initial axial load and flow velocity, the system may lose stability either via flutter or via buckling. The boundaries of these two forms of instability are predicted analytically. To explore the post-instability dynamics of the system, a Runge-Kutta scheme is used to solve the nonlinear governing equation of motion. Three typical behaviors, including limit cycle motions of the system, are obtained. It is shown that, for relatively low flow velocity, with increasing initial axial load, just beyond the pitchfork bifurcation the cylinder would settle in a buckled equilibrium position; and for high flow velocity, however, this phenomenon only occurs when the initial axial load becomes sufficiently large.

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An analytical approach for predicting the free vibration and elastic critical load of functionally graded material (FGM) thin cylindrical shells filled with internal pressured fluid is presented in this study. The vibration of the FGM cylindrical shell is described by the Flügge shell theory, where the internal static pressure is considered as the prestress term in the shell equations. The motion of the internal fluid is described by the acoustic wave equation. The natural frequencies of the FGM cylindrical shell under different internal pressures are obtained with the wave propagation method. The relationship between the internal pressure and the natural frequency of the cylindrical shell is analyzed. Then the linear extrapolation method is employed to obtain the elastic critical load of the FGM cylindrical shell from the condition that the increasing pressure has resulted in zero natural frequency. The accuracy of the present method is verified by comparison with the published results. The effects of gradient index, boundary conditions and structural parameters on the elastic critical load of the FGM cylindrical shell are discussed. Compared with the experimental and numerical analyses based on the external pressure, the present method is simple and easy to carry out.

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