Fluttering Behavior of a Flexible Thin Sheet in High-Speed Flow : (1st Report, Theoretical method for Prediction of the Sheet Behavior for Small Perturbed Motion)

Abstract

A theoretical method has been proposed for prediction of the fluttering of a flexible thin sheet or web of such as paper blown in high speed flow of fluid. It assumes self-excited aeroelastic oscillation of the sheet with infinitesimally small amplitude. The flow and the sheet motion are expressed terms of discretized vortices over the sheet and the wake, and motions of a number of short segments of flexible beams connected each other. The connecting conditions yield a homogeneous linear simultaneous equations concerning the unknowns including the strength of vortices and the sheet motions at each connecting points. The coefficient matrix of the equations determines the oscillation modes, the frequencies, the amplifying/damping rates, and thus the modes and the stability/instability of the system. The method is particularly suited to solve the situation where the oscillation modes are far from those in vacuum and progressive waves are predominant.