Abstract
Abstract
Highlights
Flutter of membranes has been a classical subject for at least seven decades
Through the revival of a classical hydrodynamical model performed in this work, we have been able to extend the stability analysis and to enhance knowledge of the underlying physics by making connections with the fundamental concepts such as negative energy waves and the anomalous Doppler effect (ADE), supported by advanced mathematical tools
An exhaustive stability analysis has been performed using the original perturbation theory of multiple roots of the dispersion relation to compare with the exact stability domains, and both computations are proven to be in excellent agreement
Summary
Dowell (1966), when critically appraising the study by Miles (1956) of an infinitely long, infinitely wide panel in a compressible flow occupying the upper semi-space, pointed out that the critical wavelength predicted in this study was infinite and the flutter velocity was zero, which was not physically meaningful. This observation has led him to the conclusion that the finite dimension of a membrane or a plate in the flow or a span direction is critical to the physically meaningful prediction of the instability (Dowell 1966).
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