The basic problem to be considered concerns the response of a fluidloaded elastic plate which is driven by a harmonic point forcing in the presence of mean flow in the fluid. In order to enforce causality a rather sophisticated technique needs to be applied, and some surprising results are found, including absolute instability and the existence of modes which contradict the usual radiation condition of outgoing group velocity. Also, it has been known for some time that this sort of system supports waves with negative activation energy. All of these effects are absent in the problem of a fluid-loaded plate in still fluid. In these notes the details of these intriguing phenomena will be described, with particular emphasis on the technique for determining causal solutions of initial value problems, and on the energetics of the problem. Extensions to include plate curvature, steady shear in the flow, and nonlinear effects will be presented.
Group Velocity Elastic Plate Convective Instability Dispersion Function Absolute Instability
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