Fluid-loaded elastic plate with mean flow: point forcing and three-dimensional effects. (Q2711515)

The authors investigate the behaviour of an infinitely long fluid-loaded elastic plate subjected to a single-frequency line forcing in the presence of a uniform mean flow. In the previous article [\textit{D. G. Crighton} and \textit{J. E. Oswell}, Philos. Trans. R. Soc. Lond., Ser. A 335, No. 1639, 557--592 (1991; Zbl 0735.76030)] the onset of absolute instability for non-dimensional flow speeds \(V\) larger than some critical speed \(V_{c}\) and various interesting propagation effects at \(V<V_{c}\) were studied. In particular, it was shown that in a particular frequency range there exists an anomalous neutral mode with group velocity directed towards the driver, in violation of the usual Lighthill outgoing radiation condition.NEWLINENEWLINEIn the reviewed article the authors extend these results and consider the essentially harder problem of a fluid-loaded elastic plate with uniform mean flow subjected to a point forcing, thereby resulting in a two-dimensional structural problem. The systematic method for the determination of the absolute instability threshold is suggested. It is shown that the flow is absolutely unstable for flow speeds \(V>V_{c}\). For flow speeds \(V<V_{c}\) the flow is marginally stable. Convective growth is found to occur downstream of the driver, in a particular frequency range depending on the transverse Fourier wave number \(k_{y}\) within a wedge-shaped region, outside of which there is only neutral mode behaviour. Asymptotic forms are found for the dominant large-distance causal flexion response downstream of the driver inside and outside the wedge region. Asymptotic forms are also established for the threshold frequencies which determine various regions of stability as a function of \(k_{y}\), compared with the previous results of \textit{D. G. Crighton}, \textit{J. E. Oswell} and \textit{N. Peake} [J. Fluid Mech. 338, 387--410 (1997; Zbl 0920.76034)].