David Crighton and structural acoustics with mean flow

David Crighton wrote a number of significant papers on structural acoustics, but the one which has provoked the most discussion is concerned with the causal response of an elastic plate to unsteady forcing in the presence of mean flow [Crighton and Oswell, Philos. Trans. R. Soc. London, Ser. A 335, 557–592 (1991)]. A number of exceedingly unusual features arise in this problem, including absolute instability at high flow speeds, negative energy waves and the existence of neutral modes which violate the usual Rayleigh–Lighthill condition of out-going group velocity. A number of developments have been made since 1991, by Crighton himself and by Peake, and some of these will be described in this presentation. These include the effects of plate curvature and the presence of a boundary layer, both of which act to push the absolute instability to unrealistically high flow speeds; the dynamics of composite plates which allow shear deformation; and the effects of nonlinearity. In the latter regard it will be shown how negative energy waves are saturated at finite amplitude, and how solitary waves can develop over a wide parameter range.