Hydroelastic Stability of a Flexible Panel: Eigen-Analysis and Time-Domain Response

A state-space model, based upon computational modeling, is used to investigate the hydroelastic stability of a finite flexible panel interacting with a uniform flow. A merit of this approach is that it allows the fluid-structure system eigenmodes to be found readily when structural inhomogeneity is included or a source of external excitation is present. The system studied herein is two-dimensional although the concepts presented can be readily extended to three dimensions. Two problems are considered. In the first, we solve the initial-value, boundary-value, problem to show how the system response evolves from a source of localized excitation. This problem is deceptively complex and has evidenced some very unusual behaviour as demonstrated by theoretical studies based on the assumption of an infinitely long flexible panel. Our contribution herein is to formulate and illustrate the use of a hybrid of theoretical and computational models that includes the effects of finiteness. In the second problem we solve the boundary-value problem to determine the long-time response and investigate the effects of adding localized structural inhomogeneity on the linear stability of a flexible panel. It is well known that a simple flexible plate first loses its stability to divergence that is replaced by modal-coalescence flutter at higher speeds. Our contribution is to show how the introduction of localized structural inhomogeneity can be used to modify the divergence-onset and flutter-onset critical flow speeds.