THE HYDROELASTIC STABILITY OF 3-DIMENSIONAL DISTURBANCES OF A FINITE COMPLIANT WALL

A theoretical investigation of the hydroelastic behaviour of a compliant panel of finite dimensions is presented. The mechanics of the wall are modelled by using a linear differential operator with a single degree of freedom, and the results herein pertain to a spring-backed flexible plate. Unsteady potential flow is assumed; thus, the onset of divergence instability defines the critical flow speed. At higher flow speeds, this static instability may give way to modal coalescence flutter which takes the form of a downstream travelling wave. Comparison is made between the present analysis and an equivalent two-dimensional (infinite width) study for a compliant wall of finite length. It is demonstrated that the simpler two-dimensional methods of instability prediction are always appropriate when the aspect ratio is greater than five. Increasing the streamwise mode number (i.e., reducing the ratio of disturbance wavelength to panel length) renders the system progressively more two-dimensional in its behaviour. The order of the critical mode is promoted by increasing the foundation-spring stiffness, reducing the width of the panel or imposing a higher order transverse mode than the fundamental. For a compliant panel of prescribed surface area, a critical aspect ratio exists in which configuration the lowest divergence-onset flow speed is found. Arrays of compliant panels are considered: the influence of neighbouring panels exercises a mildly adverse effect on the stability of a panel in a comparison with the response of a similar panel in isolation. © 1993 Academic Press Limited.