Flutter of laminated plates in supersonic flow

Abstract

A procedure has been developed for solving flutter problems of simply supported laminated plates using linear small deflection theory. The plate construction may be arbitrary as long as it satisfies the assumptions of linear small deflection theory. For such plates, the bending and extensional governing equations are coupled and have cross-stiffness terms which do not appear in classical plate theory. The coupling and cross-stiffness terms occur as a result of the lamina principal directions (fibers) not coinciding with the neutral surface of the plate. The extended Galerkin method is used to obtain approximate solutions to the governing equations where the aerodynamic pressure loading used in the analysis is that given by linear piston theory with flow at arbitrary cross-flow angles. Flutter solutions were obtained for typical symmetric, angle-ply, and general laminated composite plates, and a limited parametric study was conducted. The parameters studied include the number, orientation, and orthotropy of the lamina; the plate length-width ratio; the inplane normal and shear loads; and the cross-flow angle. In addition, flutter solutions for several composite stiffened aluminum plate designs were obtained to determine the most flutter resistant design. The bending-extensional coupling and the cross-stiffness terms both have a large destabilizing effect on the flutter of unstressed laminated plates, but increasing the number of laminas, reducing the lamina orthotropy, and stacking the laminas in the"best" order reduce the destabilizing effect. For a square plate, aligning the fibers with the direction of flow (x-axis) results in the highest flutter stability, but for a plate with a length-width ratio of 2, large improvements in flutter stability may be obtained by rotating the fibers away from the x-axis. For angle-ply plates, inplane normal and shear loads and crossflow have a destabilizing effect on flutter similar to that obtained for orthotropic plates. However, for symmetric plates with the fibers not aligned with the x-axis, the cross-stiffness terms give rise to an improvement of the flutter stability with cross-flow angle. Flutter calculations for equivalent symmetric, angle-ply, and general unsymmetric plates indicate that for no cross-flow and no inplane shear loads, plates with an angle-ply construction will have the highest flutter stability. If cross-flow or inplane shear loads are present, symmetrically constructed plates may have higher flutter stability. Classical plate theory does not consider bending-extensional coupling and cross-stiffness terms, and therefore gives inaccurate and usually nonconservative flutter boundaries for laminated plates. Reduced bending stiffness theory, an approximate flutter theory which accounts for the coupling by reducing the plate bending stiffness as determined by the coupling terms and then neglects the coupling in solving the equations, gives flutter solutions that are adequate for all plates for which numerical results were obtained.