Supersonic flutter of sandwich panels: effects of face sheet bending stiffness, rotary inertia, and orthotropic core shear stiffnesses

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Virginia Polytechnic Institute and State University


A theoretical analysis is presented for the supersonic flutter of flat rectangular, biaxially stressed sandwich panels. On the basis of two-dimensional static aerodynamic theory an exact solution is obtained for panels having simply supported edges parallel to the airflow. The leading and trailing edges may be simply supported or clamped. The mathematical model describing the panel motion includes terms that account for rotary inertia, face sheet bending deformations, and transverse shear deformations of an orthotropic core such as honeycomb. Damping forces are neglected.

The linear system of partial differential equations governing the lateral deflection and the two transverse shear angles is eighth order and has constant coefficients. For simply supported edges parallel to the flow these equations have a separable solution. The characteristic equation associated with this solution is an eighth-order polynomial; its roots are determined numerically for given values of dynamic pressure and panel frequency. For each of the two sets of leading and trailing-edge boundary conditions considered, a corresponding frequency determinant is obtained that provides a second relation between the dynamic pressure and frequency. For either set of boundary conditions the corresponding frequency determinant equation and the characteristic equation are simultaneously satisfied by various combinations of dynamic pressure and frequency. Flutter occurs when the dynamic pressure attains a level that causes two panel frequencies to coalesce and become complex.

For a panel with an isotropic core, a second-order differential operator factors from the eighth-order system of differential equations. The remaining sixth-order system has been used in a previous flutter analysis (but with rotary inertia neglected). Flutter solutions based on the sixth-order system are shown to be correct when the complete solution from the eighth-order system uncouples. (This occurs for the isotropic panel if all edges are simply supported.) The sixth-order system, however, is inherently incomplete and is generally not applicable to the more general case where the solutions from the eighth-order system do not uncouple.

Numerical results from the complete eighth-order system show that the face sheet bending stiffness has a negligible effect on flutter if the faces are thin compared to the core thickness. As the face-to-core thickness ratio increases, the face bending stiffness becomes more important, especially for panels having relatively flexible cores.

The frequency coalescence behavior can be markedly changed by the combined effects of rotary inertia and core shear flexibility. Failure to account for this combined effect can lead to significant overestimates of flutter dynamic pressure values. Rotary inertia also causes the flutter solution to depend slightly on the crossflow in-plane loading.

The directional shear stiffness properties of the core are of comparable importance for square panels. As the panel width increases, the importance of the shear stiffness in the crossflow direction decreases.