On the vibrations of cylindrically curved elastic sandwich plates part 1 with the solution for flat plates part 2 the solution for cylindrical plates

Abstract

In Part I, consideration of the equilibrium of the anisotropic core of a cylindrically curved sandwich plate leads to the three simultaneous differential equations for the three orthogonal deformations. Boundary conditions on two sides are found by considering the equilibrium at the core/face-plate interface. A separable solution leads to the two sets (symmetric and anti-symmetric) of three homogeneous equations for the flat sandwich plate with a honeycomb core. These two sets lead to non-dimensional determinantal frequency equations for the flexural and bubbling modes. The calculation of mode shapes is indicated and the non-dimensional frequency is plotted against other variables for all likely aircraft panel configurations. In Part II, a solution is found for curved sandwich plates by assuming that a flat-plate.core solution bounded by curved-plate edge conditions holds true. An indication, though not a proof, of the validity of this assumption is given. A determinantal frequency equation is thus found for curved plates and an expected anomalous frequency variation with circumferential wavelength becomes evident. The variation of frequency with wavelength for bubbling modes is only very slight for both flat and curved plates.