Wave propagation and dynamic correction factors for composite structures

Shear and normal correction factors are used within first-order equivalent single layer theories in order to improve the description of the transverse strains and the accuracy of the solutions of static and dynamic problems in layered structures. Dynamic correction factors may be derived by imposing that certain wave propagation frequencies, e.g., the first cut-off frequencies of the thickness-modes as originally proposed by Mindlin, match those of three-dimensional elasticity. The exact frequencies can be derived only through complex computational procedures and, as a consequence, correction factors obtained for homogeneous plates are typically used also for layered plates, at the expense of accuracy. In this chapter, we consider cross-ply laminated plates with arbitrary layups and elastic constants and show how using a homogenized zig-zag structural theory allows the accurate closed-form derivation of the first thickness-modes of wave propagation and of the dynamic correction factors of first-order equivalent single layer theories. The correction factors accurately reproduce those obtained by matching the exact elasticity solutions in highly inhomogeneous bilayer media.