A study of the buckling of laminated composite plates

for short axial wavelengths become parallel to the sector line (Pi = 0) with the least slope. For shells with /i = 1, p = 2, the frequency lines of the third and fourth axisymmetric nontorsional modes become parallel to the frequency line of the Rayleigh waves in the material of the outer shell, prior to becoming parallel to the sector line /32 = 0 (Fig. 9), whereas, in the case of shells with p = 2, p — 1, they become parallel to the frequency line of the Rayleigh waves in the material of the inner shell prior to becoming parallel to the sector line ft = o. The frequency lines of the fourth, fifth and sixth torsional modes and the fifth and sixth nontorsional modes for shells with jit = 1, p = 2, become parallel to the sector line /32 = 0 before, for higher values of f not included in the figures, becoming parallel to the sector line ft. = 0. Analogous behavior is observed for shells with /x = 2, p = 1. The behavior of the frequency lines of the flexural modes (n > 1,) is similar to that of the axisymmetric modes, except that they do not exhibit the tendency of becoming parallel to the sector line A = 0, with the greatest slope. For n = 1, for large axial wavelengths the first mode is essentially a uniform translation of the entire cross section, the second mode involves essentially longitudinal shear motion, whereas the third mode is associated with predominantly radial motion (breathing). The three lowest flexural modes are those contained in the bending shell theories, wherein the radial component of the displacement is assumed constant across the thickness of the shell and the tangential and axial components are assumed to vary linearly with the thickness coordinate.