Free Vibrations of Multilayer Anisotropic Cylindrical Shells

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Abstract
A theoretical analysis is presented for determining the free vibra tional characteristics of thin-walled, circular cylindrical shells with layers of anisotropic elastic material arbitrarily laminated either sym metrically or unsymmetrically about the shell middle surface. An arbitrarily laminated, anisotropic version of Love's first-approximation shell theory is used to formulate the coupled equations of motion. An exact solution with a classical checkerboard nodal pattern is found for the case of a shell with specially orthotropic layers arbitrarily laminated and with freely supported ends. For a boron/epoxy composite cylinder, the significant effect of omitting bending-stretching coupling is demonstrated and various lamination arrangements are investigated. Also, a general solution is presented for the axisymmetric modes of an arbitrarily laminated anisotropic shell. Finally, an approximate solution, using a combination of two helical-nodal-pattern modes, is obtained for the unsymmetric modes of the same general class of shell with a supported boundary condition.