TORSIONAL VIBRATIONS OF LAYERED COMPOSITE PARABOLOIDAL SHELLS

An analysis is presented for the torsional vibration characteristics of layered composite paraboloidal shells. The conditions for the uncoupling of the torsional modes from the bending and extensional modes are first determined for a layered shell of revolution. A finite difference scheme is developed for the solution of the resulting governing equation for the uncoupled torsional frequencies. The results of the finite difference solution for the paraboloids are compared with the analytical solution of uncoupled torsional frequencies of circular plates, in the limit as the curvature of the paraboloid goes to zero. As a result of the analysis of different paraboloids, the non-dimensional uncoupled torsional frequency parameters of the paraboloids are found to be inversely proportional to the ratio of the meridional arclength to the thickness of the paraboloid for a given edge angle