Finite Vibrations of a Free Rotating Anisotropic Membrane

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Abstract
Using the von Kármán field equations extended to the dynamical and anisotropic case, large amplitude vibrations of a spinning, cylindrically orthotropic membrane are analyzed. The membrane is assumed to be free, and its deflection is represented by a simple monomial. Free nonlinear vibrations manifest the familiar decrease of period of vibrations with an increase of amplitude and show a marked dependence on the degree of anisotropy. A vibration mode associated with two nodal diameters is studied in more detail. The dependence of a representative stress on the degree of anisotropy, as well as on the amplitude of vibrations and velocity of rotation, is also discussed.

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