Nonlinear vibration of transversely-loaded spinning membranes

The paper studies the transverse nonlinear vibration of an isotropic and homogeneous annular membrane spinning at constant angular velocity, under the action of a uniform transverse load. The equilibrium configuration of the membrane, clamped along the inner edge and free along the outer edge, and the natural frequencies of vibration of the membrane are calculated. A Galerkin procedure is used to determine a reduced order model describing the weakly nonlinear vibration of the membrane, and it is shown that near-resonance vibration can be modeled as a single degree of freedom Helmholtz-Duffing oscillator. A detailed study at vibration frequencies close to the fundamental, axisymmetric vibration mode shows a transition from softening to hardening behavior, and jump phenomena or hysteretic behavior depending on the angular velocity, the transverse load, the amplitude of dynamic excitation and the damping ratio. The results are in agreement with dynamic implicit finite element simulations in Abaqus/Standard and direct experimental measurements.