This work investigates the asymptotic structure of a boundary-value problem proposed recently in connection with in-plane instabilities of spinning disks. Assuming an orthotropic elastic material with cylindrical symmetry we consider a perturbation with respect to the constitutive behavior. The material is assumed to be very stiff in the azimuthal direction, a situation which is commonly encountered in the case of composite flywheels based on hoop-wound carbon fibers in a flexible polyurethane resin. The accuracy of the asymptotic strategy is confirmed by a number of direct computer simulations of the original problem.
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