Effect of taper ratio on parametric stability of a rotating tapered beam

Out-of-rotation plane bending vibrations of a rotating tapered beam with periodically varying speed are considered. The integro-partial differential equation of the beam is discretized via Galerkinʹs method and a set of ordinary differential equations with periodic coefficients (Mathieu–Hill type equations) is obtained. Dynamic stability of this parametrically excited system is studied via a monodromy matrix method, the effect of taper ratio on the stability of the system is examined and the results are presented in the form stability charts.