The parametric dynamical behavior of a spinning slender beam under elastic support is studied.A spinning Rayleigh beam under constant axial force is considered,sustained by an elastic support at one end and a simply support at the other end.The dynamical model is obtained based on the Hamilton princi-ple,and the motion equations for the generalized mode coordinates are derived through the Galerkin meth-od.The parametric vibration characteristics of the spinning Rayleigh beam with elastic support are analyzed according to the multiple scale method.The instability type and form of the beam under different parame-ters are analyzed,and the stability diagram of the system under the excitation of elastic support parameters is drawn.The effect of the elastic support boundary on the stability zone of the beam system is emphasized.The results show that the system contain two types of parametric resonance:main resonance and combined resonance.The stability diagram reflects the influence of the speed and the external load on the stability zone of the system under the excitation of the elastic support.
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