The stability of translating flexible beam that passes through the elastic support is investigated. We modeled the flexible beam using the finite segment method to account for the geometric nonlinearities due to the large rotation, as it is the time variant system. Numerical simulation results show the instability of the beam, that is stable in the low axial moving velocity, is observed as the axial moving velocity increases. It is clarified from the consideration with the simplified rigid beam model that the mass and damping coefficient ratio of the elastic support yields negative damping effect of the system and the damping coefficient and stiffness ratio of the elastic support yields negative stiffness effect of the system as the axial moving velocity increases. These results show that the property of the elastic support gives the significant effect on the instability of the translating beam.

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