Dynamics analysis of the hub and tapered beam coupled system with tip mass

The intrinsic characteristics and the flexible motion of tapered Euler-Bernoulli beam with tip mass and a rotating hub are investigated. The breadth and the depth of the tapered beam vary linearly along its length. Integration-differential governing equations are derived from the extended Hamilton principle and the first-order approximation coupling model. The governing equations, describing rigid-flexible and axial-transverse coupled action, are not only fully coupled equations, but also time dependent, which can be used to simulate the high-speed mechanisms because the centrifugal stiffening effect has been taken into account. Simplifying the above coupled equations and using the finite element method, the finite dimension dynamics formulation is obtained. Meanwhile, the damp, stiffness and mass matrices of the system are derived. The numerical simulations of the four kinds of structures are present to show the differences in dynamics response. By comparing the uniform and the tapered system in the same condition, the obtained results indicate that a little difference in section can cause significant difference in natural frequencies and dynamics response. To gain more accurate results, it is necessary to use the tapered beam in the practical system.