Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross-Section

Abstract

Problems related to the transverse vibration of a rotating tapered cantilever beam with hollow circular cross-section are addressed, in which the inner radius of cross-section is constant and the outer radius changes linearly along the beam axis. First, considering the geometry parameters of the varying cross-sectional beam, rotary inertia, and the secondary coupling deformation term, the differential equation of motion for the transverse vibration of rotating tapered beam with solid and hollow circular cross-section is derived by Hamilton variational principle, which includes some complex variable coefficient terms. Next, dimensionless parameters and variables are introduced for the differential equation and boundary conditions, and the differential quadrature method (DQM) is employed to solve this differential equation with variable coefficients. Combining with discretization equations for the differential equation and boundary conditions, an eigen-equation of the system including some dimensionless parameters is formulated in implicit algebraic form, so it is easy to simulate the dynamical behaviors of rotating tapered beams. Finally, for rotating solid tapered beams, comparisons with previously reported results demonstrate that the results obtained by the present method are in close agreement; for rotating tapered hollow beams, the effects of the hub dimensionless angular speed, ratios of hub radius to beam length, the slenderness ratio, the ratio of inner radius to the root radius, and taper ratio of cross-section on the first three-order dimensionless natural frequencies are more further depicted.