Nonlinear free vibrations of centrifugally stiffened uniform beams at high angular velocity

摘要: Abstract In this paper, we study the bending nonlinear free vibrations of a centrifugally stiffened beam with uniform cross-section and constant angular velocity. The intrinsic equations motion used here are geometrically exact specific to beams exhibiting large amplitude displacements rotations associated small strains. Based on Timoshenko model, these derived from Hamilton׳s principle, in which warping is considered. All coupling terms considered including Coriolis terms. studied isotropic clamped-free boundary conditions. By combining Galerkin method harmonic balance method, converted into quadratic function treated continuation method: Asymptotic Numerical Method, where generalized displacement vector presented as series expansion. While analysing effect velocity, determine versus frequency variations plotted backbone curves. Considering first lagging flapping modes, changes behaviour hardening softening investigated identified velocity shear. Particular attention paid high velocities for both Euler–Bernoulli natural frequencies so obtained compared results available literature.