Nonlinear forced vibration and stability analysis of a rotating three-dimensional cantilever beam with variable cross-section

This article investigates the nonlinear forced vibration of a rotating three-dimensional variable cross-section cantilever beam under uniformly distributed harmonic loads. Incorporating the effects of Coriolis terms, static axial deformation, and geometric nonlinearity, the nonlinear partial differential equations for a rotating variable cross-section Euler-Bernoulli beam are derived using Hamilton's principle. The Galerkin method discretizes these equations into nonlinear ordinary differential equations. Numerical simulations are conducted to present the amplitude-frequency and time-history responses, illustrating the nonlinear dynamic characteristics of the rotating variable cross-section cantilever beam. The effects of rotational speed, hub radius, excitation amplitude, and cross-section change rate on the stability, nonlinear principal resonance, and superharmonic resonance of the rotating beam system are discussed. Results show the fundamental natural frequency increases with the increase of the hub radius, rotational speed, and cross-section change rate. Furthermore, the cross-section change rate significantly impacts the nonlinear vibration response of the system.