Nonlinear dynamics of an eccentrically rotating flexible hub-beam system

Rotating axis eccentricity is a prevalent and virtually unavoidable challenge in rotating machinery and aerospace structures, stemming from geometric deviations introduced during manufacturing, assembly, or prolonged operation. This work investigates the nonlinear dynamics of a flexible hub-beam system with rotating axis eccentricity, with a spacecraft’s deployable solar panel and its main body as the engineering prototype. Unlike ideal symmetric configurations, unavoidable eccentricity produces time-varying moments of inertia and induces strong coupling between rigid hub rotation and flexible beam vibration. Based on Hamilton’s variational principle, a nonlinear dynamic model is developed. A salient feature of this model is the strong coupling between the ordinary differential equations governing the eccentrically rotating rigid hub and the partial differential equations describing the transverse and axial vibrations of the flexible beam. Numerical simulations are conducted using a complex structure preserving algorithm to systematically examine how varying eccentric distances influence the system’s dynamic response. The results demonstrate that increasing eccentric distance markedly amplifies transverse displacement amplitudes, induces asymmetry between positive and negative response peaks, and triggers a “double-peak” phenomenon during the transient response. Modal analysis further indicates that the first vibration mode dominates the overall dynamic behavior. Nonlinear bifurcation analysis then reveals a three-stage transition from linear periodic vibration through period-doubling bifurcation near resonance to chaotic motion at high rotational speeds, governed by distinct frequency-dependent mechanisms: stiffness-dominated deformation at low frequencies, resonance-activated geometric nonlinearity at intermediate frequencies, and the centrifugal-elastic coupling at high frequencies. This study elucidates the physical mechanisms underlying the nonlinear coupling induced by inevitable rotating axis eccentricity, establishing a theoretical basis for fault diagnosis and vibration control of rotating flexible structures in aerospace and mechanical engineering.