Static and dynamic analysis of the postbuckling of axially moving spin beams

Abstract

This paper aims to investigate the static and dynamic behaviors of the postbuckling of axially moving spin beams (bi-gyro system). The Hamilton’s principle is used to derive the nonlinear governing equations of bi-gyro systems, which are based on the Euler-Bernoulli beam model and account for von Karman geometric nonlinearity. After neglecting the time-dependent terms, the static equations are discretized using the differential quadrature method and then solved as a nonlinear algebraic system via the Newton-Raphson iteration method. Subsequently, the linear vibration problem is accurately solved for axially moving spinning beams in their first buckled configuration. Finally, numerical calculations are conducted to investigate the impact of axial and spinning velocities on the steady-state dynamic responses of bi-gyro systems. The findings are as follows: (a) the critical axial velocity where trivial equilibrium is unstable remains unaffected by the presence of spinning velocity; (b) the bifurcation point of the axial velocity corresponding to amplitude is reduced by spinning velocity, resulting from centrifugal force; (c) the vibration amplitude of the bi-gyro system will diverge under a weaker displacement constraint spring; and (d) stable buckled and straight configurations can coexist under certain axial and spinning velocities.