Nonlinear Dynamics Analysis of a Large Flexible Slender Truss-Structure Carrying a Manipulator for On-Orbit Assembly

Nonlinear dynamic of a flexible slender truss-structure mounted manipulator for on-orbit assembly, which can be simplified as a beam–rotating link interaction system, is theoretically investigated. The governing partial differential equations (PDEs) of beam with time-varying coefficients is established by using the D’Alembert principle incorporated with the moment balance method where the beam is of a Euler–Bernoulli type and the influence of slope is considered. Such system is a typical parametrically excited system. The multiple scales method is used to determine the approximate solution and the conditions of the primary resonance ($\omega _{1}\approx \omega _{ref}$) and sub-harmonic resonance ($\omega _{1}\approx ~2\omega _{ref}$,$\omega _{1}\approx ~3\omega _{ref}$and$\omega _{1}\approx ~4\omega _{ref}$) are obtained. In addition, the nonlinear response, stability and bifurcations for primary and sub-harmonic resonance conditions have also been investigated by varying system parameters. Moreover, the results of some specific conditions by the perturbation analysis are compared with the numerical solution and are found to be in good agreement. This work has certain guiding significance for autonomous on-orbit assembly task and the method can be extended to the more general three-dimensional case.