Nonlinear dynamic characteristics of deployable structures with joints and cables based on incremental harmonic balance method

A purely bending dynamic model considering clearance, stiffness and damping of joints and nonlinear cables was established to show the nonlinear dynamic characteristics of jointed deployable structures. Taylor series expansion of variables for the nonlinear differential equation and harmonic description of parameters were used to convert the nonlinear dynamic equation to a nonlinear algebraic one. The dynamic response of a deployable structure was computed with the iteration method. The numerical analysis with Runge-Kutta method for a deployable structure was performed, its results were compared with those using the incremental harmonic balance (IHB) method. The comparison showed the correctness of the IHB method. The IHB method was used to analyze the response stability for a deployable structure when exciting frequency changed using the nonlinear dynamic model. The stability of the deployable structure response was presented in a frequency range when clearance and stiffness of joints, exciting force and cable changed. It was shown that the IHB method is very effective for dynamic analysis of deployable structures with multi-DOF, and it provided a basis for further study of large-scale deployable structures with joints and cables.