Dynamic modeling and vibration control of a large flexible space truss

Dynamic equivalent modeling is convenient to the vibration controller design of large space truss structures. Consequently, it is important to study the effectiveness of designed vibration controller of the original truss structures based on the equivalent dynamic models. In this study, the dynamic modeling and vibration control for a large flexible space truss are investigated. The space truss is typical periodic triangular prism structure which consists of beams and rods. Considered the transverse deformation of the whole structure, the equivalent dynamic model of the space truss is established using energy equivalence principle. The fourth-order governing equations of the cantilevered equivalent beam model are derived and solved by adopting the Hamilton principle and the Galerkin method to achieve its discrete dynamic model. To obtain analytical mode shapes of the established equivalent model, an exact analytical approach is exploited for purpose of constructing state space equation of the space truss. Then the validity and accuracy of the equivalent beam model are demonstrated by comparing the natural frequencies and mode shapes with the original space truss finite element model. More importantly, to further design the active vibration controller of the space truss based on the equivalent beam model, the LQR vibration controller is designed when the space truss is subjected to periodic and impulse excitations. The control moment is applied to the full-scale finite element model of the space truss and the numerical simulations prove the effectiveness of the designed LQR vibration controller for the vibration suppression of the space truss. Results indicate that the established equivalent beam model is valid and particularly convenient for the vibration suppression of the large space truss, which can successfully settle the difficulty caused by the high degree of freedom of the finite element model of the large truss to its vibration controller design.