Equivalence and dynamic analysis for jointed trusses based on improved finite elements

Deployable trusses that are widely applied in space missions utilize many hinged members to adapt to different geometrical shapes and work conditions. This paper presents two improved finite elements for a link and a bending beam to calculate dynamic characteristics of non-jointed and jointed trusses. First, the axial and transverse wave motion equations of a beam are used to get the shape functions of the link and the beading beam in their axial and transverse directions. Second, the dynamic matrices of stiffness and mass for a link and a bending beam are established on the basis of virtual work principle. The dynamic matrix and a theoretical equation are used to calculate the natural frequency of a cantilever bar. The comparison of the two results shows the effectiveness of the dynamic stiffness matrix. These improved elements are proved to be more accurate in calculating the responses of structures at high frequencies than common elements. Equivalent models of non-jointed and jointed structures are obtained on the basis of the displacement and strain energy equivalence of a truss unit. The result of the period truss confirms the accuracy of the equivalent model of the non-jointed truss expressed by dynamic matrices. The dynamic influences of cubic joints on a jointed structure are evaluated by giving the simulations of the equivalent jointed structure based on improved matrices. The results indicate that the natural frequencies of the jointed structure increase with the excitation force and the stiffness of joints. A relational function among the natural frequencies, joint stiffness, and excitation force is also presented.