Model Reduction for Dynamic Analysis to Rod Component with Frequency-Dependent Damping

This paper proposes a dynamic model-reduction method for damping rods that vary stiffness and damping characteristics with frequency. The damping rod considered in the paper is an elongated cylindrical body with two orthogonal symmetric planes, which can withstand tension, compression, bending, and torsion. The cross-sectional geometric shapes and the material properties are nonuniform along the rod axis. By performing numerical approximations on the frequency responses calculated from a three-dimensional finite element model, an analytical expression for the interface dynamic stiffness of the damping rod is obtained in the form of rational fractions. Based on this expression, a reduced dynamic model of only 22 degrees of freedom is established through an equivalent mathematical transformation. Examples of a single damping rod component and a satellite-bracket adapter assembly constructed using multiple damping rods demonstrate that the reduced model achieves satisfactory numerical results after degrees of freedom are substantially reduced.