Study on the Quantitative Relationship between Static Stiffness and Modal Parameters of an Aluminum Space Frame

In this article, the quantitative relationship between the static stiffness, lightweight factor, and modal parameters of an aluminum space frame was investigated. Modal theory calculation and finite element method were employed in the analysis. Fifty modal parameters were extracted from the finite element model of the frame to calculate the bending stiffness, torsional stiffness, and lightweight factor of the frame. The deviations of the bending stiffness, torsional stiffness, and lightweight factor obtained from the modal theory and the finite element theory were found to be 0.91%, 1.72%, and 1.71%, respectively. It indicates that these two methods have similar accuracy. It was confirmed that the sum of each order modal compliance could be used to calculate the static compliance of the aluminum space frame. The first-order bending mode was found to be the corresponding mode order, which made the largest contribution to the bending stiffness. This method is also applicable for identifying the first-order torsional mode. The results also show that such a modal identification method can avoid effectively the interference of local mode on the major body mode identification. The results obtained from finite element analysis and modal theory method were both verified by the experimental testing results. It proved that both of these two methods were effective in calculating the bending stiffness, torsional stiffness, and lightweight factor. As a comparison, the modal theory showed higher accuracy with lower deviation in the calculated parameters to the experimentally measured ones. The modal theory results of the bending stiffness, torsional stiffness, and lightweight factor were closer to the experimental results with deviations of 4.64%, 3.61%, and 3.64%, while they are 5.82%, 5.53%, and 5.29% for the finite element method, respectively. This article supplies important guidance for the lightweight design and target setting of aluminum space frames in the concept stage.