Modeling method study for transfer matrix of space rigid bodies supported by multiple elastic hinges

Abstract

When rigid bodies as well as elastic hinges connected are modeled by using a transfer matrix method, they need to be defined as multi-input and multi-output space rigid bodies, resulting in higher dimensions of the whole transfer matrix and complexity of modeling. To reduce the dimensions of the whole matrix and improve computational efficiency and accuracy, the elastic hinges and the rigid bodies are integrated into a unified model in this paper. Then a single 12×12 matrix is obtained through theoretical derivation. The resulting transfer matrix of space rigid bodies supported by multiple elastic hinges not only reduces the dimensions of the whole matrix but also simplifies the configuration of the transfer matrix model by which some tree-like systems can be simplified into chain-like systems. Subsequently, the effectiveness of the matrix is validated through computational comparative analysis of typical systems. The modeling method is an important optimization to the calculation method of the dynamics characteristics of the transfer matrix.