A Fast Calculation Method for Sensitivity Analysis Based on Multibody System Transfer Matrix Method

Sensitivity analysis is an essential step for the optimization design of mechanical systems. To improve the efficiency of sensitivity analysis based on the multibody system transfer matrix method, this study proposes a fast calculation method (FCM) and its operator formulas for any order derivative of the overall transfer matrix (DOTM). First, the formulas for the [Formula: see text]-order DOTM are derived by the definition-based method (DM). To reduce the computational time complexity, a FCM for DOTM is established through directly differentiating the recursive formula of the overall transfer matrix for chain mechanical systems and reducing the computational time complexity from [Formula: see text] in DM to [Formula: see text] in FCM. Then, to simplify the deduction process of DOTM for the chain mechanical systems and branch mechanical systems, the operator formulas for FCM are established by defining and applying a successive derivative operator and a combinatorial product operator. The operator formulas reveal the calculation rules similar to the automatic assembly theory for the overall transfer matrix in branch systems. Meanwhile, the proposed method and operator formulas are also applicable to a general mechanical system containing closed-loops. Finally, the natural frequency sensitivity of a chain multibody system, frequency response sensitivity of a branch system and the natural frequency sensitivity of a complex mechanical system demonstrate that the proposed FCM has remarkably higher computation efficiency than DM and is user-friendly to be realized with a computer.