Summary
On one hand, the new version of transfer matrix method for multibody systems (NV‐MSTMM), has been proposed by formulating transfer equations of elements in acceleration level instead of position level as in the original discrete time transfer matrix method of multibody systems to study multibody system dynamics. This new formulation avoids local linearization and allows using any integration algorithms. On the other hand, sensitivity analysis is an important way to improve the optimization efficiency of multibody system dynamics. In this paper, a totally novel direct differentiation method based on NV‐MSTMM for sensitivity analysis of multibody systems is developed. Based on direct differentiation method, sensitivity analysis matrix for each kind of element is established. By assembling transfer matrices and sensitivity analysis matrices based on differentiation law of multiplication, the sensitivity analysis equation of overall transfer equation is deduced. The computing procedure of the proposed method is also presented. All these improvements as well as three numerical examples show that the direct differentiation method based on NV‐MSTMM is suitable for optimizing the dynamic sensitivity in multi–rigid‐body systems.
In this study, the transfer matrix method for multibody systems is used to study the vibration characteristics of a tracked vehicle system. The transfer matrix method has the advantages of not needing the global dynamics equations of the system, low order of system matrices, and fast dynamics computation speed. According to the solution process of vibration characteristics, a detailed dynamics model considering the rigid–flexible coupling effect is developed to describe the structural relationship of the tracked vehicle system. Then, a topology figure for representing the transfer direction of the dynamics model is proposed to derive the overall transfer equation of the system. Dynamics equations governing the motion of the system and rocket are given. Next, through comparisons of the simulation and relevant experiments, the validity and correctness of the proposed method are verified. Based on this, the coupling dynamics responses of the system with different firing orders and firing intervals are simulated and analyzed, which shows that the firing order and interval have great influences on the vibration of the system. In this case, with the adaptive genetic algorithm, a multivariable optimization method is proposed. The optimization results show that the vibration is greatly reduced by using the optimized scheme.
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