Dynamics design for complex mechanical systems has become an important research field and development direction at present, capturing attentions of an increasing number of engineers and scientists worldwide. Based on many advantages of the transfer matrix method for multibody system in studying multibody system dynamics, a design problem of a multiple launch rocket system is solved in this paper. Particular attention is addressed to model actions of the exhaust flow on the multiple rocket launcher, which are associated with firing order and firing intervals of rockets. Combined with a genetic algorithm, firing order and firing intervals are optimized to achieve optimum impact point dispersion reduction. The results of numerical simulation and verification tests show good agreement, while the dispersion characteristics of rockets have been improved in a low-cost way.
The transfer matrix method for multibody system is a new method developed in recent 20 years for studying multibody system dynamics. The new version of transfer matrix method for multibody system and automatic deduction theorem of system overall transfer equation have been formed in 2012. The overall transfer equation plays one of the key roles for transfer matrix method for multibody system. In order to study branch system dynamics with new version of transfer matrix method for multibody system, the automatic deduction theorem of overall transfer equation has been expanded in this article, which made it practicable to deduce automatically the overall transfer equation for branch system with new version of transfer matrix method for multibody system. The transfer equations and transfer matrices of typical elements are developed for the automatic deduction theorem of overall transfer equation. Thereby new version of transfer matrix method for multibody system owns the following features: there is no need to establish the global dynamics equation of system, by which the study on multibody system dynamics will be simplified greatly; the automatic deduction of overall transfer equation for multibody system is realized, consequently the algorithm is simple and highly programmable; moreover, the order of system matrix is always low, which result in high computational speed. The branch multibody system dynamics has been computed with the automatic deduction theorem of overall transfer equation as well as ordinary multibody system dynamics method. The computational results obtained by the two methods have good agreements, which validate the automatic deduction theorem of overall transfer equation for branch multibody system.
In the multibody system transfer matrix method (MSTMM), the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations. However, regarding the transfer matrices of hinge elements, typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t. various types of outboard body's output links. This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper. Systematic procedures for chain, tree, closed-loop, and arbitrary general systems are defined, respectively, to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process. As a result, accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.
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