Abstract
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.
Highlights
The dynamics equation of an individual rigid body that established by Newton’s1 Law and Euler[2] Theorem has promoted the development of rigid body dynamics and mechanical system dynamic design technology
The automatic deduction theorem of overall transfer equation for branch system for new version of MSTMM has been established
The multibody system dynamics (MSD) has been computed using the automatic deduction theorem of overall transfer equation for branch system and ordinary multibody system dynamics (MSDM), respectively, with the good agreements of both results, the effectiveness of automatic deduction theorem of overall transfer equation for branch multibody system has been validated
Summary
The dynamics equation of an individual rigid body that established by Newton’s1 Law and Euler[2] Theorem has promoted the development of rigid body dynamics and mechanical system dynamic design technology. Combined with TMM and finite element method (FEM), Dokanish[31] (1972) proposed the FE-TMM to solve two-dimensional thin board and increased the computational speed of FEM.[13] Combined with TMM and numerical integrating method, Kumar and Sankar[14] developed the discrete-time transfer matrix method (DTTMM) for time-variant system structure dynamics.
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