Substructuring technique for dynamics analysis of flexible beams with large deformation

Multibody system transfer matrix method: The past, the present, and the future

“…A flexible body undergoing large rigid motion and relatively small deformation may be described in the inertial Cartesian coordinate system oxyz and a floating reference frame o x y z R R R R , respectively, as shown in Figure 4. The flexible body is discretized into finite elements, and the deformation coordinates of the nodes are expressed using the modal superposition method 35 :…”

“…The flexible body dynamics is governed by partial differential equations, which may be transformed into ordinary differential equations using various approximation methods rooted in the separation of variables. The transfer equations of the flexible body can then be established according to Zhang et al, 35 and Zhou et al 36 …”

Study on automatic deduction method of overall transfer equation for tree systems as well as closed-loop-and-branch-mixed systems

“…Transfer matrix method for multibody system (MSTMM) was developed for the exact target with above algorithms. Rui and colleagues 12–19 have put forward MSTMM and tried to perfect it constantly since 20 years ago. The MSTMM has been applied widely in engineering for following aspects: the study procedure of MSD is simplified because of no need to establish the system global dynamics equation; the computational speed is increased greatly because the system matrix order is always low, and it is highly programmable.…”

“…Besides, comparing to algorithms in Featherstone, 8 Brandl et al 9 , Rodriguez et al 10 and Saha 11 , the expression of new version of MSTMM is the most concise and evident since the kinematics and dynamics information are contained in the transfer matrix of each element, different from others that these information are processed separately makes the computational process tedious. Moreover, the consistency in the form of transfer matrices of elements will make it easier to solve rigid-flexible coupling system dynamics 18 with same state vectors. The automatic deduction theorem of overall transfer equation of chain systems and closed-loop systems 19 for the new version of MSTMM was presented in 2014.…”

“…Moreover, the consistency in the form of transfer matrices of elements will make it easier to solve rigid-flexible coupling system dynamics 18 with same state vectors. The automatic deduction theorem of overall transfer equation of chain systems and closed-loop systems 19 for the new version of MSTMM was presented in 2014.…”