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

Rui, Xiaoting; Zhang, Jianshu; Wang, Xun; Bao, Rong; He, Bin; Jin, Zhan

doi:10.1002/msd2.12037

Cited by 116 publications

(31 citation statements)

References 81 publications

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“…For any strip element, say the ith element in Figure 9A, its vibration equation can be set up analytically. Alternatively, according to the Strip Distributed Transfer Function Method, [35][36][37][38][39] the transverse displacement in the strip lateral direction can be interpolated by polynomials in terms of nodal line displacements, which are functions of the strip longitudinal coordinate and time.…”

Section: The Main Idea and Process Of Solving The Difficultiesmentioning

confidence: 99%

Vibration control for the solar panels of spacecraft: Innovation methods and potential approaches

Li,

Liu

2023

Int Journal of Mech Sys Dyn

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Solar panels on spacecraft are typical kinds of flexible structures. Low‐frequency and large‐amplitude vibrations usually occur due to the inevitable disturbances of deployment impact, attitude/orbit maneuver, separation/docking impact, and so forth. These vibrations degrade the stability of the spacecraft platform, leading to a reduction in imaging quality and pointing direction accuracy. Vibration control is obligatory during flight missions. Here, we summarize the researches on vibration control of the solar panels. First, typical solar panels used in spacecraft and the specific difficulties in dynamic modeling and control design are introduced. Next, the researches on dynamic modeling methods, decentralized vibration control strategy, and in‐orbit vibration controller design technologies are presented sequentially. Finally, a practical example where our method was successfully applied in‐orbit is described. In conclusion, the theories, methods, and technologies presented in this review hold significant value for achieving high‐precision performance in large spacecraft.

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Section: The Main Idea and Process Of Solving The Difficultiesmentioning

confidence: 99%

Vibration control for the solar panels of spacecraft: Innovation methods and potential approaches

Li,

Liu

2023

Int Journal of Mech Sys Dyn

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“…The finite element method (FEM) allows easier modeling of complex structures, and can provide powerful post-processing functions and good performance in the study of beam and plate vibration response and acoustic radiation, 16 while its numerical accuracy and computational time are closely related to the mesh division. The transfer matrix method (TMM) and the multibody system transfer matrix method (MSTMM) [17][18][19] have been widely used in engineering practice due to their feature of fast calculation and not requiring the overall dynamic equations of the system. MSTMM extends TMM from one dimensional to higher dimensional system and can deal with many complex problems TMM cannot solve such as dynamics of multi-rigid-body systems and of rigid-flexible coupling system, especially with time-varying feature, nonlinearity and large motion characteristics.…”

Section: Introductionmentioning

confidence: 99%

Vibration isolation by a periodic beam with embedded acoustic black holes based on a hybrid dynamics method

Yao

Zhang

Zhou

et al. 2023

Journal of Low Frequency Noise, Vibration and Active Control

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The acoustic black hole (ABH) has been proved to reduce broadband vibration response in beams and plates. While the traditional analytical and semi-analytical methods can only deal with the response of simple ABH structures; for complex ABH structures, the numerical methods such as the finite element method (FEM) have to be resorted and these methods are too often time-consuming. In this work, the vibration isolation by a beam structure embedded with periodic embedded symmetric ABHs is investigated. The vibration transmission of a single embedded symmetric ABH beam unit is first studied by the Riccati transfer matrix method (RTMM). A comparative analysis of the convergence speed and the computation efficiency of the unit by the RTMM and the FEM demonstrates the computation time using the RTMM increases linearly with the number of segments while that using the FEM increases exponentially and quickly exceeds the former as the number of segments increases. The computation time is consistent with the computational complexity associated with their respective algorithms. A hybrid dynamics method (HDM) is then proposed to derive for the vibration transmission solution of the beam with single and multiple periodically embedded symmetric ABHs. A comparison of the responses with those calculated by the RTMM demonstrates that the proposed HDM provides an efficient tool for solving the vibration response of the finite beam with periodic embedded ABHs, leading to much improved computational efficiency with ensured numerical stability and accuracy. This advantage in computation efficiency becomes even more obvious for larger structures when the number of the ABH units increased considerably. The proposed hybrid dynamic approach provides a basis for solving the vibration transmission/isolation problems of more complex ABH structures.

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“…To enhance the computational efficiency, the classical transfer matrix method (TMM) was used for the dynamic analysis of the spindle component in the machine tool 19 . While the theory of TMM is suitable for a single element, challenges are encountered when using TMM for multibody systems (MSTMM), referred to as the “Rui Method.” 10,20,21 Compared to conventional dynamic methods, MSTMM has several advantages, such as replacing the global dynamic equations with low‐order transfer equations, high computational speed, and simplified computational implementation 22 . In our previous studies, 23–25 the dynamic models of an ultra‐precision fly‐cutting machine tool consisting of rigid body elements, beam elements, and hinge elements were developed by MSTMM.…”

Section: Introductionmentioning

confidence: 99%

Hybrid multibody system method for the dynamic analysis of an ultra‐precision fly‐cutting machine tool

Rui

et al. 2022

Int Journal of Mech Sys Dyn

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The dynamics of an ultra‐precision machine tool determines the precision of the machined surface. This study aims to propose an effective method to model and analyze the dynamics of an ultra‐precision fly‐cutting machine tool. First, the dynamic model of the machine tool considering the deformations of the cutter head and the lathe head is developed. Then, the mechanical elements are classified into M subsystems and F subsystems according to their properties and connections. The M‐subsystem equations are formulated using the transfer matrix method for multibody systems (MSTMM), and the F‐subsystem equations are analyzed using the finite element method and the Craig–Bampton reduction method. Furthermore, all the subsystems are assembled by combining the restriction equations at connection points among the subsystems to obtain the overall transfer equation of the machine tool system. Finally, the vibration characteristics of the machine tool are evaluated numerically and are validated experimentally. The proposed modeling and analysis method preserves the advantages of the MSTMM, such as high computational efficiency, low computational load, systematic reduction of the overall transfer equation, and generalization of its computational capability to general flexible‐body elements. In addition, this study provides theoretical insights and guidance for the design of ultra‐precision machine tools.

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

Cited by 116 publications

References 81 publications

Vibration control for the solar panels of spacecraft: Innovation methods and potential approaches

Vibration control for the solar panels of spacecraft: Innovation methods and potential approaches

Vibration isolation by a periodic beam with embedded acoustic black holes based on a hybrid dynamics method

Hybrid multibody system method for the dynamic analysis of an ultra‐precision fly‐cutting machine tool

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