Reduced multibody system transfer matrix method using decoupled hinge equations

Xue, Rui; Bestle, Dieter

doi:10.1002/msd2.12026

Cited by 69 publications

(14 citation statements)

References 16 publications

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“…The term “reduced” signifies that lower‐dimensional subvectors and matrices are used compared with the original element and overall transfer equations. Moreover, the strategy using independent hinge transfer equations 31 makes it much easier than NV‐MSTMM.…”

Section: Reduced Multibody System Transfer Matrix Methods (Rmstmm)mentioning

confidence: 99%

“…It can be proved that the reduced transformations for the state vector of a connection point located out of a closed‐loop system and a closed‐loop subsystem, and located in chain, subchain, tree, and subtree systems, are defined and share the same form as follows 31–33 :

{bold-italicz}_{a} = S {bold-italicz}_{b} + e,

where, for each boundary end,

{bold-italicz}_{a}

consists of the known half of state variables, while the remaining half of state variables makes up

{bold-italicz}_{b}

. Using boundary conditions like ()–(), the initial values of

S

and

e

can be, therefore, determined as

S = {bold-italicO}_{6 \times 6}, e = {bold-italicO}_{6 \times 1} .

…”

Section: Reduced Multibody System Transfer Matrix Methods (Rmstmm)mentioning

confidence: 99%

“…Unfortunately, closed loops do not have a boundary, and the dummy cut‐off point state does not share the property that half state variables are known ahead of time. Rui and Bestle 31–33 presented a new method to determine the initial values of the reduced transfer matrices by defining a new reduced transformation of Equation () as

{bold-italicz}_{a} = S {bold-italicz}_{b} + D {bold-italicz}_{a, C} + e

accompanied by complementary equations

{bold-italicz}_{b, C} = {bold-italicB}_{b} {bold-italicz}_{b} + {bold-italicB}_{a} {bold-italicz}_{a, C} + b,

where

{bold-italicz}_{a, C}

and

{bold-italicz}_{b, C}

are substate vectors of the dummy cut‐off point. In this way, the initial values of the reduced transfer matrices

{bold-italicS}_{1, I} = {bold-italicO}_{6 \times 6}, {bold-italicD}_{1, I} = {bold-italicI}_{6}, {bold-italice}_{1, I} = {bold-italicO}_{6 \times 1}, {bold-italicB}_{b, 1, I} = {bold-italicI}_{6}, {bold-italicB}_{a, 1, I} = {bold-italicO}_{6 \times 6}

, and

{bold-italicb}_{1, I} = {bold-italicO}_{6 \times 1}

can be obtained directly at the dummy cut‐off point combining extra closed‐loop conditions

{bold-italicz}_{a, 1, I} \equiv {bold-italicz}_{a, n, O} ≕ {bold-italicz}_{a, C}

{bold-italicz}_{b, 1, I} \equiv {bold-italicz}_{b, n, O} ≕ {bold-italicz}_{b, C}

.…”

Section: Reduced Multibody System Transfer Matrix Methods (Rmstmm)mentioning

confidence: 99%

“…For an attached closed loop in a general system, Rui and Bestle 31–33 further defined the reduced transformation and complementary equation, respectively, as

{bold-italicz}_{a} = S {bold-italicz}_{b} + D {bold-italicz}_{a, C} + {bold-italicD}^{true'} {bold-italicz}_{a, A} + e

and

{bold-italicz}_{b, C} = {bold-italicB}_{b} {bold-italicz}_{b} + {bold-italicB}_{a} {bold-italicz}_{a, C} + {bold-italicB}_{a}^{true'} {bold-italicz}_{a, A} + b,

where the new terms

{bold-italicD}^{true'} {bold-italicz}_{a, A}

and

{bold-italicB}_{a}^{true'} {bold-italicz}_{a, A}

are related to the attached forces and torques. A similar procedure as for an isolated closed loop is applied to treat the attached closed loop, while the remaining part of the general system can be treated as a tree system.…”

Section: Reduced Multibody System Transfer Matrix Methods (Rmstmm)mentioning

confidence: 99%

See 3 more Smart Citations

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

Rui

Zhang

Wang

et al. 2022

Int Journal of Mech Sys Dyn

116

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The multibody system transfer matrix method (MSTMM), a novel dynamics approach developed during the past three decades, has several advantages compared to conventional dynamics methods. Some of these advantages include avoiding global dynamics equations with a system inertia matrix, utilizing low-order matrices independent of system degree of freedom, high computational speed, and simplicity of computer implementation. MSTMM has been widely used in computer modeling, simulations, and performance evaluation of approximately 150 different complex mechanical systems. In this paper, the following aspects regarding MSTMM are reviewed: basic theory, algorithms, simulation and design software, and applications.Future research directions and generalization to more applications in various fields of science, technology, and engineering are discussed.

show abstract

Section: Reduced Multibody System Transfer Matrix Methods (Rmstmm)mentioning

confidence: 99%

{bold-italicz}_{a} = S {bold-italicz}_{b} + e,

where, for each boundary end,

{bold-italicz}_{a}

consists of the known half of state variables, while the remaining half of state variables makes up

{bold-italicz}_{b}

. Using boundary conditions like ()–(), the initial values of

S

and

e

can be, therefore, determined as

S = {bold-italicO}_{6 \times 6}, e = {bold-italicO}_{6 \times 1} .

…”

Section: Reduced Multibody System Transfer Matrix Methods (Rmstmm)mentioning

confidence: 99%

{bold-italicz}_{a} = S {bold-italicz}_{b} + D {bold-italicz}_{a, C} + e

accompanied by complementary equations

{bold-italicz}_{b, C} = {bold-italicB}_{b} {bold-italicz}_{b} + {bold-italicB}_{a} {bold-italicz}_{a, C} + b,

where

{bold-italicz}_{a, C}

and

{bold-italicz}_{b, C}

are substate vectors of the dummy cut‐off point. In this way, the initial values of the reduced transfer matrices

{bold-italicS}_{1, I} = {bold-italicO}_{6 \times 6}, {bold-italicD}_{1, I} = {bold-italicI}_{6}, {bold-italice}_{1, I} = {bold-italicO}_{6 \times 1}, {bold-italicB}_{b, 1, I} = {bold-italicI}_{6}, {bold-italicB}_{a, 1, I} = {bold-italicO}_{6 \times 6}

, and

{bold-italicb}_{1, I} = {bold-italicO}_{6 \times 1}

can be obtained directly at the dummy cut‐off point combining extra closed‐loop conditions

{bold-italicz}_{a, 1, I} \equiv {bold-italicz}_{a, n, O} ≕ {bold-italicz}_{a, C}

{bold-italicz}_{b, 1, I} \equiv {bold-italicz}_{b, n, O} ≕ {bold-italicz}_{b, C}

.…”

Section: Reduced Multibody System Transfer Matrix Methods (Rmstmm)mentioning

confidence: 99%

“…For an attached closed loop in a general system, Rui and Bestle 31–33 further defined the reduced transformation and complementary equation, respectively, as

{bold-italicz}_{a} = S {bold-italicz}_{b} + D {bold-italicz}_{a, C} + {bold-italicD}^{true'} {bold-italicz}_{a, A} + e

and

{bold-italicz}_{b, C} = {bold-italicB}_{b} {bold-italicz}_{b} + {bold-italicB}_{a} {bold-italicz}_{a, C} + {bold-italicB}_{a}^{true'} {bold-italicz}_{a, A} + b,

where the new terms

{bold-italicD}^{true'} {bold-italicz}_{a, A}

and

{bold-italicB}_{a}^{true'} {bold-italicz}_{a, A}

Section: Reduced Multibody System Transfer Matrix Methods (Rmstmm)mentioning

confidence: 99%

See 2 more Smart Citations

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

Rui

Zhang

Wang

et al. 2022

Int Journal of Mech Sys Dyn

116

View full text Add to dashboard Cite

show abstract

“…Riccati transformation is also combined with TMM to form the Riccati transfer matrix method (RTMM) 20 originally for linear chain systems, to improve the numerical stability at higher frequencies or for long chains. RTMM is then extended by Bin He et al 21 to a general chain system with large overall motion, by J. Gu et al 22,23 to general linear systems with trees and closed loops topology and by X. Rui and D. Bestle 24 to a more general system with various topology and time-variance, nonlinearity and large motion. RTMM has been recently used by Cameron A. McCormick et al 25 To solve and optimize the vibration response of a beam with a single asymmetric ABH termination.…”

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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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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Reduced multibody system transfer matrix method using decoupled hinge equations

Cited by 69 publications

References 16 publications

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

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

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

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

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