A new version of the Riccati transfer matrix method for multibody systems consisting of chain and branch bodies

Xue, Rui; Bestle, Dieter; Wang, Guoping; Zhang, Jiangshu; Rui, Xiaoting; He, Bin

doi:10.1007/s11044-019-09711-2

Cited by 24 publications

(8 citation statements)

References 9 publications

(19 reference statements)

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“…A chain system as shown in Figure 1A with its corresponding topology graph in Figure 3A always has at least one free boundary end, which is regarded as the tip corresponding to the first element of the system. In such a case, the Riccati transformation 9 assumes that one part of state vectors () can be expressed as a function of the other, for example, as follows:

z_{a} = bold-italicS z_{b} + bold-italice .

…”

Section: Recursive Equations For Chain Systemsmentioning

confidence: 99%

“…always has at least one free boundary end, which is regarded as the tip corresponding to the first element of the system. In such a case, the Riccati transformation9 assumes that one part of state vectors(11) can be expressed as a function of the other, for example, as follows: forces and torques at a free boundary, this is obvious for the tip body 1 reading as follows:…”

mentioning

confidence: 99%

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Reduced multibody system transfer matrix method using decoupled hinge equations

Xue

Bestle

2021

Int Journal of Mech Sys Dyn

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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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z_{a} = bold-italicS z_{b} + bold-italice .

…”

Section: Recursive Equations For Chain Systemsmentioning

confidence: 99%

mentioning

confidence: 99%

Reduced multibody system transfer matrix method using decoupled hinge equations

Xue

Bestle

2021

Int Journal of Mech Sys Dyn

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“…Some methods are particularly effective for analyzing quantities of engineering cases. For instance, spectral element method (SEM) [ 19 , 20 ] using higher order polynomials as basis functions, transfer matrix method (TMM) [ 21 , 22 , 23 , 24 ] generally applied in the grand partition function, and finite element method (FEM) [ 25 , 26 , 27 , 28 ] commonly used in calculation are conventional approaches. In the case of the existing traditional methods, the analysis of modeling and modifying models is still limited.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Locally Resonant Beams with L-Joint Using an Exact Wave-Based Vibration Approach

Zhang

Chen

et al. 2023

Materials

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This paper employed and developed the wave-based vibration approach to analyze the band-gap characteristics of a locally resonant (LR) beam with L-joint, which is common in engineering practices. Based on the proposed modular approach, where the discontinuities on the beam are created as modules, the design and modeling work for such an LR beam can be simplified considerably. Then, three kinds of LR beams with an L-joint suspended with transverse-force type resonators and two cells of longitudinal-force-moment type resonators are analyzed, respectively, to show their suppression ability on the axial wave’s propagation and widened effect on the low-frequency band-gaps, where the longitudinal-force-moment type resonators at the 3rd–4th cells can better suppress the propagation of the axial waves. Meanwhile, the proposed analysis results are compared with the ones obtained with the finite element method and further verified the accuracy and efficiency of the wave-based vibration approach. The aim of this paper is to provide an efficient method for the analysis and design of the LR beam with L-joint for low-frequency vibration attenuation in engineering practices.

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“…[23][24][25] This problem can be dealt with Riccati transfer matrix method (Riccati TMM). 26 However, the characteristic equations established by Riccati TMM may have asymmetric poles. When zero search technique based on the sign change (such as bisection method) is used to solve such characteristic equations, these asymmetric poles will be mistaken as the solution.…”

Section: Introductionmentioning

confidence: 99%

“…This method can efficiently solve the buckling problem of complicated tree-section thin-walled members under various support conditions. In this paper, we introduced the Riccati TMM for tree multi-body systems 26 in FSTMM, and the transfer matrix of branch in tree-section thin-walled member was defined. On this basis, we introduced the high order finite strip method 28 is introduced, and presented the high order finite strip-Riccati transfer matrix method (Riccati HFSTMM) for buckling analysis of tree-section thin-walled members.…”

Section: Introductionmentioning

confidence: 99%

Finite strip-Riccati transfer matrix method for buckling analysis of tree-branched cross-section thin-walled members

Zhou

et al. 2022

Advances in Mechanical Engineering

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Thin-walled components are gaining wide application in the field of modern engineering structures. The buckling analysis of thin-walled structures has thus become an important research topic. Here, we developed a new method named as finite strip-Riccati transfer matrix method (Riccati FSTMM) for buckling analysis of tree-branched cross-section thin-walled members. The method integrates Riccati transfer matrix method (Riccati TMM) for tree multi-body system with semi-analytical finite strip method (SA-FSM). Compared to SA-FSM, Riccati FSTMM features a smaller matrix and higher calculation efficiency, with no need for global stiffness matrix. In addition, by arranging uniformly distributed middle nodal lines inside strip elements, we developed the high order finite strip-Riccati transfer matrix method (Riccati HFSTMM) for buckling analysis of tree-branched cross-section thin-walled members. This method further improves the efficiency and accuracy of Riccati FSTMM. We tested the two proposed methods with two numerical examples, and demonstrated their superior reliability and efficiency over the finite element method (FEM).

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A new version of the Riccati transfer matrix method for multibody systems consisting of chain and branch bodies

Cited by 24 publications

References 9 publications

Reduced multibody system transfer matrix method using decoupled hinge equations

Reduced multibody system transfer matrix method using decoupled hinge equations

Vibration Analysis of Locally Resonant Beams with L-Joint Using an Exact Wave-Based Vibration Approach

Finite strip-Riccati transfer matrix method for buckling analysis of tree-branched cross-section thin-walled members

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