Study on the Mixed Method of Transfer Matrix Method and Finite Element Method for Vibration of Multibody System

2019 ◽  
Author(s):  
Hanjing Lu ◽  
Xiaoting Rui ◽  
Jianshu Zhang ◽  
Yuanyuan Ding
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Matrix ◽  
Mixed Method ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Multibody System ◽  
Mass Matrix ◽  
Element Method

Abstract The mixed method of Transfer Matrix Method for Multibody System (MSTMM) and Finite Element Method (FEM) is introduced in this paper. The transfer matrix and transfer equation of multi-rigid-body subsystem are deduced by MSTMM. The mass matrix and stiffness matrix of flexible subsystem are calculated by FEM and then its dynamics equation is established. The connection point relations among subsystems are deduced and the overall transfer matrix and transfer equation of multi-rigid-flexible system are established. The vibration characteristics of the system are obtained by solving the system frequency equation. The computational results of two numerical examples show that the proposed method have good agreements with MSTMM and FEM. Multi-rigid-flexible-body system with multi-end beam can be solved by proposed method, which extends the application field of MSTMM and provides a theoretical basis for calculating complex systems with multi input end flexible bodies of arbitrary shape.

scholarly journals Circular Space Curve Frame (3D) with any Load and Spring Supports by Transfer Matrix Method and Finite Element Method

2019 ◽  
Vol 8 (12) ◽  
pp. 3981-3987
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Complex Problem ◽  
Fem Method ◽  
Circular Space ◽  
Element Method

In this paper, authors present a new numerical method, combining the Transfer Matrix Method and Finite Element Method (TMM - FEM), to analyze spatially circular curved bar, with general load and elastic support. Analysis space curved bar is complex problem because conventional methods will not simultaneously calculate the entire structure, or difficulty in establish the stiffness matrix, or the size of stiffness matrix is too large due to multiple elements. TMM - FEM method is proposed to promote the advantages of each method. Due to being directly generated from the parametric equations of the bar axis, the analytical results are accurate. Results are programed in Matlab and verified with SAP2000 programe.

Coupling transfer matrix method to finite element method for the analysis of hollow body networks with passive or reactive elements

2008 ◽  
Vol 123 (5) ◽  
pp. 3926-3926
Author(s):  
Fabien Chevillotte ◽  
Raymond Panneton ◽  
Hakim Bougrab ◽  
Christophe Chaut ◽  
Jean‐Luc Wojtowicki
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Reactive Elements ◽  
Element Method

Finite Element and Transfer Matrix Methods for Rotordynamics: A Comparison

2001 ◽  
Author(s):  
Jorgen L. Nikolajsen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Free Vibration Analysis ◽  
Accurate Method ◽  
The Finite Element Method ◽  
Rotor Systems ◽  
Element Method

A quantitative comparison is made between the Finite Element Method and four variants of the Transfer Matrix Method, as applied to free vibration analysis of rotor systems. The results are as follows: The Finite Element Method is the most robust method and can identify the largest number of natural frequencies. The finite-element-based Transfer Matrix Method is the most accurate method and uses the least amount of memory. The Polynomial Transfer Matrix Method is the fastest. The Riccati Transfer Matrix Method performed well but did not live up to its superior reputation. The Lund Transfer Matrix Method also performed well except on processing speed where it fell far short of the other methods.

scholarly journals A Comparison of a One-Dimensional Finite Element Method and the Transfer Matrix Method for the Computation of Wind Music Instrument Impedance

2019 ◽  
Vol 105 (5) ◽  
pp. 838-849 ◽  
Author(s):  
Robin Tournemenne ◽  
Juliette Chabassier
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Equivalent Radius ◽  
Fem Method ◽  
Dimensional Finite Element ◽  
Planar Wave ◽  
Element Method

This work presents a computation tool for the calculation of wind instrument input impedance in the context of linear planar wave propagation with visco-thermal losses. The originality of the approach lies in the usage of a specific and simple 1D finite element method (FEM). The popular Transfer Matrix Method (TMM) is also recalled and a seamless formulation is proposed which unifies the cases cylinders vs. cones. Visco-thermal losses, which are natural dissipation in the system, are not exactly taken into account by this method when arbitrary shapes are considered. The introduction of an equivalent radius leads to an approximation that we quantify using the FEM method. The equation actually solved by the TMM in this case is exhibited. The accuracy of the two methods (FEM and TMM) and the associated computation times are assessed and compared. Although the TMM is more efficient in lossless cases and for lossy cylinders, the FEM is shown to be more efficient when targeting a specific precision in the realistic case of a lossy trumpet. Some additional features also exhibit the robustness and flexibility of the FEM over the TMM. All the results of this article are computed using the open-source python toolbox OpenWind.

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

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878875
Author(s):  
Lu Sun ◽  
Guoping Wang ◽  
Xiaoting Rui ◽  
Xue Rui
Keyword(s):  
System Dynamics ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Closed Loop ◽  
Multibody System ◽  
Mixed System ◽  
Global Dynamics ◽  
Mixed Systems

The transfer matrix method for multibody systems has been developed for 20 years and improved constantly. The new version of transfer matrix method for multibody system and the automatic deduction method of overall transfer equation presented in recent years make it more convenient of the method for engineering application. In this article, by first defining branch subsystem, any complex multibody system may be regarded as the assembling of branch subsystems and simple chain subsystems. If there are closed loops in the system, the loops should be “cut off,” thus a pair of “new boundaries” are generated at each “cutting-off” point. The relationship between the state vectors of the pair of “new boundaries” may be described by a supplement equation. Based on above work, the automatic deduction method of overall transfer equation for tree systems as well as closed-loop-and-branch-mixed systems is formed. The results of numerical examples obtained by the automatic deduction method and ADAMS software for tree system dynamics as well as mixed system dynamics have good agreements, which validate the features of proposed method such as high computational speed, more effective for complex systems, no need of the system global dynamics equation, highly programmable, as well as convenient popularization and application in engineering.

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