scholarly journals Estimation of Wheelset Natural Vibration Characteristics Based on Transfer Matrix Method with Various Elastic Beam Models

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Pengfei Liu ◽  
Hongjun Liu ◽  
Qing Wu
Keyword(s):  
Transfer Matrix ◽  
Timoshenko Beam ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Elastic Beam ◽  
Vibration Characteristics ◽  
Bernoulli Beam ◽  
Flexible Wheelset ◽  
Euler Bernoulli Beam

The elastic vibration of the wheelset is a potential factor inducing wheel-rail defects. It is important to understand the natural vibration characteristics of the flexible wheelset for slowing down the defect growth. To estimate the elastic free vibration of the railway wheelset with the multidiameter axle, the transfer matrix method (TMM) is applied. The transfer matrices of four types of elastic beam models are derived including the Euler–Bernoulli beam, Timoshenko beam, elastic beam without mass and shearing stiffness, and massless elastic beam with shearing stiffness. For each type, the simplified model and detailed models of the flexible wheelset are developed. Both bending and torsional modes are compared with that of the finite element (FE) model. For the wheelset bending modes, if the wheel axle is modelled as the Euler–Bernoulli beam and Timoshenko beam, the natural frequencies can be reflected accurately, especially for the latter one. Due to the lower solving accuracy, the massless beam models are not applicable for the analysis of natural characteristics of the wheelset. The increase of the dividing segment number of the flexible axle is helpful to improve the modal solving accuracy, while the computation effort is almost kept in the same level. For the torsional vibration mode, it mainly depends on the axle torsional stiffness and wheel inertia rather than axle torsional inertia.

Natural vibration characteristics determination of elastic beam with attachments based on a transfer matrix method

2021 ◽  
pp. 107754632098064
Author(s):  
Dongyang Chen ◽  
Chaojie Gu ◽  
Minjiao Li ◽  
Bowen Sun ◽  
Xiaoyin Li
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Multibody System ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Vibration Characteristics ◽  
Boundary State

The transfer matrix method for multibody system takes into account the accuracy of the equations of motion and the efficiency of the algorithm. Especially if a system is composed of flexible and rigid components, transfer matrix method for multibody system reduces the dynamics problem to an overall transfer equation which only involves boundary state vectors. The state vectors at the boundary are made up of rotation angles, displacements, shear forces, and bending moments, which are normally half known and half unknown. The proposed transfer matrix method for multibody system of multibody system dynamics to determine the vibration characteristics is easy to formulate, systematic to apply, and simple to code. The purpose of this study is to introduce a modeling and simulation idea of beam with attachments based on transfer matrix method for multibody system. Numerical results for several examples of beam with attachments are presented to demonstrate the validity of this method.

Study on the Natural Vibration Characteristics of Flexible Missile With Thrust by Using Riccati Transfer Matrix Method

2015 ◽  
Vol 83 (3) ◽  
Author(s):  
Gangli Chen ◽  
Xiaoting Rui ◽  
Fufeng Yang ◽  
Jianshu Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Compressive Force ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Engine Thrust ◽  
Natural Vibration Characteristics

Due to the mass consumption and engine thrust of a flexible missile during the powered phase flight, its natural vibration characteristics may be changed significantly. The calculation of natural frequencies and mode shapes plays an important role in the structural design of the missile. Aiming at calculating the natural vibration characteristics of the missile rapidly and accurately, a nonuniform beam subjected to an engine thrust is used to model the free vibration of the missile and Riccati transfer matrix method (RTMM) is adopted in this paper. Numerical results show that the natural frequencies of a typical single stage flexible missile are increased unceasingly in its powered phase, and its mode shapes are changed a lot. When the presented methodology is used to study the natural vibration characteristics of flexible missiles, not only the mass, stiffness, and axial compressive force distributions are described realistically but also numerical stability, high computation speed, and accuracy are achieved.

Study on the Natural Vibration Characteristics of Single-Point Diamond Fly Cutting Machine Tool Based on Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Yuanyuan Ding ◽  
Xiaoting Rui ◽  
Gangli Chen ◽  
Xingbao Liu ◽  
Xiaoyun Zeng
Keyword(s):  
Machine Tool ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Natural Vibration ◽  
Single Point ◽  
Vibration Characteristics ◽  
Cutting Machine ◽  
Natural Vibration Characteristics

Natural vibration characteristics play a very important role in the evaluation of the dynamics characteristics and the machined surface of a single-point diamond fly cutting machine tool (SDFCMT). In this paper, the natural vibration characteristics are studied from aspects of theory, computation, and experiment. By adopting the transfer matrix method for multibody systems (MSTMM), the dynamics model and its topology figure are established, and its natural vibration characteristics are computed. The computation results are verified by a modal test.

Vibration Analysis of Linear Beam With Moving Loads Based on Riccati Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Lu Sun ◽  
Xue Rui ◽  
Dieter Bestle ◽  
Guoping Wang ◽  
Jianshu Zhang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Mode Shapes ◽  
Moving Loads ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

The paper presents the dynamic response of an Euler-Bernoulli beam supported by an elastic foundation and subjected to a moving step load. The Riccati transfer matrix method for linear multibody systems (Riccati MSTMM) is employed to find eigenfrequencies and mode shapes of the supported beam. A comparison of results obtained with the finite element method (FEM) indicates that the Riccati MSTMM is more accurate when using the same number segments. Based on these results, the dynamic response of the beam with moving step load is investigated for different propagation velocities by mode superposition, and the effect of loads is discussed.

scholarly journals Transfer Matrix Method for the Determination of the Natural Vibration Characteristics of Realistic Thrusting Launch Vehicle—Part I

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Laith K. Abbas ◽  
Li Min-Jiao ◽  
Rui Xiao-Ting
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Weight Ratio ◽  
Flight Test ◽  
Launch Vehicle ◽  
Frequency Equation ◽  
Vibration Characteristics ◽  
Natural Vibration Characteristics

The feasibility of using the transfer matrix method (TMM) to compute the natural vibration characteristics of a flexible rocket/satellite launch vehicle is explored theoretically. In the approach to the problem, a nonuniform free-free Timoshenko and Euler-Bernoulli beamlike structure is modeled. A provision is made to take into consideration the effects of shear deformation and rotary inertia. Large thrust-to-weight ratio leads to large axial accelerations that result in an axial inertia load distribution from nose to tail which causes the development of significant compressive forces along the length of the launch vehicle. Therefore, it is important to take into account this effect in the transverse vibration model. Once the transfer matrix of a single component has been obtained, the product of all component matrices composes the matrix of the entire structure. The frequency equation and mode shape are formulated in terms of the elements of the structural matrices. Flight test and analytical results validate the present TMM formulas.

Vibration Analysis of Drug Delivery CNTs Using Transfer Matrix Method

2011 ◽  
Author(s):  
Anooshiravan Farshidianfar ◽  
Ali A. Ghassabi ◽  
Mohammad H. Farshidianfar ◽  
Mohammad Hoseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Equation Of Motion ◽  
Beam Model ◽  
Multi Wall Carbon Nanotubes ◽  
Resonance Frequencies ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

The free vibration and instability of fluid-conveying multi-wall carbon nanotubes (MWCNTs) are studied based on an Euler-Bernoulli beam model. A theory based on the transfer matrix method (TMM) is presented. The validity of the theory was confirmed for MWCNTs with different boundary conditions. The effects of the fluid flow velocity were studied on MWCNTs with simply-supported and clamped boundary conditions. Furthermore, the effects of the CNTs’ thickness, radius and length were investigated on resonance frequencies. The CNT was found to posses certain frequency behaviors at different geometries. The effect of the damping corriolis term was studied in the equation of motion. Finally, a useful simplification is introduced in the equation of motion.

Application of Transfer Matrix Method to Analysis of Transient Response of Beam

1987 ◽  
Vol 109 (3) ◽  
pp. 248-254 ◽  
Author(s):  
Moriaki Goya ◽  
Takuo Hayashi ◽  
Koichi Ito ◽  
Hiroshi Ohki
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Nonlinear Differential Equations ◽  
Effective Means ◽  
Linear Equations ◽  
Elastic Beam ◽  
Transient Responses ◽  
Concentrated Mass ◽  
Finite Difference Equations

The transient responses of an elastic beam to large dynamic deformations were analyzed numerically, using the transfer matrix method. Geometrically nonlinear differential equations were linearized by introducing increments of unknown functions, and the resulting linear equations were approximated by finite difference equations. A field transfer matrix was introduced for the analyses of large deformations; this determined the relationship between the incremental state vectors at both ends of the elastic segments. The Newmark β formulation was chosen to approximate the equation of motion for concentrated masses. A concentrated mass point transfer matrix and an inhomogeneous vector were introduced for analyses of the transient responses of the beams. A superposition scheme for the transfer matrix method was proposed as an effective means of obtaining a solution satisfying the boundary conditions at both ends of the beam.

scholarly journals Transfer Matrix Method for Natural Vibration Analysis of Tree System

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Bin He ◽  
Xiaoting Rui ◽  
Huiling Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Damage Identification ◽  
Continuous System ◽  
Dynamical Response ◽  
Transfer Matrices ◽  
Chain System ◽  
Mechanics Model

The application of Transfer matrix method (TMM) ranges from linear/nonlinear vibration, composite structure, and multibody system to calculating static deformation, natural vibration, dynamical response, and damage identification. Generally TMM has two characteristics: (1) the TMM formulae share similarity to the chain mechanics model in terms of topology structure; then TMM often is selected as a powerful tool to analyze the chain system. (2) TMM is adopted to deal with the problems of the discrete system, continuous system, and especial discrete/continuous coupling system with the uniform matrix form. In this investigation, a novel TMM is proposed to analyze the natural vibration of the tree system. In order to make the TMM of the tree system have the two above advantages of the TMM of the chain system, the suitable state vectors and transfer matrices of the typical components of the tree system are constructed. Then the topology comparability between the mechanics model and its corresponding formulae of TMM can be adopted to assembling the transfer matrices and transfer equations of the global tree system. Two examples of natural vibration problems validating the method are given. The formulation of the proposed TMM is mathematically intuitive and can be held and applied by the engineers easily.

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