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.

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.

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.

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.

Free vibration analysis of axial-loaded beams with variable cross sections and multiple concentrated elements

2021 ◽  
pp. 107754632110128
Author(s):  
Yunxing Du ◽  
Peng Cheng ◽  
Fen Zhou
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Cross Sections ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Free Vibration Analysis ◽  
Frequency Equation ◽  
Variable Cross ◽  
Bending Vibrations ◽  
Euler Bernoulli Beam

A transfer matrix method is used to study free vibration characteristics of an axial-loaded Euler–Bernoulli beam with variable cross sections and multiple concentrated elements in the article. The differential equation for bending vibrations of the beam element is solved by the Frobenius method, and the solution is in power series form. Then, the transfer matrix method is applied to establish the state vector equation for both ends of the beam. Combined with boundary conditions, the frequency equation is obtained and expressed in a two-order determinant. The numerical results in this article are compared with those of the finite element method, which illustrates the accuracy of the method we proposed. The influence of the size of each concentrated elements and axial force on the natural frequency coefficients and the influence of the concentrated elements on the first critical buckling load are discussed.

Dynamic Analysis of Complex Composite Rotor Systems With Substructure Transfer Matrix Method

1985 ◽  
Author(s):  
Yan Litang
Keyword(s):  
Dynamic Analysis ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Synthesis Method ◽  
Frequency Equation ◽  
Rotor System ◽  
Combination Method ◽  
Rotor Systems ◽  
Modal Synthesis

A substructure transfer matrix method for the dynamic analysis of multi-Rotor systems and complex composite systems is presented. When calculating, the rotor system should be decomposed into several single rotor shafts (substructures). Corresponding unknown external loads and deflections are applied to the separated surfaces, rigid support sections and ball joint sections respectively to replace the original connections. According to the connective and boundary conditions of the whole rotor system, a system of equations is established, from which the frequency equation results. The calculating formulas of vibration modes and of unbalanced response will be easily formed by linear combination method. All computations are performed with the transfer matrix method. This method is intelligible, readily programmed and much simpler than the current transfer matrix method and modal synthesis method.

Study on the Model of a Single-Point Diamond Fly Cutting Machine Tool at Different Rotational Speed Based on Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Yu Chang ◽  
Jianguo Ding ◽  
Hui Zhuang ◽  
Peng Chen ◽  
Wei Wei ◽  
...  
Keyword(s):  
Machine Tool ◽  
Transfer Matrix Method ◽  
Rotational Speed ◽  
Multibody Systems ◽  
Natural Vibration ◽  
Single Point ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Cutting Machine ◽  
Natural Vibration Characteristics

Natural vibration characteristics are important factors affecting the processing quality for an ultra-precision machine tool. The rapid and accurate calculation method for solving natural vibration characteristics has a significance in machine tool dynamics design. By applying the transfer matrix method for multibody systems (MSTMM), the dynamics model of a single-point diamond fly cutting machine tool is established and the rapid computation of natural vibration characteristics at different rotational speed is completed. The results calculated by MSTMM is compared with those by finite element software ABAQUS, the error between the first ten frequencies calculated by MSTMM and ABAQUS is less than 5.68%. However, as the rotational speed increases, the first eight frequencies and mode shapes have no obvious change, while the 9th and 10th modal change significantly. The mode shapes of 9th and 10th orders are vacillation of the spindle. The results show that the rotation of aerostatic spindle has significant effect on the spindle system and little effect on the other parts.

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