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 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.

scholarly journals Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping

2012 ◽  
Vol 19 (6) ◽  
pp. 1167-1180 ◽  
Author(s):  
A.M. Yu ◽  
Y. Hao
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Axial Deformation ◽  
Cross Sectional ◽  
Helical Springs

Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. In the formulation, the warping effect upon natural frequencies and vibrating mode shapes is first studied in addition to including the rotary inertia, the shear and axial deformation influences. The natural frequencies of the springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad'e approximations. Three examples are presented for three types of springs with different cross-sectional shapes under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FEM results using three-dimensional solid elements (Solid 45) in ANSYS code. Numerical results reveal that the warping effect is more pronounced in the case of non-cylindrical helical springs than that of cylindrical helical springs, which should be taken into consideration in the free vibration analysis of such springs.

Dynamic characteristics of coupling shaft system in tufting machine based on the Riccati whole transfer matrix method

2016 ◽  
Vol 231 (2) ◽  
pp. 356-371 ◽  
Author(s):  
Shuang Huang ◽  
Xinfu Chi ◽  
Yang Xu ◽  
Yize Sun
Keyword(s):  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Complex Dynamic ◽  
Rotor Systems ◽  
Machine Type ◽  
Shaft System

Focusing on tufting machine type DHUN801D-400, the complex dynamic model of coupling shaft system is built by using Riccati whole transfer matrix method, and the natural frequencies and mode shapes are analyzed. First, the components of coupling shafts system in tufting machine are introduced. Second, the structures of coupling shafts system are discretized and simplified. Third, the transfer matrix is constructed, the model is solved by using Riccati whole transfer matrix method, and then natural frequencies and mode shapes are obtained. Finally, the experimental results are quoted to demonstrate the applicability of the model. The results indicate that the Riccati whole transfer matrix method is well applicable for modeling the dynamics of complex multi-rotor systems.

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.

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.

scholarly journals The free vibration characteristics of isotropic coupled conical-cylindrical shells based on the precise integration transfer matrix method

2017 ◽  
Vol 4 (1) ◽  
pp. 272-287
Author(s):  
Fuzhen Pang ◽  
Chuang Wu ◽  
Hongbao Song ◽  
Haichao Li
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Shell Thickness ◽  
Natural Frequencies ◽  
Integration Method ◽  
Vibration Characteristics ◽  
Precise Integration

Abstract Based on the transfer matrix theory and precise integration method, the precise integration transfer matrix method (PITMM) is implemented to investigate the free vibration characteristics of isotropic coupled conicalcylindrical shells. The influence on the boundary conditions, the shell thickness and the semi-vertex conical angle on the vibration characteristics are discussed. Based on the Flügge thin shell theory and the transfer matrix method, the field transfer matrix of cylindrical and conical shells is obtained. Taking continuity conditions at the junction of the coupled conical-cylindrical shell into consideration, the field transfer matrix of the coupled shell is constructed. According to the boundary conditions at the ends of the coupled shell, the natural frequencies of the coupled shell are solved by the precise integration method. An approach for studying the free vibration characteristics of isotropic coupled conical-cylindrical shells is obtained. Comparison of the natural frequencies obtained using the present method with those from literature confirms the validity of the proposed approach. The effects of the boundary conditions, the shell thickness and the semivertex conical angle on vibration characteristics are presented.

An Improved Extended Transfer Matrix Method for a Damped System

1991 ◽  
Author(s):  
Yuan Mao Huang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Good Method ◽  
Mode Shapes ◽  
Vibration Effect ◽  
Damped System ◽  
Matrix Products ◽  
The Matrix

Abstract Installation of a damper is a good method to reduce the torsional vibration effect and to prolong the life of a system. However, consideration of the damping effect results in a complicated system. This study derives a mathematical model for the analysis of a single branch damped system. The extended transfer matrix method is used with Newton-Raphson iterative technique. The procedures automatically eliminate the complicated operations of the matrix inversion and reduce the multiplication of the matrix products. The natural frequencies, both real and imaginary parts of the state vectors and mode shapes of the system can be determined.

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