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.

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.

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.

Generalized Solutions of Piezoelectric Vibration-Based Energy Harvesting Structures Using an Electromechanical Transfer Matrix Method

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Timothy Reissman ◽  
Adam Wickenheiser ◽  
Ephrahim Garcia
Keyword(s):  
Energy Harvesting ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Generalized Solutions ◽  
Mode Shapes ◽  
Transition Matrices ◽  
Tip Mass ◽  
Piezoelectric Vibration

Piezoelectric vibration-based energy harvesting (pVEH) offers much potential as renewable energy structures. Within the literature, often geometry-specific models are developed, making designs of new structures difficult. In this work, a generalized linear algebraic method is developed. The method incorporates the transfer matrix method (TMM) into the well-accepted distributed parameter electromechanical model for a composite-piezoelectric, Euler–Bernoulli beam. The result is an electromechanical TMM which is highly accurate at predicting both structural and energy harvesting performances for a wide variety of designs which have chainlike topologies. A simplification is made within the method to model structures which operate solely within bending modes, reducing the computation to analyses of only four-by-four state transition matrices, regardless of structural complexity. As many applications aim to optimize the large bending mode piezoelectric effect, this simplification does not limit the versatility of the method. To demonstrate the validity of this statement, comparisons were performed to evaluate the accuracy of the method's predictions for six piezoelectric topologies, including a unimorph without a tip mass, a bimorph with a tip mass, several partial-length bimorphs without a tip mass, and three different multibeam bimorph structures with inline and folded-back designs. The results show differences no greater than 2.24% for the first and second natural frequencies of the structures. Likewise, the method yields excellent predictions for the mode shapes, their slopes, and the voltage frequency responses, especially within the ±10% bounds of the natural frequencies. Thus, the future design of new structures is shown to be simplified using this generalizable method.

Dynamic Analysis of Geared Rotor-Bearing Systems by the Transfer Matrix Method

1995 ◽  
Author(s):  
Siu-Tong Choi ◽  
Sheng-Yang Mau
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Transmission Error ◽  
Mode Shapes ◽  
Rotor Systems ◽  
Gear Mesh ◽  
Mass Unbalance ◽  
Rotor Bearing

Abstract In this paper, an analytical study of the dynamic characteristics of geared rotor-bearing systems by the transfer matrix method is presented. Rotating shafts are modeled as Timoshenko beam with shear deformation and gyroscopic effects taken into account. The gear mesh is modeled as a pair of rigid disks connected by a spring-damper set and a transmission-error exciter. The transfer matrix of a gear mesh is developed. The coupling motions of the lateral and torsional vibration are studied. In free vibration analysis of geared rotor systems, natural frequencies and corresponding mode shapes, and the whirl frequencies under different spin speeds are determined. Effects of bearing stiffness, isotropic and orthotropic bearings, pressure angle of the gear mesh are studied. In steady-state vibration analysis, responses due to the excitation of mass unbalance and the transmission error are studied. Parametric characteristics of geared rotor systems are discussed.

scholarly journals Calculation of Natural Frequencies of Retaining Walls Using the Transfer Matrix Method

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Xu ◽  
Guanlu Jiang
Keyword(s):  
Natural Frequency ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Great Influence ◽  
Retaining Walls ◽  
Health State ◽  
Loading Frequency ◽  
Fundamental Frequencies

The dynamic response magnitudes of retaining walls under seismic loadings, such as earthquakes, are influenced by their natural frequencies. Resonances can occur when the natural frequency of a wall is close to the loading frequency, which could result in serious damage or collapse. Although field percussion tests are usually used to study the health state of retaining walls, they are complicated and time consuming. A natural frequency equation for retaining walls with tapered wall facings is established in this paper using the transfer matrix method (TMM). The proposed method is validated against the results of numerical simulations and field tests. Results show that fundamental frequencies decrease gradually with wall height; soil elastic modulus exerts a great influence on the fundamental frequency for walls with smaller facing stiffness; fundamental frequencies are smaller for a hinged toe than a fixed toe condition, and this difference is smaller in taller walls.

A Method for the Calculation of Natural Frequencies of Orthotropic Axisymmetrically Loaded Shells of Revolution

1994 ◽  
Vol 116 (1) ◽  
pp. 16-25 ◽  
Author(s):  
A. Kayran ◽  
J. R. Vinson ◽  
E. Selcuk Ardic
Keyword(s):  
Numerical Integration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Shell Of Revolution ◽  
Initial Stresses ◽  
Integration Technique ◽  
Shells Of Revolution ◽  
Axisymmetric Loading

A methodology is presented for the calculation of the natural frequencies of orthotropic axisymmetrically loaded shells of revolution including the effect of transverse shear deformation. The fundamental system of equations governing the free vibration of the stress-free shells of revolution are modified such that the initial stresses due to the axisymmetric loading are incorporated into the analysis. The linear equations on the vibration about the deformed state are solved by using the transfer matrix method which makes use of the multisegment numerical integration technique. This method is commonly known as frequency trial method. The solution for the initial stresses due to axisymmetric loading is omitted; since the application of the transfer matrix method, making use of multisegment numerical integration technique for both linear and nonlinear equations are available in the literature. The method is verified by applying it to the solution of the natural frequencies of spinning disks, for which exact solutions exist in the literature, and a deep paraboloid for which approximate solutions exist. The governing equations for a shell of revolution are used to approximate circular disks by decreasing the curvature of the shell of revolution to very low values, and good agreement is seen between the results of the present method and the exact solution for spinning disks and the approximate solution for a deep paraboloid.

Research on Vibration and Instability of the Double-Span Beam Base on Transfer Matrix

2009 ◽  
Vol 16-19 ◽  
pp. 160-163 ◽  
Author(s):  
Ting Liu ◽  
Fei Feng ◽  
Ya Zhe Chen ◽  
Bang Chun Wen
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Axial Compression ◽  
Axial Force ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Euler Beam ◽  
Intermediate Support ◽  
Critical Axial Force

The vibration and instability of a beam which is Double-span Euler Beam with axial force is studied by transfer matrix method. The transfer matrix of transverse free vibration and axial compression of the beam is derived. Then based on the assembled transferring matrix, the effect of the position of intermediate support on the natural frequencies and Euler critical axial force of the beam is discussed, which offered a useful method to start research of vibration of complicated framework.

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