scholarly journals THE TRANSFER MATRIX METHOD FOR MODAL ANALYSIS OF CRACKED MULTISTEP BEAM

2017 ◽  
Vol 55 (5) ◽  
pp. 598
Author(s):  
Nguyen Tien Khiem ◽  
Vu Thi An Ninh ◽  
Tran Thanh Hai
Keyword(s):  
Modal Analysis ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Arbitrary Number ◽  
Matrix Method ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Modal Testing ◽  
Testing Technique

The present study addresses the modal analysis of multistep beam with arbitrary number of cracks by using the transfer matrix method and modal testing technique. First, there is conducted general solution of free vibration problem for uniform beam element with arbitrary number of cracks that allows one to simplify the transfer matrix for cracked multistep beam. The transferring beam state needs to undertake only at the steps of beam but not through crack positions. Such simplified the transfer matrix method makes straightforward to investigate effect of cracks mutually with cross-section step in beam on natural frequencies. It is revealed that step-down and step-up in beam could modify notably sensitivity of natural frequencies to crack so that the analysis provides useful indication for crack detection in multistep beam. The proposed theory was validated by an experimental case study

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.

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.

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.

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.

An Open Crack Model for Vibration Simulation of Beam Structures by Transfer Matrix Method

2007 ◽  
Vol 348-349 ◽  
pp. 893-896
Author(s):  
Ke Ming Wang ◽  
Song Xiang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Crack Detection ◽  
Vibration Monitoring ◽  
Crack Model ◽  
Open Crack ◽  
Element Analysis ◽  
Beam Structures ◽  
Stiffness Reduction

Crack detection of critical beam structures such as bridges and aircraft wings by vibration monitoring is based on understanding how a crack affects the vibration characteristics of a beam structure. Transfer matrix method is a convenient, effective, and hence widely used approach to beam vibration analysis, but a crack in the beam makes this method ineffective. This paper proposes an open crack model that simulates the local stiffness reduction effect of a transverse crack by a rectangular slot to make the transfer matrix method able to analyze vibrations of a cracked beam. The depth of the slot is identical to the depth of the crack, and the equivalent width of the slot is obtained by comparison of stiffness reductions of finite element analysis results and the counterpart transfer matrix method results. Different dimensions of rectangular beams, different crack positions and loading conditions are considered and statistic method is used to improve the generality and accuracy of the model. A calculation example of a cracked cantilever beam is given and the validity of the proposed model is verified with available results of existing models.

scholarly journals Comparative study of direct and inverse problems of cracked beams

2018 ◽  
Vol 149 ◽  
pp. 02015
Author(s):  
Chettah Mahieddine ◽  
Lassoued Rachid
Keyword(s):  
Inverse Problem ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Cracked Beam ◽  
Simply Supported Beam ◽  
Rotational Spring ◽  
Simply Supported ◽  
Cracked Structures

In recent decades, the analysis and evaluation of the cracked structures were hot spots in several engineering fields and has been the subject of great interest with important and comprehensive surveys covering various methodologies and applications, in order to obtain reliable and effective methods to maintain the safety and performance of structures on a proactive basis. The presence of a crack, not only causes a local variation in the structural parameters (e.g., the stiffness of a beam) at its location, but it also has a global effect which affects the overall dynamic behavior of the structure (such as the natural frequencies). For this reason, the dynamic characterization of the cracked structures can be used to detect damage from non-destructive testing. The objective of this paper is to compare the accuracy and ability of two methods to correctly predict the results for both direct problem to find natural frequencies and inverse problem to find crack’s locations and depths of a cracked simply supported beam. Several cases of crack depths and crack locations are investigated. The crack is supposed to remain open. The Euler–Bernoulli beam theory is employed to model the cracked beam and the crack is represented as a rotational spring with a sectional flexibility. In the first method, the transfer matrix method is used; the cracked beam is modeled as two uniform sub-segments connected by a rotational spring located at the cracked section. In the second method which is based on the Rayleigh’s method, the mode shape of the cracked beam is constructed by adding a cubic polynomial function to that of the undamaged beam. By applying the compatibility conditions at crack’s location and the corresponding boundary conditions, the general forms of characteristic equations for this cracked system are obtained. The two methods are then utilized to determine the locations and depths by using any two natural frequencies of a cracked simply supported beam obtained from measurements as inputs. The two approaches are compared with a number of numerical examples for simply supported beams including one crack. The theoretical results show that the accuracy of the Rayleigh’s method to predict natural frequencies decreases for higher modes when crack depth increases. It is also found that for the inverse problem, the transfer matrix method show a good agreement with those obtained from previous works done in this field.

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