scholarly journals Critical Loads of Variable Cross-Section Compressive Rods Based on Precise Integration Method and Transfer Matrix Method

2017 ◽  
Vol 06 (02) ◽  
pp. 101-113
Author(s):  
蝶 王
Keyword(s):  
Transfer Matrix ◽  
Cross Section ◽  
Transfer Matrix Method ◽  
Critical Loads ◽  
Matrix Method ◽  
Integration Method ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Precise Integration ◽  
Precise Integration Method

scholarly journals Torsional vibration of suspension bridge with a variable cross section

1981 ◽  
Vol 3 (2) ◽  
pp. 22-26
Author(s):  
Nguyen Van Tinh
Keyword(s):  
Computer Program ◽  
Transfer Matrix ◽  
Cross Section ◽  
Cross Sections ◽  
Torsional Vibration ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Suspension Bridge ◽  
Variable Cross Section ◽  
Variable Cross

The transfer matrix method to torsion’ al vibrations of a suspension bridge with variable cross sections is reported. The method described above is particularly suitable for implementing an efficient computer program. A numerical example is also givens.

A Transfer Matrix Method for Free Vibration Analysis of Tapering Pipe

2019 ◽  
Author(s):  
Qingna Zeng ◽  
Fenggang Zang ◽  
Yixiong Zhang ◽  
Donghui Wang
Keyword(s):  
Bessel Function ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Low Frequency ◽  
Free Vibration Analysis ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Nature Frequency ◽  
Discrete Uniform

Abstract In this paper, theoretical solutions of free transverse vibration for tapering pipe considering variable cross section have been investigated using Bessel function in low frequency domain. Natural frequency was calculated by transfer matrix method (TMM) based on an accurate theoretical model. The effectiveness and validity of TMM with Bessel function was confirmed in comparison with TMM of discrete uniform pipe and Finite Element Method. Furthermore, dimensionless model was proposed to avoid the singularity, instability and overflow in calculation. The geometry effect, such as tapering ratio, thickness-radius and length-radius ratio influence on the nature frequency was explored. The present study was envisaged to provide useful insights for dynamic analysis of pipeline systems.

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.

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.

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