Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media

Ultrasonics ◽  
2001 ◽  
Vol 39 (6) ◽  
pp. 413-424 ◽  
Author(s):  
L. Wang ◽  
S.I. Rokhlin
Keyword(s):  
Wave Propagation ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Anisotropic Media

Analysis of Wave Propagation in Overhead Contact Wire of Trains Using the Transfer Matrix Method

2013 ◽  
Author(s):  
Takahiro Fukui ◽  
Toshihiko Asami ◽  
Tomohiko Ise
Keyword(s):  
Wave Propagation ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Stop Band ◽  
Excitation Frequency ◽  
Pass Band ◽  
Cell Models ◽  
Vibration Properties

In this paper, we propose a method for analyzing the vibration properties of contact wires (trolley wires) using the transfer matrix method (TMM), by treating them as a periodic structure. When the speed of the train increases, self-excitation vibration of the wires may occur. When the trolley wires repeatedly contact and separate from the pantograph, the pantograph is worn by the sparks. Therefore, the vibration of the trolley wires must be kept as small as possible. For such problems, many researchers have proposed vibration analysis of the wires. However, these methods are not suitable for the vibration analysis of wires because of the very complicated wave propagation phenomenon. The TMM proposed in this study is an easy technique for studying wave propagation since the vibration properties can be simplified greatly by handling the smallest unit of repetition of the structure. Using this method, we can identify the frequencies of the vibration-attenuating domain (stop-band) and the vibration-amplifying domain (pass-band). If we can bring the excitation frequency of the wire to the stop-band domain, wear of the pantograph can be reduced. Here, we introduce three cell models; two of them do not take into account the elasticity of the trolley wire, and the other does. Then, we discuss how the stop-band appears in these models.

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