Analytical solution of harmonic travelling waves in N-segment strings

A closed-form solution for the response of waves travelling in N-segment taut strings subjected to harmonic displacement or force excitation at the end is derived by a novel method. The reflection and transmission of the travelling wave caused by the property changes of string segments and the wave...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2000-09, Vol.456 (2001), p.2115-2126
Main Author: Hsueh, Wen-Jeng
Format: Article
Language:English
Subjects:
Boundary conditions
Frequency response
Harmonic excitation
Harmonic Travelling Wave
Harmonics
Research Article
Sine function
String Wave
Two-Way State-Flow
Vibrating Segmented String
Vibration
Wave excitation
Wave propagation
Wave reflection
Waves
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Summary:A closed-form solution for the response of waves travelling in N-segment taut strings subjected to harmonic displacement or force excitation at the end is derived by a novel method. The reflection and transmission of the travelling wave caused by the property changes of string segments and the wave reflection at the boundary are considered. In this study, two new two-way state-flow graph models for describing the dynamics of the wave propagation in each segment of the string with free and fixed ends are developed. According to the developed models, the response of the wave in the entire string is derived by a topology method. Moreover, the frequency equation of the N-segment string can be obtained from the derived formulae. Since these derived formulae are expressed as analytical and concise forms, it is convenient to directly apply them to the numerical computation and advanced research without solving equations or other operations.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2000.0605