Comprehensive Exploration on Sinusoidal and Hyperbolic Components of Mode Shape Functions for Tension Determination of Elastic Cable with Complicated Boundary Constraints

碩士 === 國立雲林科技大學 === 營建工程系 === 105 === Tension determination typically plays the most crucial role in the structural health monitoring of cable-stayed bridges with stay cables, box girder bridges with external tendons, and through-type arch bridge with suspenders. The tension estimation by ambient vi...

Full description

Bibliographic Details
Main Authors: CHEN, SHIN-YI, 陳欣怡
Other Authors: CHEN, CHIEN-CHOU
Format: Others
Language:zh-TW
Published: 2017
Online Access:http://ndltd.ncl.edu.tw/handle/p8a969
Description
Summary:碩士 === 國立雲林科技大學 === 營建工程系 === 105 === Tension determination typically plays the most crucial role in the structural health monitoring of cable-stayed bridges with stay cables, box girder bridges with external tendons, and through-type arch bridge with suspenders. The tension estimation by ambient vibration method has been broadly utilized in practical applications. This approach usually begins with identifying the modal frequencies from the ambient vibration measurements and then employing a pre-determined formula or finite element (FE) analysis to decide the tension. According to the string theory based on the simplified model of a transversely vibrating string with hinged boundary conditions at both ends, the tension of an elastic cable or tendon is conventionally obtained from an analytical formula requiring the identified frequencies together with the given vibration length and mass per unit length. In practical situations, special anchorage systems with rubber constraints are normally installed near the boundaries of a stay cable or suspender and intermediate diaphragms often appear in the application of external tendons to adjust the tendon direction. Such design details definitely result in much more involved boundary conditions and raise a great challenge in deciding an accurate vibration length. For efficiently handling the difficulties associated with complicated boundary constraints, an innovative concept combining the mode shape functions and the modal frequencies was recently proposed by the authors to develop an accurate tension determination method. Although the accuracy of the new method incorporating the mode shape functions has been verified in a variety of practical applications, a question is still raised from time to time about the legitimacy of using an equivalent cable with hinged constraints at both ends to represent the actual case with complicated boundary constraints. Therefore, the current research is aimed to establish a rigorous mathematical foundation for this methodology with more solid derivations and comprehensive analysis. Special efforts are first made in to elegantly derive the frequency equations and mode shape functions for the vibrating cables with various types of boundary conditions. According to these analytical results in terms of elaborately defined dimensionless parameters, it is confirmed that the mode shape functions of the cables with complicated boundary conditions are all dominantly contributed by their sinusoidal components to provide a more convenient option for dealing with the tension than the frequency equations. For systematically evaluating the interference effect of the hyperbolic component near the boundaries to deteriorate the accuracy in tension estimation with the developed method, parametric study is also conducted on the derived mode shape functions in this work. Finally, with the numerical verification analysis and laboratory experiments in the current study to comprehensive certify its broad applicability and exceptional accuracy.