Piecewise-Fitted Formula for Cable Force Identification Considering Bending Stiffness, Sag, and Inclination
Publication: Journal of Bridge Engineering
Volume 28, Issue 7
Abstract
The identification of cable forces plays an important role in the construction, vibration control, and health monitoring of cable structures. In practice, cable vibrations are mainly affected by the coupling of bending stiffness, sag, inclination, and boundary conditions, so it is difficult to establish an explicit functional relationship between frequency and cable force through the vibration method for facilitating application to engineering. To overcome this difficulty, the explicit expression of the frequency of the cable considering bending stiffness, sag, and inclination is derived for the first time and a novel cable force identification method for determining the piecewise-fitted formula (PFF) according to the cable parameters is proposed. The paper first reviews the cable force identification formulas based on cable frequencies. Then, the theoretical analysis model and differential equation of cable vibration considering the aforementioned factors are established. Based on these derivations, the explicit general formula of cable force identification based on fundamental frequency is derived. Next, according to the cable parameters, the value ranges of two nondimensional parameters characterizing the bending stiffness and sag of cables are divided to fit the corresponding coefficients of the PFF. Finally, numerical simulation and experimental data show that the PFF is more accurate and applicable than the existing formulas. This method can be conveniently applied to the field detection and online monitoring of cable forces.
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Data Availability Statement
All data, models, or codes generated or used during the study are available from the corresponding author by request.
Acknowledgments
This research work was jointly supported by the National Natural Science Foundation of China (Grant Nos. 52250011, 52078100, and 12002224) and the Fundamental Research Funds for the Central Universities (Grant Nos. DUT22ZD213 and DUT22QN235).
Notation
The following symbols are used in this paper:
- A
- sectional area of the cable;
- d
- sag at the midspan of the cable;
- ds
- arc length of the cable differential segment;
- E
- elastic modulus of the cable;
- g
- gravitational acceleration;
- H
- chordwise component of the cable force;
- h(t)
- dynamic increment of the cable force in the x-direction;
- I
- section moment of inertia of the cable cross section;
- Le
- effective length of the cable;
- l
- cable length;
- mass per unit length;
- q(t)
- modal coordinate for the cable vibration response;
- T
- axial force of the cable;
- u
- longitudinal components of the in-plane motion;
- v(x, t)
- in-plane lateral displacement caused by vibrations;
- w
- out-of-plane displacement component;
- y(x)
- static deflection caused by the own weight of the cable;
- θ
- inclination angle of the cable;
- λ2
- nondimensional parameter characterizing the sag of the cable;
- ξ
- nondimensional parameter characterizing the bending stiffness of the cable;
- τ
- dynamic increment of the cable force;
- φ(x)
- modal shape of the cable;
- ωn
- natural angular frequency of the nth order;
- natural frequency of a cable according to the string theory;
- approximate value of a nondimensional angular frequency; and
- theoretical value of a nondimensional angular frequency.
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Published In
Journal of Bridge Engineering
Volume 28 • Issue 7 • July 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Oct 25, 2022
Accepted: Mar 1, 2023
Published online: Apr 21, 2023
Published in print: Jul 1, 2023
Discussion open until: Sep 21, 2023
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Cited by
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