Abstract
A method is proposed to study the dynamic characteristics of cable structures from the perspective of traveling waves based on the modified Timoshenko beam axial tension model. Considering the propagation characteristics of the bending wave in a beam structure, once the frequency response of the three measuring points is measured, the wave component coefficients can be obtained by the least squares method, and then the cable force and bending stiffness can be identified with the aim of minimizing the fitting residual. The accuracy of this method is verified by a numerical simulation experiment of the cable vibration. Compared with the traditional frequency method, this method focuses on the cable force identification of the substructure, so the effect of the shock absorber is invalid. Moreover, the cable force of each position of the cable can be calculated reversely by static analysis with the identified cable force of the substructure, which breaks the concept that the cable force is a single value. Furthermore, the cable force can be identified at each frequency sampling point, reducing the impact of the external disturbance.
Highlights
A method is proposed to study the dynamic characteristics of cable structures from the perspective of traveling waves based on the modified Timoshenko beam axial tension model
Considering the propagation characteristics of the bending wave in a beam structure, once the frequency response of the three measuring points is measured, the wave component coefficients can be obtained by the least squares method, and the cable force and bending stiffness can be identified with the aim of minimizing the fitting residual. e accuracy of this method is verified by a numerical simulation experiment of the cable vibration
Introduction e cable is the core component of the cable-stayed bridge. e accurate identification of the cable force is of great importance in bridge construction and operation. e conventional methods to measure the cable force in civil engineering structures include the pressure gauge method, pressure sensor method [1, 2], wave method, magnetic flux method, and vibration-based method [3]. e frequency method with the widest range [4, 5] depends on the natural frequency of the cable to identify the cable force. us, the accuracy of the method depends entirely on the calculation formula under the condition of an accurate frequency measurement. e taut string model was the first cable model used in vibration-based cable tension estimation methods
Summary
From the Timoshenko beam theory, the shear force Qy, bending moment Mz, and lateral displacement y(x, t) have the following relations: zy. At higher frequencies, the near-field wavenumber solution of the Euler–Bernoulli beam has an infinite increasing trend, which is obviously caused by ignoring the shear deformation and bending stiffness. For the cutoff frequency of the Timoshenko beam, the essence is that only the bending stiffness generated by bending deformation is considered so that the frequency of the fourth power exists in the wavenumber solution. While the rotational inertia caused by shear deformation is considered in the modified Timoshenko beam, the fourth power of frequency in the wavenumber solution is canceled out; the cutoff frequency is avoided [21]
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