A Calculation Method for Lateral Vibration Frequency of Cables with Arbitrary Boundary Constraints

Abstract

The invention discloses a method for solving lateral oscillation frequencies of inhaul cables under any boundary constraint condition. The method comprises the following steps of: firstly establishinga lateral oscillation functional of an inhaul cable; solving the lateral oscillation functional of the inhaul cable by adoption of a Chebyshev series method so as to obtain a lateral oscillation circular frequency of the inhaul cable; and finally calculating a lateral oscillation frequency f of the inhaul cable through a formula f=<omega> / 2<pi>. In the process of constructing the lateral oscillation functional, boundary constraint parameters at two ends of the inhaul cable are set; after boundary constraint conditions at the two ends of the inhaul cable are obtained, the boundary constraint parameters at the two ends of the inhaul cable can be obtained to be used in the lateral oscillation functional of the inhaul cable; and in the process of solving the lateral oscillation functional ofthe inhaul cable by adoption of the Chebyshev series method, a feature matrix equation of the inhaul cable is obtained through selecting a proper inhaul cable lateral oscillation displacement distribution function, and the lateral oscillation circular frequency of the inhaul cable is obtained through solving the feature matrix equation. The method has the advantages of being relatively small in error and relatively high in precision on the basis of a simple solution process.

Description

technical field [0001] The invention relates to a method for solving the lateral vibration frequency of a cable, in particular to a method for solving the lateral vibration frequency of a cable under arbitrary boundary constraints. Background technique [0002] As the main force-bearing part of the bridge, the stay cable plays a vital role in the safety of the bridge. In the process of bridge construction and operation, it is necessary to obtain the actual cable force of the cable to judge whether the bridge is in a safe state. Since there is a specific relationship between the cable force of the cable and its lateral vibration frequency, the cable force of the cable can be obtained indirectly by converting its lateral vibration frequency. The transverse vibration frequency is converted to obtain the cable force of the cable. [0003] The existing methods for solving the lateral vibration frequency of the cable are mainly based on the boundary constraints at both ends of t...

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Problems solved by technology

When the boundary constraints at both ends of the cable are selected as fixed supports at both ends, it is necessary to solve the transcendental equation of the hyperbolic function to obtain the transverse vibration frequency. Although this method has high accuracy, the solution process is very complicated

When the boundary constraints at both ends of the cable are simply supported, the frequency can be calculated using a mature frequency solution formula. The solution process is simple, but in this solution method, the boundary constraints at both ends of the cable are regarded as an ideal state , but in practical application, the end of the cable is connected with the main beam and the cable tower through the anchorage. , there is a large error between the idealized boundary constraint conditions at both ends of the cable and the actual boundary constraint conditions at both ends of the cable, which leads to a large error in the calculated lateral vibration frequency of the cable, and then through the conversion of the lateral vibration frequency of the cable to get The cable force error of the cable is also large

When the boundary constraints at both ends of the cable are selected as one end is fixed and one end is simply supported, it is also necessary to solve the transcendental equation of the hyperbolic function, and the solution process is still very complicated

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