| In recent years,the method of cable force dynamic measurement is widely used in cable force testing.Under the condition of satisfying six assumptions,the traditional string theory formula can be used to obtain more accurate results.The results show that the influence factors such as the sag,bending stiffness and boundary conditions of the cable will cause errors which cannot be ignored.Considering the bending stiffness and simply supported boundary conditions,the internal force identification of cable force has been able to obtain the analytical expression of frequency-cable force.In recent years,many scholars have proposed a variety of practical formulas for calculating cable force considering the bending stiffness under the fixed support boundary conditions through the dimensionless and fitting numerical methods.Most of these methods need to know the bending stiffness value in advance,but due to the internal structure of the cable,the bending stiffness value of the cable cannot be directly measured,so it is difficult to accurately calculate the cable force.On this basis,a new method of cable force without knowing the bending stiffness value in advance is proposed under the boundary condition of fixed support.The main research work is as follows:1.The course of the research on the influence of bending stiffness on the test result of cable force is reviewed.The importance of accurate identification of cable force is stated,the factors affecting the accuracy of cable force dynamic measurement and the research on these factors at home and abroad are listed,and the difficulties in the identification of bending stiffness and the limitations of the existing methods are emphatically summarized.The basic theoretical formula of measuring cable force by vibration method based on string theory and beam theory is explained and derived,and the dimensionless method,separation of variables method and Euler formula are introduced.2.Under the boundary condition of fixed support,the dynamic equation of cable considering bending stiffness is established and derived.Constant tension beam dynamics equation,the paper introduced a concept of beam string than not appear explicitly in the equation of bending rigidity,the dynamic equation of dimensionless thoroughly,generation into the clamped boundary conditions,using the method of separation of variables and mathematical tools such as euler’s formula is deduced clamped beam symmetric and antisymmetric vibration frequency equation,the frequency equation only contains two unknown parameters,analyze the frequency equation,is proposed in this paper,the method of calculating process.3.The finite element model of cable is established,the influence of different factors on cable frequency is analyzed,and the precision of parameter value in this method is determined.By establishing the finite element models of cables with different beam-string ratios and different boundary conditions,the relationships between the natural vibration frequency of cables and the cable length,cable force value,bending stiffness and boundary conditions are analyzed.The cable parameters which are widely used in engineering are investigated and the cable finite element model is established.The value range of the beam-string ratio,the value precision of the data in the table and the application form of the table are determined.4.The calculation method of cable force in this paper is compared with the calculation results of literature formulas considering bending stiffness.To the clamped boundary conditions considering the bending stiffness of cable force calculation and practical formula a lot of research on related literature,select the bending rigidity as unknown parameters for cable force calculation of 4 references,finite element data and measurement data of a bridge cable force calculation and analysis show that the method has high accuracy,the advantages of actual engineering application more convenient. |
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