| More and more large-span structures and bridges are used in the construction of themotherland with the rapid economic development of our country in recent years because of the merit of simplicity,beautiful appearance,easy to assemble and so on.The common characteristics of these structures are the main bearing truss components,such as the hollow rod of space truss structures and cable of suspension bridges.The indispensable way to ensure the safety of structure,life and property is monitoring the axial force of these bars.There are some methods can identify the axial force of different bars under certain conditions such as hydraulic method,magnetic flux method,frequency method and so on.But they cannot be apply to short bars with high frequency and the precision are affected by bar length,boundary constraint and cross-section.As the Timoshenko beam theory is applied to the recognition,the method which has attracted more and more scholars pay attention to not only improves the identification precision but also expands its application scope.But previous research mostly on the basis of thin plate,without considering the second spectrum’s influence of Timoshenko beam theory and using it in practical engineering structure.Therefore,this paper tries to further explore the modified coefficient in the modified Timoshenko beam theory.The experimental research of axial force identification has been done in hollow and circular section bars of practical engineering.First,Reissner energy method is used to deduce Modified Timoshenko beam theory’s partial differential vibration equation.The conclusion that wave velocity in beam increases with the increasing of wave number to shear wave velocity is obtained by researching the wave velocity and wave numbers of Timoshenko beam theory.The wave velocity and circular frequency’s relationship is obtained by the conclusion that wave number in beam increases with the increasing of circular frequency.Modified Timoshenko beam theory only has one velocity and one frequency spectrum which can avoid the influence of the second wave velocity and frequency spectrum.The first frequency spectrum of Timoshenko beam theory is used to modify Modified Timoshenko beam theory’s frequency spectrum.A more precision modified coefficient which calculated by change wave velocity instead of the fixed shear wave velocity is introduced for general beam partial differential vibration equation.And it is concluded that the bending deformation of beam section during low frequency has a small influence on modified coefficient,the shear deformation during high frequency has a greater influence on modified coefficient.Consistent mass matrix,stiffness matrix and external force matrix of Modified Timoshenko beam theory is deduced based on Hamilton principle.Also the axial force identification equation based on Modified Timoshenko beam theory is deduced.Free vibration of rectangular cross-section bar with axial force is simulated by MATLAB to get circular frequencies and modal information for axial force identification.Results show that the new finite element model and axial force identification equation have good accuracy.Then,axial force identification of hollow section,hollow circular section and hollow square section bars are studied on the basis of new finite element and axial force identification equation.The modal order parameters,sensor location,length of bar,bar sectional size and coefficient of shear deformation which influence accuracy of axial force identification are mainly considered.Solutions for multi-valued problems of axial force identification are proposed.Later then,the effectiveness of the proposed method is verified by doing experiment on the same size bars.Finally,experiments of hollow steel truss structure are performed.The accuracy and applicability in practical engineering of the proposed method is verified by comparing the identification results with Fiber Bragg Grating and strain gauges measured results. |
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