Study On Dynamic Characteristics Of Thin-Walled Curved Box Girder With Shear Lag Effect

Based on the thin-walled curved bar theory and finite element method,a finite segment approach in structural dynamic analysis of the thin-walled curved box girder considered the shear lag effect is presented.Based on the principle of energy method,a set of dynamic analysis theory and calculation method suitable for shear lag effect of thin-walled curved box girder are established,and the variation law of shear lag effect in dynamic problem is discussed.This method enriching and developing the theories of the dynamic system,and laying a foundation for the study of the shear lag of thin-walled curved box girders in dynamic analysis.The major achievements of this paper are as follows:1.Based on the thin-walled curved bar theory and finite element method,a finite segment approach for free vibration analysis of the thin-walled curved box girder is proposed.The homogeneous solution of the differential equation of the static control of the thin-walled curved box girder is taken as the peak function in the displacement mode of the curved beam element.Based on the Hamilton principle,the free vibration equation of the curved beam element is derived,the solution of the free vibration frequency and the corresponding vibration mode are obtained and compared with the analytic solutions,which are in good agreement.On this basis,the influence law of the radius of curvature on the natural frequency of thin-walled curved box beam for several common Structural forms(simply supported,cantilever,continuous)is further explored.2.The displacement function of longitudinal shear lag warping of thin-walled curved box girder wing plate is assumed and the static control differential equation of curved box girder with bending,torsion and shear lag coupling is established.The homogeneous solution of static shear lag control differential equation is taken as the peak function of the beam segment curved beam element displacement mode.The free vibration equation of curved beam element is deduced by Hamilton principle,and the element stiffness matrix and element mass matrix are obtained.The question of natural frequencies for curved box beam is converted to the generalized eigenvalueproblem to deal through the combination of matrix,the natural frequency and vibration mode of the thin-walled curved box girder considered the shear lag effect can be obtained.3.The displacement mode of the curved beam element of the thin-walled curved box girder section under the forced vibration is proposed,the shape function of the displacement mode is the shape function under the free vibration in this paper.the forced vibration equilibrium differential equation of the curved beam element considered the shear lag effect is deduced by the energy method principle.The time history change of displacement,stress and shear lag coefficient of thin-walled curved box girder under the forced vibration are solved by using Newmark direct integration method through external load discretization,the dynamic response results under the forced vibration are obtained.4.Based on the finite element technology,the finite element model of thin-walled curved box girder considered the shear lag effect is established by using the plate element in MIDAS/FEA,the dynamic characteristic and dynamic response of curved box girder are calculated,then compared with the theoretical results,which verify the correctness of the method in this paper and it has good accuracy.5.Based on theoretical and numerical research,the influence of various parameters on the shear lag effect of curved box girder combined structure form and structure dimension of thin-walled curved girder are systematically studied,which reveals the general law of vibration characteristics and dynamic response considered shear lag effect,some important conclusions are obtained.According to the main influence parameters,some diagrams which can be used for engineering reference have been compiled,which have certain practical value.