Dynamic Study On Elastic Constrained Cable-stayed Shallow Arch Model Of Cable-stayed Bridge

Cable-stayed shallow arch structure is an assumption for the modeling of long-span cable-stayed bridges.The minimum span ratio can be up to 1/100,which can meet the requirements of bridge deck slope specification in bridge design.It is a new cable-stayed bridge composite model.In order to carry out more detailed nonlinear dynamic analysis,and make the cable-stayed bridge model better reflect the nonlinear phenomena in real bridges.We considers the geometric nonlinearity of cable-stayed bridge caused by construction pre－camber and bridge deck drainage in this paper,and the common deformation of the rubber isolation bearing and its appendages at the bearing,established a cable-stayed shallow arch model with elastic rope on both ends.Then,the inplane free vibration and 1:2:2 internal resonance of cable-shallow arch structures are studied.This paper mainly completes the following aspects of the work:(1)A multi-cables-shallow arch model with vertical elastic constraints is established.Then,we derive the equations of in-plane free vibration motion of the multi-cable shallow arch,and the coupling boundary conditions of the cable and the shallow arch,and the mechanical boundary conditions of the vertical elastic constraints at both ends of the front arch are obtained.Based on the classical dynamic equations of cable and shallow arch,the theory of in－plane free vibration of elastic constrained multi-cables and shallow arch is derived by placing shallow arch in the coupling section of cable and shallow arch.Then the method of separating variables and self-programming are used to solve the eigenvalue problem.At the same time,the corresponding finite element model is established by taking the double-cables-shallow arch as an example,and the frequency and mode calculated by the theory in this paper are compared with the results of the finite element one,so as to verify the correctness of the theory in this paper.(2)The eigenvalue of the double-cable-shallow arch model are studied.The first nine modes of the double-cable-shallow arch model with vertical elastic constraints at both ends are analyzed.The influence of bearing stiffness,shallow arch height,cable sag and cable dip Angle on structural frequency is discussed.(3)The motion equation of double-cable-shallow arch is simplified by multi-scale method.The nonlinear motion equation and the corresponding boundary conditions of the cable-stayed shallow arch with vertical elastic constraint at both ends under the external excitation are established by applying the vertical uniform load on the cable-stayed shallow arch,and the motion equation and boundary conditions of the cable-stayed shallow arch are dimensionless.Then the Galerkin method is used to completely discrete the motion equation and the average equation of shallow arch and cable in polar coordinate system is derived by means of the multi-scale perturbation method.The secular term in the modulation equations of 1:2:2 internal resonance is extracted by set the secular term equal to zero.(4)The structure was analyzed by 1:2:2 internal resonance.Riks method is used to solve the modulation equation,and the frequency-response curves and force-response curves of the system are obtained.The fourth order RungeKutta method is used to integrate these modulation equations to verify the results.The nonlinear dynamic response of cable-stayed shallow arch with vertical elastic support is analyzed.The effects of the external excitation amplitude,the supporting stiffness at both ends and the tuning parameters on the frequency-response curves of the shallow arch and the stay cables are investigated.At the same time,the influence of external excitation amplitude,support stiffness and different cable tuning parameters on the force-response curves of shallow arch and cable is studied.