Application Study On Structural Calculation Method Of Bridge Based On The Transfer Matrix Method

The transfer matrix method,rising gradually with the development of multi-body system dynamics,is a structural calculation method,which has been applied widely in structure mechanics and dynamics system.When using the transfer matrix method,the global dynamics equations are unnecessary and the orders of involved matrices are decreased significantly.In the present work,based on the existing technique and application results involving the transfer matrix method,the transfer matrix analysis theory for bridge structures,is investigated systematically.Taking MATLAB as the platform,the numerical simulation program of the transfer matrix method is developed for bridge-structure computation.This study includes the following main parts:(1)The global transfer matrices of several typical bridge types are derived,which are composed of multi-classification substructures.Considering the geometric irregularity of contact surfaces between bridges and external objects,the linear transfer matrix method for dynamic time-history analysis of bridges is derived by applying the modal superposition method and the Newmark-beta integral.By numerical examples and compared with the finite element method,it has been verified that the proposed linear transfer matrix theory is effective for dynamic characteristics and dynamic time-history analysis of bridges.(2)The static transfer matrix of cable is derived from the tangent stiffness matrix.The transfer-matrix model of a suspension bridge at cable finished stage is established based on the transfer relations between the state vectors of structural boundaries.In order to adjust the anchor span cable forces and the saddle angle of suspension bridge in security and speediness,the transfer matrix theory is developed.And then taking a building suspension as the research object,the effectiveness of the proposed algorithm is demonstrated for the construction control of cable supported bridge.(3)Taking into account the time-variant and non-periodic effects,the discrete time transfer matrix of Timoshenko beam is derived by combining Newmark-beta integral method.A methodology of the dynamic analysis for beam-bridge is proposed,with regard to both moving excitation and seismic loading.Taking a three-span rigid frame bridge as an example,the reliability and high computational efficiency of the proposed algorithm are verified by the numerical results as compared to the finite element method.(4)Based on the discrete time transfer matrix of Timoshenko beam,two algorithms for vehicle-bridge coupled vibration analysis,named coupling method and separation iteration method,are established independently.And then the dynamic time-history analysis is finished for a three-span rigid frame bridge under simplified moving vehicle group.It has been verified that the proposed methodology is effective and efficient,compared to the extensive analysis by means of the finite element method.(5)Taking a simplified cable-beam composite structure as the research object,its dynamic calculation model is established based on the discrete time transfer matrix method.By means of the developed numerical simulation program,the dynamic analyses of the cable-stayed bridge under train loading and seismic excitation are separately implemented.According to the study,the discrete time transfer matrix can be successfully applied to the bridge-vehicle coupling analysis and seismic response analysis of modern large-span bridges,which further provides a new research way for improving the calculation efficiency of numerical simulations involving modern large-span bridges.