Study On Stochastic Dynamic Analysis Method Of Coastal Cable-stayed Bridges Under Complex Excitations

Coastal cable-stayed bridges are generally located in a complex environment,and are subjected to single action or various actions,such as strong wind,strong waves and seismics,during the construction and service.Recently,rare research has been conducted on the wind-wave model,and the studies on the linear or nonlinear random response of coastal cable-stayed bridges subjected to single or combined actions.To guarantee the safety and reliability of coastal cable-stayed bridges which are important parts of lifeline engineering,and to refine the design theory of coastal cable-stayed bridges,the stochastic dynamic analysis method of coastal bridges under complex excitions is developed.The main research work and creative conclusions are as follows:(1)A wind-wave power spectrum model is established.The quasi-laminar flow model is used to derive the theoretical solution of wind-induced wave energy.The measured solution of wave energy is obtained and calculated by NDBC.Then the statistical model of wind speed,wave height and wind-wave energy contribution rate is proposed,and the wind-wave power spectrum model is established.Stochastic dynamic analysis of a coastal cable-stayed bridge subjected to wind and waves is then carried out.The results show that the wind-wave power spectrum model can be used for the stochastic dynamic analysis of structures in shallow water subjected to wind and waves.The example shows that the wind-wave correlation causes the axial force of the underwater structure of the pylon and the X-moment of the pylon to increase by 19.7% and 28.6%,respectively.(2)A stochastic analysis method for coastal cable-stayed bridges under combined actions of multi-dimensional multi-point seismic and waves is established.The Morison equation,radiated wave theory and diffraction wave theory are used to solve dynamic water pressures and wave forces of the pile foundation and cap,respectively.The traveling wave effect,spatial coherence effect and local field effect are considered.The Monte Carlo method is used to calculate the response when considering and not considering the nonlinearity of the loads.The applicability of the proposed method is verified by comparison.The influence of hydrodynamic pressures and wave forces on the root mean square of random seismic response of underwater structures is analyzed.The results show that the proposed method can consider the randomness of excitations and calculate the random response of cable-stayed bridges under combined actions of seismic and waves.The increase of longitudinal internal force of the underwater structure is caused by the additional mass of hydrodynamic pressures.The influence of hydrodynamic pressures and wave forces on the seismic response of the underwater structure changes with the site conditions.When the seismic input energy is distributed in the high frequency domain,the hydrodynamic pressures and wave forces have greater influence on the underwater structure.The example shows that the longitudinal shear force can increase by more than 20%.(3)An efficient stochastic simulation method for multi-degree-of-freedom(MDOF)nonlinear structures based on reduced order model is established.The modal selection criterion by the strain energy is proposed.The modal nonlinear coefficient is solved by finite element software.The nonlinear system governing equation based on the reduced order model is established under modal coordinates.Combined with the equivalent excitation method and Newmark-? integration method,the efficient stochastic simulation of MDOF nonlinear structure is realized,and the stochastic dynamic analysis under different excitations is carried out for three typical models.The results show that the proposed method can be applied to MDOF nonlinear structures.Compared with traditional stochastic simulation methods,this method can significantly improve the computational efficiency and has good computational accuracy.The average calculation efficiency increases by 20.3 times.The nonlinear contribution mode selection should be added.The absolute value of the average relative error decreases from 18.9% to 6.8%.(4)A stochastic non-stationary wind and wave synchronization simulation method is established.The nonlinear stochastic response of coastal cable-stayed bridges under various complex excitations is studied.In order to consider the wind-wave correlation,based on the wind-wave power spectrum model,the stochastic non-stationary wind and wave synchronization simulation method is established based on harmonic synthesis method and evolutionary spectrum theory,and the method is then verified.Based on the degradation model,the response of cable-stayed bridges under wind excitation,wind-wave excitation,seismic excitation and combined excitation of seismic and wave.The nonlinear stochastic response of coastal cable-stayed bridges under various complex excitations is studied.The results show that the proposed method can simultaneously consider the non-stationary characteristics and wind-wave correlation,and realize the stochastic non-stationary wind and wave synchronous simulation with good simulation accuracy.The geometric nonlinearity causes the buffeted displacement of the beam increasing slightly,the maximum increase is only 4.9%.Considering the wind-wave correlation,the geometric nonlinearity further increases the displacement of the beam,the axial force of the superwater structure and the X-moment of the underwater structure,but the maximum increase is only 2.5%.Geometric nonlinearity has significant influence on the displacements of the beam under seismic excitation,and has the greatest influence on the longitudinal displacement.The impact on longitudinal displacement is 10.6%,but no influence on pylons and piers.