Research On Dynamic Response Of Floating Pier Under Wave Action

In bridge engineering,floating bridges are often used when crossing deep water or soft seabed waters.The floating pier,as the main structure directly contacting with water,will withstand the wave action that cannot be ignored in waters,which poses a challenge to the construction of floating bridges.For the floating bridge,one of the key problems limiting its wide application is how to improve the dynamic stability of the floating pier under waves.In view of the above problem,this paper takes the floating pier in the curved floating bridge as the research object to research the dynamic response of the floating pier under the constraint of the curved beam.At the same time,in order to improve the dynamic stability of the floating pier,this paper puts forward the measures of installing heteroaxial heave plate at the bottom of the floating pier and installing submerged annular rippled breakwater at the bottom of the water.Based on the potential flow theory,the interaction model of heteroaxial double-layer cylinder structure and wave is established,and the interaction model of floating pier-submerged annular rippled breakwater structure and wave is established.The main research contents,methods and conclusions are as follows:(1)Different from other floating structures,the superstructure of the floating bridge has a constraint effect on the floating pier,and the curved floating bridge can greatly reduce the horizontal displacement of the floating pier due to the arch effect,which has been widely used.In order to obtain the dynamic response of floating pier under the constraint of curved beam,a theoretical model of multi-floating pier curved floating bridge is established.Among them,the wave excitation force and hydrodynamic coefficient of the floating pier in the curved beam bridge are obtained by the potential flow theory.The constraint effect of the curved beam on the floating pier is transmitted through the hinge,and the response amplitude operators(RAOs)of the floating pier is obtained.The influence of curvature radius and stiffness of curved beam on RAOs is analyzed.(2)When the upper-and lower-layer cylinders of the two-layer cylindrical structure have different axes due to the manufacturing process or some functional requirements,its diffraction effect under waves will be different from that of the symmetric structure,and the wave force on itself needs to be studied.The mathematical formulas of the wave action of the heteroaxial double-layer single-cylinder structure are derived based on the potential flow theory,and the influence caused by the different axes of the upper and lower double-layer cylinders is analyzed.Among them,the heteroaxial double-layer cylindrical structure is the structure of the upper cylinder penetrating the water surface and the lower single cylinder embedded in the bottom.The computational domain is divided into two regions,and their respective coordinate systems are established to describe the velocity potential function.The interface function between the regions is processed by Fourier series,and the velocity potential function of each region is solved by matched eigenfunction expansion method(MEEM).Finally,the wave force on the surface of the structure is obtained.After verifying the accuracy of this model with other literature and numerical simulation,the influence of different axis of the structure is analyzed.It is found that compared with the coaxial structure,the heteroaxial structure can make the wave force smaller in some wave number ranges.(3)To reduce the dynamic response of the floating pier under waves,the installation of the heteroaxial heave plate at the bottom of the floating pier is proposed.Based on the research content(2),the mathematical model of the wave interaction of the floating pier-heteroaxial double-layer floating cylindrical structure is established.The wave diffraction and radiation problems of the structure are solved,and the wave excitation force,added mass and radiation damping coefficient of the structure are obtained.On the basis of the research content(1),the RAOs of the floating pierheteroaxial double-layer floating cylindrical structure are obtained after considering the constraint effect of the curved beam.The respective cylindrical coordinate systems are established in the axis of the upper and lower cylinders,and the water area is divided into three regions.The boundary conditions corresponding to different problems are given.The MEEM and Fourier series are used to solve the semi-analytical solution of the velocity potential in different regions of the wave diffraction and radiation problems,and finally the wave excitation force and hydrodynamic coefficient of the structure are obtained.After comparing with the boundary element software,the influence of the relative distance and angle between the upper-and lower-layer cylinder axes on the wave force and hydrodynamic coefficient of the structure is analyzed,and the effect of the height ratio of the upper-and lower-layer cylinder is discussed.Finally,considering the constraint of curved beam on floating pier,the RAOs of floating pier are investigated.(4)For the influence of submerged annular ripple breakwater on the dynamic response of floating pier,a theoretical model of the interaction between cylindrical floating pier and wave constructed around submerged annular ripple breakwater is established,and the RAOs of floating pier is obtained after considering the constraint of curved beam.Firstly,the domain is divided into four regions: the exterior region,the mild-slope region,the gap region,and the interior region.The velocity potential expression of the mild-slope region where the breakwater is located is established by modified mild-slope equation(MMSE).Then,the semi-analytical solutions of the wave diffraction and radiation problems of the floating pier are derived by using MEEM.After the accuracy of the mathematical model is ensured by comparative verification and convergence analysis,the ripple amplitude,length and the space between floating piers and breakwater are analyzed.