The Whole Process-based Dynamic Response And Coupled Vibration Analysis Of Extradosed Cable-stayed Bridge

The extradosed cable-stayed bridge,recently introduced this century,has been recognized for its outstanding mechanical properties,high aesthetic values,flexible span layout and good economical properties.Because of these characteristics,this young bridge type has been widely adopted for traffic junctions,river crossing and mountain road bridging,despite its short history.However,the extradosed cable-stayed bridge is soft by nature,so the characteristics of its vibration and dynamic response during the cantilever construction and final operation have always been the focus of experts and scholars.One important fact is that when people drive vehicles over the bridge,internal factors like rough road surface work together with external factors like wind force and result in coupled vibration between vehicles and the bridge,which can be a fatal safety issue for operation.Therefore,for the construction to operation of extradosed cable-stayed bridge,it is of both theoretical and practical value to research the dynamic characteristics embedded in the whole process and the dynamic response of the coupled vibration between vehicles and bridge.Based on the finite element method and structural dynamics,author leveraged the traditional spring mass system to set up vibration equation models for the bridge and typical three-axis nine degree-of-freedom vehicle,and couple them according to force balance and displacement coordination conditions.In order to calculate the coupled relationship in concern,I utilized the mode synthesis superposition method and the implicit Newmark-β numerical calculation method as a combination to program,simulate,and ultimately solve the coupled in MATLAB.Taking the Jinghang Canal Bridge as the subject,author established a grillage model for the entire process of its construction,from cantilever casting to operation,in accordance with the shear flexible grillage theory in Midas/Civil.The topics he analyzed and calculated include the first ten natural vibration characteristics of the main beam and pylon in the operation stage,the change of the main beam’s first three natural vibration frequencies with the increase of the cantilever length in the cantilever casting construction stage,and the influences of the mass of hanging baskets,possible asymmetric lateral load or vertical impact load on the dynamic characteristics of the main beam in construction.The results show that the basic vibration mode of Jinghang Canal Bridge is the positive symmetrical vertical bending of the main beam.This structure gives its main beam large rigidity against horizontal lateral displacement,but the modes are relatively dense,so the excitation of a dynamic load may cause strong vibration of multiple modes in a certain frequency range.During the construction,hanging baskets or possible asymmetric load turns out to have limited influence on the vibration characteristics of the main beam,but in the case that the main beam is in its maximum double cantilever state,the vertical displacement on the end of cantilever and the bending moment at the bottom of the cable tower are amplified by 1.75 and 2.05 times respectively given the possible vertical impact load,which is very sensitive.Given the fitting formula of the road power spectral density function in Chinese standard GB / T 7031-2005,author adopted the harmonic superposition method to simulate road roughness curves of grade A,B and C roads where vehicles are moving in the speed of 36km/h to 144km/h.Taking the surface roughness into consideration,His program in MATLAB solved the maximum static and dynamic effect values of Jinghang canal bridge,analyzed and calculated different influences exerted by seven speeds(36km/h,54km/h,72km/h,90km/h,108km/h,126km/h and 144km/h)and three road grades(A,B and C)on the dynamic amplification coefficient and impact coefficient of Jinghang canal bridge,and compared the results with those calculated through formulas given in JTG D60-2015,the current general code for design of highway bridges and culverts.The results show that dynamic amplification coefficient or impact coefficient is not linear correlated with vehicle speed,in fact,their relationships are rather more complicated.However,dynamic amplification coefficient and impact coefficient are observed to monotonously increases with the road roughness factor,so the worse the road condition or road grade,the greater the dynamic amplification coefficient and impact coefficient.When the road grade is A or B,the dynamic amplification coefficient and impact coefficient calculated are basically consistent with standard values,but the standard values are generally low when the road grade is reduced to C.To sum up,some defects still exist in the formula of relevant impact coefficient given by the code of China.It is not comprehensive enough to cover all possible situations,so further optimization and improvement are needed in the future.