Free Vibration Characteristics Analysis Of Small And Medium Span Cracked Beam Bridges Considering Bridge-vehicle Interaction

It's known that cracks often appear in beam-type bridges,which will inevitably lead to the change of the stiffness.While the physical properties are changed and the dynamic characteristics including modal frequency and shapes will be changed.which provides the theoretical basis for the structural damage identification based on the dynamic characteristics.As the dynamic load test has the advantages of short test time,strong objectivity,no need for closing traffic and finding the hidden disease,the dynamic characteristics of bridge structures have been widely applied to structural damage identification and condition assessment so far.Thus,the accuracy of the dynamic characteristics directly results in the quality of structural damage identification,which is not determined by the test method.The traffic on bridges and the ambient temperature will lead to variation in dynamic characteristics,and sometimes this variation will completely cover the characteristics variation caused by structural damage.Therefore,it is necessary to consider these variations caused by external factors in structural damage identification and condition assessment.For small and medium beam-type bridges,traffic-induced excitation is often adopted to get satisfactory results of signal to noise ratio in the dynamic test.In general,traffic-induced excitation includes vehicle bump test and vehicle travelling test.In any case,the test dynamic characteristics are actually the characteristics of the vehicle-bridge coupling system based on the main vibration of bridges,including the influence of vehicle.Cracks often appear in beamtype bridges and the mechanism how cracks affect dynamic characteristics has not yet formed a unified understanding.In the dynamic test of structural damage identification,the test dynamic characteristics include the influences of vehicle and cracks.The dynamic characteristics calculation method of beam-type bridges under the effects of vehicle and crack is established to find out the mechanism how cracks and vehicles affect dynamic characteristics,which is the foundation of the structural damage identification based on the dynamic characteristics.With the supports of the National Natural Science Foundation of China “Natural frequency analysis of small-to-medium span bridges considering vehicle and temperature coupling” and seed fund project of Jilin University “Natural frequency analysis of small-tomedium span bridges under vehicles”,the main research has been carried out as follow:1.According to the continuous deformation and moment equilibrium at intermediate supports,the dynamic characteristics equations of continuous bridge under the vehicles by usiing the numerical assembly method based on the equation of motion and displacement function for vehicle and bridge.Then,the dynamic characteristics equations of non-uniform simply supported bridge under the vehicles could be formed by the transfer matrix method.Numerical simulation is presented to verify the proposed method and discuss the influence of vehicle.2.Firstly,based on the simulation of crack using massless rotational spring,the transfer relationship of modal shape function at cracks is obtained.Next,according to the equation of motion for vehicle,the dynamic characteristics equations of cracked simply supported bridge under the vehicles could be established and solved.Finally,through some numerical examples,the influences of vehicle and crack on the dynamic characteristics are discussed.3.Based on the simulation of vehicle using single degree of freedom of spring-mass system,an equivalent model of a uniform continuous beam with an arbitrary number of cracks and spring-mass systems is established firstly.According to the improved method,the mode shape functions of a single-span uniform beam are derived by using fundamental solutions and recurrence formulas.Next,the equations of motion of spring-mass systems and the compatibility conditions at intermediate supports are used to establish the dynamic characteristics equations of continuous beam with an arbitrary number of cracks and springmass systems.Numerical simulation on continuous beam is carried out and discussed in this paper.