Dynamic Characteristics Analysis Of Beam-Like Bridges Under The Coupling Effect Of Temperature And Vehicles

Due to the continuously arising of bridge safety accidents,people have made higher demands on the safety of bridges.Damage identification methods based on vibration characteristics of bridges are more and more widely used in the field of bridge health monitoring and damage identification.However,these methods,which have been proved to be effective in theory and experiments have encountered some difficulties in practical application.When the measured modal characteristics of bridges are applied directly to the damage identification and condition assessment of bridges,it has been found that the assessment results have large errors and sometimes even wrong.The reason for this phenomenon is not the damage identification method itself,but the actual structures are often in complex operating conditions and environmental factors.The structural modal characteristics obtained from the test also include the effect of these factors.These so-called indicators that sensitive to structural damage in the damage identification method are also sensitive to the operating environment.Therefore,only by seriously understanding the influence of external factors such as environmental conditions,the structural damage identification method could be truly applied in practice.The existing researches have shown that the effects of temperature and vehicles are the two most important factors that cause structural dynamic characteristics variation.These two factors tend to act on the bridge structure at the same time,and some coupling effects will be generated.Accordingly,it will be a very meaningful and urgent work to analyse the internal mechanism of the effect of temperature and vehicles on bridge modal characteristics,then to establish the vibration equations of the modal characteristics of the bridge under the coupling effect of temperature and vehicles,and to solve the influence rule of temperature and vehicles on bridge modal characteristics obtained from the vibration equations,and finally to eliminate the effect from the measured data to obtain “pure” natural mode of bridges.This paper was founded by the projects of National Natural Science Foundation of China “Research on natural frequency analysis method for the small and medium span beam bridges considering the coupling effect of vehicles and temperature” and “Research on modal parameter identification and damage detection of bridge structure considering temperature effect”.Theoretical and experimental research on the influence of vehicles and temperature on the dynamic characteristics of three types of bridges: simply supported beam bridge,continuous beam bridge and rigid frame bridge were developed.First,the theoretical equations for the dynamic characteristics of three types of bridges under the influence of temperature and vehicles were derived.Then,the variation law of modal characteristics of the bridge under different temperature modes and vehicle parameters was found based on these equations,and the sensitivity parameters of the modal characteristics of the bridge are obtained.Finally,the empirical formula of eliminating the effect of vehicles and temperature was refined from these parameters and laws.The specific works carried out in this paper are as follows:1?An approach for calculating modal characteristics of simply supported beam under the effect of temperature was presented,in which the change of elastic modulus and deflection induced by temperature and shear stiffness of bearing were taken into account.Then,the modal test of a simply supported beam with a rectangular cross-section was carried out and the test results were used to verify the correctness of the proposed method.Through theoretical analysis,it was found that for bridges with small spans and small original deflections,the variation of elastic modulus induced by temperature is the main reason resulting in the changes of modal characteristics of the test beam.When the structural deflection increases,the influence of the deflection induced by temperature and the stiffness of bearing on modal characteristics will be more obvious.From the calculation results of mode shape,one sees that the first three radial modal shapes under different temperature are basically unchanged.However,the tangential and rotational modal shapes have obvious variations.2?The relationship between moment,shear,shear coefficient of cross section of Timoshenko beam and the temperature distribution function of cross section under temperature effect were derived,and a free vibration analysis method for Timoshenko beam carrying several spring-mass systems considering the internal temperature distribution of the structure was proposed.Based on this method,the influence law of different temperature distribution modes and spring-mass system parameters on the dynamic characteristics of Timoshenko beam was discussed.It could be found that the modal characteristics especially frequencies were vulnerable to temperature for RC Timoshenko beam.It was mainly reflected on the effect of temperature on the elastic modulus and shear modulus of concrete,which lead to the variations of the shear coefficient and inertia of moment.The structural frequencies decrease with the increasing temperature,however,the effect of different temperature distribution modes on frequencies is not the same.3?A semi-analytical theoretical analysis method for modal characteristics of rigid-frame bridges with variable cross-section and continuous beam bridges under the effect of temperature was presented.This method can not only easily analyze the inherent mechanism of influences of temperature on the modal characteristics of rigid-frame bridges,but also has high computational efficiency.The results has revealed that the variation of Young's modulus and secondary internal force induced by temperature will both affect the modal characteristics of rigid-frame bridges.The variation of the frequency caused by Young's modulus is greater than that caused by the internal force.However,for the first few frequencies,the variation caused by the internal force could not be neglected.4?The dynamic stiffness matrix of one-half vehicle model was established,and then combined with the dynamic stiffness matrix of the bridge under the effect of temperature to form the characteristic equation of the bridge structure under the coupling effect of temperature and vehicles.For simply supported beam structures,there is a coupling effect of temperature and vehicles on the modal characteristics of the bridge,while the coupling effect is not obvious.For continuous beam bridges,the effect of temperature and vehicles on the frequency of bridges is more complex,and both two effect are relatively large.Only when considering the effects of the two,more accurate bridge modes could be obtained.For rigid-frame bridges,when the temperature and vehicle change,not only changes in the material properties brought about by the temperature,but more importantly,there are effect of secondary internal forces,which both have an impact on the dynamic characteristics of the bridge.5?To better serve the actual project,the author try to eliminate the effects of temperature and vehicles from the tested bridge frequencies.Through the established theoretical model,different vehicle loads(vehicle parameters,vehicle positions),temperature loads,and frequency values under different bridge models were analyzed.Then empirical formulas for frequency variation coefficients were obtained by statistical methods and other mathematical means,which could appropriately remove the effects of temperature and vehicles to obtain the "pure" natural frequency of the bridge.