Research Of Deck Irregularity Excitation On Highway Vehicle-bridge Coupling Random Vibrations

It is well know that bridge roughness irregularity is a main factor which can cause random vibration of vehicle-bridge coupling among many factors which affecting the dynamic response of vehicle-bridge system.Due to varieties of simulate method and randomicity of bridge roughness excitation,there has very evident scattering treated the bridge deck surface irregularity as a time-history sample in order to compute the dynamic responses of vehicle-bridge system.Treated the road bridge as the researched object considering non-stationary road surface random excitation,the project will deal with non-stationary random vibration of vehicle-bridge coupling system such as building model,analysis of algorithm and influencing factor.According to the superiority of the mode superposition,a new numerical algorithm based on precise integration method(PIM)is proposed to solve vehicle-bridge coupling vibration.Cotes algorithm is introduced to solve Duhamel nonhomogeneous term's following the vehicle load regarded as coordinating load in an integration step has been resolved into nodes load through shape function.Taking a moving constant force running on simple supported beam as an example,the veracity of Cotes algorithm has been verified through comparing the analytical solution with several numerical integral results.The effects of integral time step and computing time on computing results using Rung-Kutta method,Newmark method and PIM method in solving a simple supported beam subjected to moving spring mass system have been analyzed.The PIM method's superiority lies in unlimited by integral step length and quick convergence in solving the problem of vehicle-bridge coupling vibration among these several numerical methods.A moving spring mass system vehicle-bridge coupling vibration model has been constructed based on mode superposition.Based on Duhamel term's PIM,Cotes and Gauss algorithms are introduced to solve the nonhomogeneous linear differential equation following the load in an integration step be regarded as coordinating load and constant load.Taking a spring mass system running on simple supported beam as an example,the effects of equivalent nodal load and numerical algorithms for nonlinear differential equation based on Duhamel term have been analyzed.The results indicated that the result of Cotes with coordinate load closer to analytical solution.The way of equivalent load has weak effect on Newmark-? numerical result in responses of vehicle-bridge coupled vibration.But the results also show that the response curve of vehicle bridge coupling vibration present disperse when the equation was solved using Gauss numerical method with coordinate load,and undermined coefficient method has overlarge error at the same time.Research results show that Newmark-?method can meet the engineering accuracy.In order to get the same accuracy as PIM-C-H,Newmark-?method will need smaller time integral step and cost more time accordingly in solving the same problem.A new model for a random vibration analysis of vehicle-bridge systems subjected to road roughness excitation is proposed.The bridge is modeled as beam elements and the vehicle is modeled as two-degrees of freedom mass-spring-damper system.The load caused by road roughness is equivalent to Pseudo Excitation load.The model is solved with PEM following by mode superposition iterative solution introduced.Compared with Monte-Carlo method,the PEM which resolved the vehicle-bridge coupling random vibration model demonstrates the briefness of theory and speediness of compute.Taking a simple beam bridge as an example,the random vibration response of vehicle bridge coupling caused by road roughness in frequency domain prove the following conclusion.The first mode of bridge plays a major role in vertical displacement and acceleration of mid-span,the third mode of bridge plays more obvious role in acceleration than displacement at mid-span.The root mean square values(RMSV)of vertical displacement at mid-span varied with the vehicle speed obviously,and the vehicle speed obvious changes the first frequency's peak and band width of displacement and acceleration power spectrum density(PSD).The peak,frequency and band width of acceleration PSD adjoining fulcrum change with vehicle speed obviously.The RMSV of vertical displacement less than double the standard deviation(SD)of random sample caused by road roughness.A new random vibration model for vehicle-bridge systems using PEM is proposed,based on the bridge modeled as beam elements and the vehicle modeled as two-degrees of freedom mass-spring-damper system.Taking three different roughness excitations such as GB7031 spectrum,Wang spectrum and ISO spectrum as input,the responses of vehicle and bridge caused by road spectrum functions have been researched.The research results reveal the following conclusions.Three road spectrums have the similarity vertical displacement root mean square(RMS)curve at mid-span.The resonance frequency appears on the bridge's fundamental frequency.The vibration responses of vehicle caused by ISO spectrum weak changed with vehicle speed,the bridge dynamic responses caused by ISO spectrum show evident sensitivity in velocity.The response and resonance frequency of vehicle and bridge coupling caused by GB7031 spectrum closed to Wang spectrum.The result of GB7031 spectrum is slightly greater than Wang spectrum.The vibration responses of 3D random model for vehicle-bridge systems subjected to vehicle running at nonconstant speed are resolved by PEM based on consistent Stimulus of Road Roughness.Taking multipoint coherent road roughness excitation into condition,a new 3D random vibration model for vehicle-bridge systems is proposed.In the vehicle-bridge coupling model,the bridge is modeled as beam-shell solid element,the vehicle is simplied as 3D nine-degree of greedom model and the load caused by road roughness is equivalent to Pseudo Excitation load.The model is resolved with PIM and Newmark-? method,and the accuracy of results is verified through comparing with the result of Monte-Carlo method.Taking some highway beam bridge in Jiangxi province as an example,different point dynamic responses of bridge subjected to uniformly accelerate vehcile have been researched.The results prove the accuracy and feasibility of vehicle-bridge coupling random vibration model which has been proposed in the paper.The vehicle speed is the most fact which led to peak displacement and peak acceleration at mid-span with the same road roughness excitation.There has more large resonance frequency region when vehicle running on bridge with nonconstant speed than constant speed.The peak displacement and peak acceleration at mid-span of growth appears fast followed by slow when vehicle speed increasing gradually.Based on road irregularity power spectrum of GB7031,the vehicle-bridge coupling vibration model with multipoint coherent stimulus input is proposed for analying the effect of spatial road roughness spectrum on vehicle-bridge coupling vibration.Taking the phase-lag and coherent mul-excitation into condition,a new 3D coherent excitation random vibration model for vehicle-bridge systems is proposed with PEM.In the model,the bridge is modeled as beam-shell solid element,the vehicle with three axles is simplied as 3D nine-degrees of freedom(DOF)model.Taking the highway beam bridge with three spans as reasearch background,the coherent effect,phased-lag effect and consistent stimulus effect on the vibration response and spectrum characteristic of vehicle-bridge coupling system have been researched.The research demonstrates results as follow.The differences of the bridge displacement and acceleration caused by three spatial road irregularity excitation input are more somewhat obvious.The spatial road roughness spectrum has more obvious effects on the responses of car body than rear suspension.There has weak effect on the resonance frequency between vehicle-bridge coupling and road roughness spectrum.The spatial effect of road irregularity stimulus input in researching bridge-vehicle coupling should be taken into account.The bridge-vehicle coupling model with multi-point coherent stimulus input is proposed with PEM in order to study the effect of road roughness coherent function on the response of bridge-vehicle coupling system.Taking the coherence of road irregularity stimulus input into condition,a 3D coherent excitation random vibration model for vehicle-bridge systems is proposed in order to research the effect of vibration response and spectrum characteristic of vehicle-bridge coupling system because of Nanyanan function,Dieter A function and Zhang function.In the model,the bridge is modeled as beam-shell solid element,the vehicle with three axle is simplied as 3D nine-degrees of greedom model.The research demonstrates the following conclusion.The different coherent functions have obvious difference in displacement root-mean-square(RMS)and acceleration mean square deviation(RMSEC).The coherent functions have more obvious effect on energy than frequency between road roughness spectrum and vehicle-bridge coupling resonance system.There has weaker effect on rear suspension displacement and acceleration than vehicle body caused by coherent function.The effect of coherent function of road irregularity spectrum should be taken into account in researching the responses of bridge-vehicle coupling random vibration.The similarity laws of bridge-vehicle interaction system are presented based on similarity theories of structure dynamic model test and vibration particularity of highway bridge-vehicle coupling.Based on the simple beam bridge and vehicle loaded with three axles,the similarity constants of the scale-model system for highway bridge-vehicle interaction are calculated which the scale factor of geometry is 10.At the same time,perspex model-bridge,testing pony truck and appendages are all set up.The dynamic particularities of model-bridge and testing pony truck are analyzed through testing and numerical analysis.The static and dynamic responses of model-bridge are studied subjected to a moving vehicle running on the smooth deck along normal lane.The comparison between the testing results of model-bridge and numerical results of practical bridge with MATLAB conform the similitude laws of bridge-vehicle interaction model text.The results also show the feasibility of model test equipment and the validity of the test results.Taking three spans continuous girder bridge as an explame,statistic test and dynamic test have been implemented in site.The single certainty numerical response resolved using newmark and random vibration analysis resolved using PEM have been performed based on the three spans continuous girder bridge.Comparison of response between testing in site,scale model test and PEM result has verified the effectiveness of the method which the vehicle-bridge coupling random vibration has been solved through PEM.The formula of IM has been proposed based on the bridge fundamental frequency through numerical simulating and experimental testing the responses of multi-highway bridges in Jiangxi province.