汽车荷载作用下梁式桥与斜拉桥的动态响应分析
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摘要
车辆在桥梁上行驶时会产生激励从而导致车辆本身和桥梁产生振动,移动车辆在桥梁结构内产生的动荷载效应要比相应的静荷载效应大。设计规范中通常采用“冲击系数”来考虑车辆的这种动荷载效应。对于不同的桥梁实际状况,其冲击系数将有很大区别。获得车辆荷载作用下桥梁的真实信息无疑会对桥梁结构的受力状态给出更加切合实际的评估。
本文的研究为湖北省交通厅项目“超高桥墩大跨预应力混凝土连续刚构桥设计与施工关键技术”和交通部科技计划项目“荆岳长江公路大桥主桥关键技术研究”中部分内容,主要的研究内容及其相应的研究成果如下：
(1)基于车桥耦合系统动力分析基本理论,导出不同自由度车辆模型的运动微分方程。根据求解非平稳振动问题的方法,模拟了四轮车辆在随机路面作用下的随机输入。计算结果表明：路面激励随着车辆速度增大而有增大的趋势,用非平稳路面模型来模拟车辆所受路面激励更加符合实际情形。
(2)以单跨梁为例,建立车桥耦合系统的运动微分方程并利用Matlab软件编制其计算程序,与已有文献实例对比验证该模型和计算程序的正确性。分析了非平稳及平稳随机路面激励模型、混凝土路面层和沥青路面层等因素对单跨梁在汽车荷载作用下动力响应的影响。计算结果表明：在分析车辆变速运动时,平稳和非平稳两种路面励所对应的梁跨中挠度和冲击系数是不同的,对于加速运动来说,平稳路面激励可能使计算值偏小,而对于减速运动来说,平稳路面激励可能导致计算值偏大；在同一种桥面不平等级,车辆初速为10m／s且加速度为5m／s2时,混凝土路面层所对应的冲击系数是沥青路面层所对应冲击系的1.35倍。
(3)以连续梁为例,分析裂缝对汽车荷载作用下连续梁振动响应的影响。结果表明：在移动车载作用时不同裂缝类型对桥梁振动频率的影响不同,忽略呼吸裂缝随载荷张开与闭合的特性而简化为开口裂缝是不可取的；裂缝类型、裂缝参数、移动车辆频率及车辆组合等都会引起梁与车辆耦合系统振动频率的变化；开口裂缝和呼吸裂缝都会使桥梁的冲击系数增大。
(4)以湖南邵怀高速上一座高墩连续梁桥(炉坪大桥)为例,测试不同工况加载时测试跨的响应。采用LXPL-1型公路连续式八轮平整度仪,测量该桥面的平整度。采用环境振动法测量了该桥的竖向和横向自振频率,并在实测静力挠度和自振频率的基础之上,引入响应面法更新了炉坪大桥有限元模型。从实测数据和数值模型更新过程看出：利用环境振动法和峰值识别模态法成功测得该桥的横向和竖向振动模态,该桥的前两阶模态都是面外振动,因此该桥的横向刚度相对较弱；利用响应面法修正桥梁模型推动了结构模型修正的发展。
(5)为分析轮胎与地面之间的面接触对车桥耦合振动的影响,建立了新的车桥耦合模型,比较了轮胎与地面的两种接触模型(点接触和面接触)对耦合系统振动的影响。计算结果表明：当路面比较光滑时,不同接触处理模拟方法对梁的振动影响是很小,这时面接触可以简化为点接触；但当路面状况变坏时,接触形式对梁跨中挠度的影响相差较大,此时面接触不能简化为点接触,点接触会增大梁的挠度值,尤其对于跳车情形点接触会带来更大的误差,如木块高度为50mm时,点接触对应计算值为实测值的1.3倍,而面接触对应计算值为实测值的1.06倍。
(6)为分析高墩连续梁桥在车辆荷载作用下的横向振动,提出了一种新的车辆模型,该模型可考虑车辆横向振动的自由度。通过与实测数据的比较发现：本文计算模型能有效分析车辆作用下高墩桥的横向振动；就本桥算例来说,乘客行驶在该桥上时会有不舒适的感觉,且这种不舒适性随着路面不平度的变坏而增加,同时高墩桥横向和竖向振动会加大乘客的不舒适性；该桥的横向振动位移随车速的增加而增加,但车速增加到110km／h左右时,桥梁横向位移有减少的趋势。
(7)以大跨度斜拉桥(荆岳长江公路大桥)为例,用统计方法分析了荆岳长江公路大桥在车载作用下的振动响应和冲击系数,为设计大跨度斜拉桥提供了理论依据。结果表明：计算主梁竖向挠度时所取路面随机输入样本数目可为15个,计算主梁横向位移时可取路面随机输入样本数目25个；当车辆驶过全桥时,主梁最大竖向挠度和横向位移值并不发生在同一个位置处,当车行驶至900m左右处时竖向挠度值出现最大且为32.7mm,而当车辆行驶至715m处时横向位移值出现最大且为7.34mm；按照规范计算荆岳长江公路大桥主桥冲击系数为0.05,参数分析发现只有当车速小于10m／s左右时,跨中和1／4跨处挠度冲击系数才小于0.05,而其余大部分情形冲击系数都大于0.05,因此按规范计算的冲击系数值要小于该桥实际所受的车辆动力作用。
The vibration of bridge structures and vehicles can be easily induced when the vehicles travel across the bridges. The dynamic responses of the bridge structures induced by the moving vehicle loads are generally larger than those induced by the static vehicle loads. In the bridge design codes, the dynamic responses are generally been considered as a factor named as Impact Factor. Due to the impact factors are different with the different bridge structures; it should be significant to obtain the accurate responses of the bridge structures induced by the moving vehicle loads for evaluating loading-response of these structures.
The dissertation is the part of the two projects:one is supported by Hubei Province Communications Department, and which name is "the design methodology and construction technology of the High-pier Long-span Continuous Concrete Rigid Bridge"; the other is supported by Ministry of Transport of the People's Republic of China, and which name is " The Research on the Key Technology of Jingyue Yangtze River Bridge". The main contents and results of this dissertation are shown as follows:
(1) Based on the studies of the bridge-vehicle coupled system, the differential equations of motion for different degree-of-freedoms (DOFs) vehicle models were obtained. Using the methodology of solving the non-stationary vibration, the non-stationary road surface inputs of the four tires were simulated. Based on the numerical simulations, the following conclusions can be drawn:the non-stationary road surface inputs may increase with the vehicle speeds increase; it can be obtained the more rational responses using the non-stationary road surface inputs.
(2) A single-span beam was given as an example for creating the differential equations of motion of the vehicle-bridge coupled system. The program solving the equations was established by the software Matlab and was verified by comparing the simulations and the others studies. The effects of the non-stationary inputs, stationary inputs, concrete pavement, and asphalt pavement on the responses of the beam induced by the moving vehicle loads. Numerical results indicate that:the effects of non-stationary inputs and stationary inputs on the impact factors are different, the amplitudes of non-stationary random responses of the wheels increase as the vehicle velocity increases; factors including the road surface, vehicle initial speed (10m/s), and acceleration (5m/s2) are the same, the impact factor corresponding to the concrete pavement is aboutl.35 times of that to the asphalt pavement.
(3) A continuous beam was given as an example for studying the dynamic responses of the damaged beams under the moving vehicle loads. Numerical results indicate that:the frequencies may change with the different crack categories, and using vibration behaviors corresponding to the open crack zone to interpret those of the breathing crack zone may lead to the incorrect conclusion. factors such as crack categories, crack factors, vehicle frequencies and the number of the vehicles can change the frequencies of vehicle-bridge coupled system; the impact factor generally increase with the presence of the open crack zones or breathing crack zones.
(4) A high-pier continuous beam bridge, named Luping Bridge, was used to test the responses for different situations of testing loads. A road roughness measured device, named LXPL-1 Highway Continuous Roughness Device, was used to test the bridge road roughness. The vertical and lateral vibration frequencies were performed using the ambient vibration method. Based on the responses corresponding to static loads and vibration frequencies, the numerical model of the bridge was updated using the response surface method. It can be seen from the results of the measurement and numerical model process that the vertical and lateral vibration models can be tested using the ambient vibration method and the identification peak method. The lateral vibration can be easily induced due to the first two natural frequencies are lateral direction. The response surface method can be used to update the structural numerical model.
(5) To study the effect of patch contact on the vibration of the vehicle-bridge coupled system, a new vehicle-bridge coupled numerical model was established. The comparison of the effects of the two inputs (point contact and patch contact) on the mid-span deflection and the impact factors were compared with different parameters including the coefficient of surface roughness, vehicle acceleration, and vehicle braking. The numerical results show that:If the road surface classification is zero-roughness, the patch contact can be simplified as the point contact; If the road surface classification ranges from the Good to Poor, the difference of the effect of the patch contact and point contact on the mid-span deflections increases as the road roughness classification increases; treating the contact condition between the tire and road surface as a point contact may overestimate the dynamic deflection of the bridge; when studying the faulting condition effect where the simulation using the point contact may result in significant errors. For example, the simulated solution corresponding to the patch contact is the 1.3times of the test solution; however, the simulated solution corresponding to the point contact is the 1.06times of the test solution.
(6) To study the lateral vibration of the high-pier continuous bridge structures, a new vehicle-bridge coupled numerical model considered the lateral degree-of-freedoms (DOFs) was established. The comparisons of the theoretical simulations and field measurements show that the proposed method can be applied to study the bridge lateral vibration induced by moving vehicles with good accuracy. For the studied bridge, the passengers may feel a little uncomfortable, and both lateral and longitudinal vibrations of the high-pier bridge can significantly affect the drive comforts and can bring up safety concerns from the passengers. The lateral displacement does generally increase with the increase of vehicle speeds; the displacement reaches a peak at the speed of 110km/h.
(7) A long-span cable-stayed bridge named Jingyue Yangtze River Bridge was given as an example for studying the vibration responses and impact factors using the statistical methodology. Numerical results indicate that:the 15 samples of the road surface inputs is enough to calculate the vertical displacement, however, the number of the samples equals 25 for calculating the lateral displacement. If the vehicle travels about at 900m, the vertical displacement may reaches a peak and equals 32.7mm; however, the lateral displacement may reaches a peak and equals 7.34mm when the vehicle moves at 715m. Based on the specifications, the impact factor equals 0.05. However, numerical results indicate:in the situation that the vehicle moves less than 10m/s, the impact factor of displacement where location at both at the mid-span and 1/4span may be less than 0.05; but for the other situations, the impact factor may be more than 0.05, therefore, the impact factor calculated follow from the code may be more conservative.
本文的研究为湖北省交通厅项目“超高桥墩大跨预应力混凝土连续刚构桥设计与施工关键技术”和交通部科技计划项目“荆岳长江公路大桥主桥关键技术研究”中部分内容,主要的研究内容及其相应的研究成果如下：
(1)基于车桥耦合系统动力分析基本理论,导出不同自由度车辆模型的运动微分方程。根据求解非平稳振动问题的方法,模拟了四轮车辆在随机路面作用下的随机输入。计算结果表明：路面激励随着车辆速度增大而有增大的趋势,用非平稳路面模型来模拟车辆所受路面激励更加符合实际情形。
(2)以单跨梁为例,建立车桥耦合系统的运动微分方程并利用Matlab软件编制其计算程序,与已有文献实例对比验证该模型和计算程序的正确性。分析了非平稳及平稳随机路面激励模型、混凝土路面层和沥青路面层等因素对单跨梁在汽车荷载作用下动力响应的影响。计算结果表明：在分析车辆变速运动时,平稳和非平稳两种路面励所对应的梁跨中挠度和冲击系数是不同的,对于加速运动来说,平稳路面激励可能使计算值偏小,而对于减速运动来说,平稳路面激励可能导致计算值偏大；在同一种桥面不平等级,车辆初速为10m／s且加速度为5m／s2时,混凝土路面层所对应的冲击系数是沥青路面层所对应冲击系的1.35倍。
(3)以连续梁为例,分析裂缝对汽车荷载作用下连续梁振动响应的影响。结果表明：在移动车载作用时不同裂缝类型对桥梁振动频率的影响不同,忽略呼吸裂缝随载荷张开与闭合的特性而简化为开口裂缝是不可取的；裂缝类型、裂缝参数、移动车辆频率及车辆组合等都会引起梁与车辆耦合系统振动频率的变化；开口裂缝和呼吸裂缝都会使桥梁的冲击系数增大。
(4)以湖南邵怀高速上一座高墩连续梁桥(炉坪大桥)为例,测试不同工况加载时测试跨的响应。采用LXPL-1型公路连续式八轮平整度仪,测量该桥面的平整度。采用环境振动法测量了该桥的竖向和横向自振频率,并在实测静力挠度和自振频率的基础之上,引入响应面法更新了炉坪大桥有限元模型。从实测数据和数值模型更新过程看出：利用环境振动法和峰值识别模态法成功测得该桥的横向和竖向振动模态,该桥的前两阶模态都是面外振动,因此该桥的横向刚度相对较弱；利用响应面法修正桥梁模型推动了结构模型修正的发展。
(5)为分析轮胎与地面之间的面接触对车桥耦合振动的影响,建立了新的车桥耦合模型,比较了轮胎与地面的两种接触模型(点接触和面接触)对耦合系统振动的影响。计算结果表明：当路面比较光滑时,不同接触处理模拟方法对梁的振动影响是很小,这时面接触可以简化为点接触；但当路面状况变坏时,接触形式对梁跨中挠度的影响相差较大,此时面接触不能简化为点接触,点接触会增大梁的挠度值,尤其对于跳车情形点接触会带来更大的误差,如木块高度为50mm时,点接触对应计算值为实测值的1.3倍,而面接触对应计算值为实测值的1.06倍。
(6)为分析高墩连续梁桥在车辆荷载作用下的横向振动,提出了一种新的车辆模型,该模型可考虑车辆横向振动的自由度。通过与实测数据的比较发现：本文计算模型能有效分析车辆作用下高墩桥的横向振动；就本桥算例来说,乘客行驶在该桥上时会有不舒适的感觉,且这种不舒适性随着路面不平度的变坏而增加,同时高墩桥横向和竖向振动会加大乘客的不舒适性；该桥的横向振动位移随车速的增加而增加,但车速增加到110km／h左右时,桥梁横向位移有减少的趋势。
(7)以大跨度斜拉桥(荆岳长江公路大桥)为例,用统计方法分析了荆岳长江公路大桥在车载作用下的振动响应和冲击系数,为设计大跨度斜拉桥提供了理论依据。结果表明：计算主梁竖向挠度时所取路面随机输入样本数目可为15个,计算主梁横向位移时可取路面随机输入样本数目25个；当车辆驶过全桥时,主梁最大竖向挠度和横向位移值并不发生在同一个位置处,当车行驶至900m左右处时竖向挠度值出现最大且为32.7mm,而当车辆行驶至715m处时横向位移值出现最大且为7.34mm；按照规范计算荆岳长江公路大桥主桥冲击系数为0.05,参数分析发现只有当车速小于10m／s左右时,跨中和1／4跨处挠度冲击系数才小于0.05,而其余大部分情形冲击系数都大于0.05,因此按规范计算的冲击系数值要小于该桥实际所受的车辆动力作用。
The vibration of bridge structures and vehicles can be easily induced when the vehicles travel across the bridges. The dynamic responses of the bridge structures induced by the moving vehicle loads are generally larger than those induced by the static vehicle loads. In the bridge design codes, the dynamic responses are generally been considered as a factor named as Impact Factor. Due to the impact factors are different with the different bridge structures; it should be significant to obtain the accurate responses of the bridge structures induced by the moving vehicle loads for evaluating loading-response of these structures.
The dissertation is the part of the two projects:one is supported by Hubei Province Communications Department, and which name is "the design methodology and construction technology of the High-pier Long-span Continuous Concrete Rigid Bridge"; the other is supported by Ministry of Transport of the People's Republic of China, and which name is " The Research on the Key Technology of Jingyue Yangtze River Bridge". The main contents and results of this dissertation are shown as follows:
(1) Based on the studies of the bridge-vehicle coupled system, the differential equations of motion for different degree-of-freedoms (DOFs) vehicle models were obtained. Using the methodology of solving the non-stationary vibration, the non-stationary road surface inputs of the four tires were simulated. Based on the numerical simulations, the following conclusions can be drawn:the non-stationary road surface inputs may increase with the vehicle speeds increase; it can be obtained the more rational responses using the non-stationary road surface inputs.
(2) A single-span beam was given as an example for creating the differential equations of motion of the vehicle-bridge coupled system. The program solving the equations was established by the software Matlab and was verified by comparing the simulations and the others studies. The effects of the non-stationary inputs, stationary inputs, concrete pavement, and asphalt pavement on the responses of the beam induced by the moving vehicle loads. Numerical results indicate that:the effects of non-stationary inputs and stationary inputs on the impact factors are different, the amplitudes of non-stationary random responses of the wheels increase as the vehicle velocity increases; factors including the road surface, vehicle initial speed (10m/s), and acceleration (5m/s2) are the same, the impact factor corresponding to the concrete pavement is aboutl.35 times of that to the asphalt pavement.
(3) A continuous beam was given as an example for studying the dynamic responses of the damaged beams under the moving vehicle loads. Numerical results indicate that:the frequencies may change with the different crack categories, and using vibration behaviors corresponding to the open crack zone to interpret those of the breathing crack zone may lead to the incorrect conclusion. factors such as crack categories, crack factors, vehicle frequencies and the number of the vehicles can change the frequencies of vehicle-bridge coupled system; the impact factor generally increase with the presence of the open crack zones or breathing crack zones.
(4) A high-pier continuous beam bridge, named Luping Bridge, was used to test the responses for different situations of testing loads. A road roughness measured device, named LXPL-1 Highway Continuous Roughness Device, was used to test the bridge road roughness. The vertical and lateral vibration frequencies were performed using the ambient vibration method. Based on the responses corresponding to static loads and vibration frequencies, the numerical model of the bridge was updated using the response surface method. It can be seen from the results of the measurement and numerical model process that the vertical and lateral vibration models can be tested using the ambient vibration method and the identification peak method. The lateral vibration can be easily induced due to the first two natural frequencies are lateral direction. The response surface method can be used to update the structural numerical model.
(5) To study the effect of patch contact on the vibration of the vehicle-bridge coupled system, a new vehicle-bridge coupled numerical model was established. The comparison of the effects of the two inputs (point contact and patch contact) on the mid-span deflection and the impact factors were compared with different parameters including the coefficient of surface roughness, vehicle acceleration, and vehicle braking. The numerical results show that:If the road surface classification is zero-roughness, the patch contact can be simplified as the point contact; If the road surface classification ranges from the Good to Poor, the difference of the effect of the patch contact and point contact on the mid-span deflections increases as the road roughness classification increases; treating the contact condition between the tire and road surface as a point contact may overestimate the dynamic deflection of the bridge; when studying the faulting condition effect where the simulation using the point contact may result in significant errors. For example, the simulated solution corresponding to the patch contact is the 1.3times of the test solution; however, the simulated solution corresponding to the point contact is the 1.06times of the test solution.
(6) To study the lateral vibration of the high-pier continuous bridge structures, a new vehicle-bridge coupled numerical model considered the lateral degree-of-freedoms (DOFs) was established. The comparisons of the theoretical simulations and field measurements show that the proposed method can be applied to study the bridge lateral vibration induced by moving vehicles with good accuracy. For the studied bridge, the passengers may feel a little uncomfortable, and both lateral and longitudinal vibrations of the high-pier bridge can significantly affect the drive comforts and can bring up safety concerns from the passengers. The lateral displacement does generally increase with the increase of vehicle speeds; the displacement reaches a peak at the speed of 110km/h.
(7) A long-span cable-stayed bridge named Jingyue Yangtze River Bridge was given as an example for studying the vibration responses and impact factors using the statistical methodology. Numerical results indicate that:the 15 samples of the road surface inputs is enough to calculate the vertical displacement, however, the number of the samples equals 25 for calculating the lateral displacement. If the vehicle travels about at 900m, the vertical displacement may reaches a peak and equals 32.7mm; however, the lateral displacement may reaches a peak and equals 7.34mm when the vehicle moves at 715m. Based on the specifications, the impact factor equals 0.05. However, numerical results indicate:in the situation that the vehicle moves less than 10m/s, the impact factor of displacement where location at both at the mid-span and 1/4span may be less than 0.05; but for the other situations, the impact factor may be more than 0.05, therefore, the impact factor calculated follow from the code may be more conservative.
引文
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