磁流变阻尼器对斜拉桥拉索振动控制的理论与试验研究
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摘要
大跨度斜拉桥拉索由于质量轻、阻尼小、柔性大,极易在风、风雨和桥面振动等外部激励下产生大幅振动,拉索的大幅振动对拉索的使用寿命和桥梁安全运营构成极大威胁,它已成为大跨度斜拉桥急需解决的关键问题之一。磁流变阻尼器具有阻尼力大小可调、响应快、性能稳定等优点而受到广泛关注。本文采用磁流变阻尼器对拉索的振动控制进行了理论和试验研究,系统深入地研究了磁流变阻尼器的力学性能及磁流变阻尼器对拉索振动的控制效果。具体的研究内容和取得的成果包括:
1.在阻尼力实测的结果上提出了磁流变阻尼器的非线性参数模型,非线性参数模型能够较好地模拟永磁调节式磁流变阻尼器与RD-1005型磁流变阻尼器的力学性能。提出了递推法计算非线性参数模型的数值计算方法,该方法能在时间步长为10-3s时模拟出磁流变阻尼器的阻尼力时程。建立了动态调节适应度和多层次压缩搜索区间的遗传算法——层次压缩遗传算法。该方法既能克服传统遗传算法的早熟和停滞现象,又能加速收敛速度,该算法在非线性物理参数识别方面具有良好的效果。
2.建立了拉索-磁流变阻尼器系统动力响应的有限单元模型,对试验索与永磁调节式磁流变阻尼器系统进行了全时程的数值仿真分析,其中阻尼器采用非线性参数模型。计算了阻尼器不同的安装高度、不同的磁场强度对系统等效模态阻尼比、钳固效应和频率变化的影响。拉索系统的等效模态阻尼比与拉索的振幅(或动能幅值)相关。随着阻尼器安装位置的提高,阻尼器对拉索的减振效果提高,系统的模态频率也略微增大。
3.提出了适合于拉索-磁流变阻尼器系统的基于位移延时反馈的Bang-Bang控制和基于位移延时反馈的自适应控制的两种半主动控制算法。以实验室所建立的模型拉索为研究对象,对拉索系统的自由衰减振动和强迫振动进行了有限元数值仿真分析。数值仿真结果表明:对于自由衰减振动的拉索系统的前三阶模态,半主动控制所获得的等效模态阻尼比比磁流变阻尼器的最优被动控制相应提高了67%、49%、44%,与粘性油阻尼器的最优被动控制相比,也可以得到基本相同的结果;对于强迫振动,半主动控制时拉索的前三阶模态位移响应比最优被动控制时分别减小37%、39%和18%。合理选择电压的开关时间是半主动控制获得良好效果的关键,对于拉索系统的前三阶模态,零电压持续时间Δτ分别为0.1s、0.08s、0.06s时,系统获得最大的等效模态阻尼比。随着阻尼器安装高度的增大和拉索振动频率的提高,半主动控制相对于最优被动控制的优势减小。
4.利用dSPACE、Matlab/simulink、MR阻尼器和电流放大器等工具,建立了磁流变阻尼器和拉索的半主动控制试验平台。采用基于位移延时反馈的Bang-Bang控制算法对拉索系统进行了半主动和被动控制试验,测量了磁流变阻尼器的输入电压、延时时间τ2和零电压持续时间Δτ对拉索减振效果、模态频率的影响,同时对拉索索力也进行了测量。试验结果同样表明:半主动控制的效果优于最优被动控制;对于拉索的前三阶模态振动,半主动控制测得的拉索-磁流变阻尼器系统等效模态阻尼比小于有限元计算结果,分别为计算值的78%、89%和74%。
5.对长沙洪山大桥S09索进行了试验,采用共振激振后突然释放的试验方法,得到了拉索分别在安装不同阻尼器时前三阶振动的自由衰减信号。结果表明:拉索在安装阻尼器后系统的模态阻尼比显著提高;永磁调节式磁流变阻尼器对拉索的减振效果优于油阻尼器;永磁调节式磁流变阻尼器对拉索的的减振效果存在一优化磁场强度,现场试验结果与理论计算结果吻合。根据理论分析与试验结果,对长沙洪山大桥拉索实施了磁流变减振。
Due to high flexibility, relatively small mass and very low inherent damping, stay cables of the long-span bridges are susceptible to vibration under wind loading, or wind incorporated rain excitation, or deck motion. Large-amplitude vibration of cables may reduce the life of cables and threaten safe traffic, and has been considered today as one of the most critical problems for this type of bridge. Therefore, investigation of mechanism and countermeasures of cable vibration is very important for construction and maintenance of the cable-stayed bridges. As semi-active control devices, magnetorheological (MR) dampers have an excellent variable damping property and their damping forces can be changed by adjusting the input of voltage to the dampers. With the aid of an appropriate control strategy, the semi-active MR system control for cables vibration can achieve much better damping effectiveness than the passive control system. This thesis is concerned with the modeling of MR dampers, and the semi-active control and the passive control for cables vibration by using MR dampers. Theoretical investigations, laboratory validation and field experiments are carried out in this study.
1. A series of cycle vibration tests with varying response amplitudes and different frequencies are first carried out for both the Adjustable-Permanent-Magnet Magneto-Rheological (APM-MR) dampers and the RD-1005 MR dampers to experimentally obtain hysteretic loops associated with the two kinds of dampers. Based on the experimental observations, a nonlinear parametric model (NLP model) is developed to describe the hysteretic loops of MR dampers. A recursive algorithm which is convergent under the time step less than order of 10-3 second is applied to discretize the governing equation of motion for MR dampers. The hierarchical compact genetic algorithm (HCGA) is proposed to identify the parameters of the NLP model. The HCGA combines the attractive merits of the global searching ability of genetic algorithm (GA) and the stable convergence of dimidiate searching root method to find the solution. It is proved that the HCGA quickly converge to the global optimum with a high probability in correctly identifying nonlinear parameter system, and the proposed NLP model matches the experimental results well over a wide range of operation conditions.
2. A geometrical nonlinear finite element formulation making use of the proposed NLP model of MR dampers is presented for analyzing the dynamic responses of the cable-MR dampers system in time domain, and applied to a field cable of Hongshan cable-stayed bridge incorporated with APM-MR dampers. The effects of response amplitude, installation height and the magnetic field intensity of dampers on the equivalently linear modal damping ratio, displacement reduction effecting (DRE), modal frequency are investigated in detail. The theoretical study concludes that large installation height is in favor of suppressing cable vibration, and magnetic field intensity whose optimum value depends on cable vibration amplitudes affects significantly the performance of dampers.
3. Two semi-active control algorithms for closed-loop cable vibration control with MR dampers are developed based on measurement displacement. Numerical simulation shows that the first three equivalent modal damping ratios obtained with semi-active control increases 67%, 49% and 44%, respectively, than those obtained with the optimum passive control with MR dampers tuned to a particular mode, and the corresponding displacement decrease 37%, 39% and 18%, respectively. The switch time of input voltage is vital in the semi-active control algorithm whenΔτ(time with zero voltage) is 0.1s, 0.08s and 0.06s, respectively. For the first three modes, the maximum equivalent modal damping ratios are obtained. The advantage of the semi-active control attenuates with increase of the installation height of MR dampers and modal frequencies of stay cables when compared to that of passive control.
4. An experimental platform based on dSPACE, Matlab/simulink and MR dampers is established in laboratory to study the performance of semi-active control algorithms. The above-proposed semi-active algorithm with MR dampers is applied experimentally to the laboratory cable, and is compared to the passive control algorithm by using MR dampers tuned to a specific mode. The experimental study validate the semi-active algorithm is superior to the passive control tuned to a particular mode. The equivalently linear modal damping ratios experimentally obtained from semi-active control is slightly smaller than those theoretically obtained from semi-active control for all the three modes (78%, 89%, and 74%).
5. Field tests are implemented on a stay cable incorporated with AMP-MR dampers of Hongshan Bridge in Changsha, China to evaluate practical mitigation vibration performance of MR damper. A series of sinusoidal exciting tests is used to measure modal damping characteristic of cable-MR dampers system. The displacement, acceleration and force time history data is obtained, then the filter and the least squares algorithm are employed to obtain the first three equivalent modal damping ratios. Vibration mitigation performance of the cable using the APM-MR dampers are compared to that using oil damper, the result shows that the APM-MR damper can more significantly suppress cable vibration than oil dampers, and have an obvious increase in equivalently linear modal damping ratios. The displacement response reduces at the location of damper of the cable when the dampers are installed. The displacement reduction effecting is studied by displacement time history data of the cable. Relationships between the DRE and the amplitude and the mode of the cable vibration and the magnetic field intensity of the APM-MR dampers are established for future applications. The field experiment results are generally in accordance with those of theoretical study.
1.在阻尼力实测的结果上提出了磁流变阻尼器的非线性参数模型,非线性参数模型能够较好地模拟永磁调节式磁流变阻尼器与RD-1005型磁流变阻尼器的力学性能。提出了递推法计算非线性参数模型的数值计算方法,该方法能在时间步长为10-3s时模拟出磁流变阻尼器的阻尼力时程。建立了动态调节适应度和多层次压缩搜索区间的遗传算法——层次压缩遗传算法。该方法既能克服传统遗传算法的早熟和停滞现象,又能加速收敛速度,该算法在非线性物理参数识别方面具有良好的效果。
2.建立了拉索-磁流变阻尼器系统动力响应的有限单元模型,对试验索与永磁调节式磁流变阻尼器系统进行了全时程的数值仿真分析,其中阻尼器采用非线性参数模型。计算了阻尼器不同的安装高度、不同的磁场强度对系统等效模态阻尼比、钳固效应和频率变化的影响。拉索系统的等效模态阻尼比与拉索的振幅(或动能幅值)相关。随着阻尼器安装位置的提高,阻尼器对拉索的减振效果提高,系统的模态频率也略微增大。
3.提出了适合于拉索-磁流变阻尼器系统的基于位移延时反馈的Bang-Bang控制和基于位移延时反馈的自适应控制的两种半主动控制算法。以实验室所建立的模型拉索为研究对象,对拉索系统的自由衰减振动和强迫振动进行了有限元数值仿真分析。数值仿真结果表明:对于自由衰减振动的拉索系统的前三阶模态,半主动控制所获得的等效模态阻尼比比磁流变阻尼器的最优被动控制相应提高了67%、49%、44%,与粘性油阻尼器的最优被动控制相比,也可以得到基本相同的结果;对于强迫振动,半主动控制时拉索的前三阶模态位移响应比最优被动控制时分别减小37%、39%和18%。合理选择电压的开关时间是半主动控制获得良好效果的关键,对于拉索系统的前三阶模态,零电压持续时间Δτ分别为0.1s、0.08s、0.06s时,系统获得最大的等效模态阻尼比。随着阻尼器安装高度的增大和拉索振动频率的提高,半主动控制相对于最优被动控制的优势减小。
4.利用dSPACE、Matlab/simulink、MR阻尼器和电流放大器等工具,建立了磁流变阻尼器和拉索的半主动控制试验平台。采用基于位移延时反馈的Bang-Bang控制算法对拉索系统进行了半主动和被动控制试验,测量了磁流变阻尼器的输入电压、延时时间τ2和零电压持续时间Δτ对拉索减振效果、模态频率的影响,同时对拉索索力也进行了测量。试验结果同样表明:半主动控制的效果优于最优被动控制;对于拉索的前三阶模态振动,半主动控制测得的拉索-磁流变阻尼器系统等效模态阻尼比小于有限元计算结果,分别为计算值的78%、89%和74%。
5.对长沙洪山大桥S09索进行了试验,采用共振激振后突然释放的试验方法,得到了拉索分别在安装不同阻尼器时前三阶振动的自由衰减信号。结果表明:拉索在安装阻尼器后系统的模态阻尼比显著提高;永磁调节式磁流变阻尼器对拉索的减振效果优于油阻尼器;永磁调节式磁流变阻尼器对拉索的的减振效果存在一优化磁场强度,现场试验结果与理论计算结果吻合。根据理论分析与试验结果,对长沙洪山大桥拉索实施了磁流变减振。
Due to high flexibility, relatively small mass and very low inherent damping, stay cables of the long-span bridges are susceptible to vibration under wind loading, or wind incorporated rain excitation, or deck motion. Large-amplitude vibration of cables may reduce the life of cables and threaten safe traffic, and has been considered today as one of the most critical problems for this type of bridge. Therefore, investigation of mechanism and countermeasures of cable vibration is very important for construction and maintenance of the cable-stayed bridges. As semi-active control devices, magnetorheological (MR) dampers have an excellent variable damping property and their damping forces can be changed by adjusting the input of voltage to the dampers. With the aid of an appropriate control strategy, the semi-active MR system control for cables vibration can achieve much better damping effectiveness than the passive control system. This thesis is concerned with the modeling of MR dampers, and the semi-active control and the passive control for cables vibration by using MR dampers. Theoretical investigations, laboratory validation and field experiments are carried out in this study.
1. A series of cycle vibration tests with varying response amplitudes and different frequencies are first carried out for both the Adjustable-Permanent-Magnet Magneto-Rheological (APM-MR) dampers and the RD-1005 MR dampers to experimentally obtain hysteretic loops associated with the two kinds of dampers. Based on the experimental observations, a nonlinear parametric model (NLP model) is developed to describe the hysteretic loops of MR dampers. A recursive algorithm which is convergent under the time step less than order of 10-3 second is applied to discretize the governing equation of motion for MR dampers. The hierarchical compact genetic algorithm (HCGA) is proposed to identify the parameters of the NLP model. The HCGA combines the attractive merits of the global searching ability of genetic algorithm (GA) and the stable convergence of dimidiate searching root method to find the solution. It is proved that the HCGA quickly converge to the global optimum with a high probability in correctly identifying nonlinear parameter system, and the proposed NLP model matches the experimental results well over a wide range of operation conditions.
2. A geometrical nonlinear finite element formulation making use of the proposed NLP model of MR dampers is presented for analyzing the dynamic responses of the cable-MR dampers system in time domain, and applied to a field cable of Hongshan cable-stayed bridge incorporated with APM-MR dampers. The effects of response amplitude, installation height and the magnetic field intensity of dampers on the equivalently linear modal damping ratio, displacement reduction effecting (DRE), modal frequency are investigated in detail. The theoretical study concludes that large installation height is in favor of suppressing cable vibration, and magnetic field intensity whose optimum value depends on cable vibration amplitudes affects significantly the performance of dampers.
3. Two semi-active control algorithms for closed-loop cable vibration control with MR dampers are developed based on measurement displacement. Numerical simulation shows that the first three equivalent modal damping ratios obtained with semi-active control increases 67%, 49% and 44%, respectively, than those obtained with the optimum passive control with MR dampers tuned to a particular mode, and the corresponding displacement decrease 37%, 39% and 18%, respectively. The switch time of input voltage is vital in the semi-active control algorithm whenΔτ(time with zero voltage) is 0.1s, 0.08s and 0.06s, respectively. For the first three modes, the maximum equivalent modal damping ratios are obtained. The advantage of the semi-active control attenuates with increase of the installation height of MR dampers and modal frequencies of stay cables when compared to that of passive control.
4. An experimental platform based on dSPACE, Matlab/simulink and MR dampers is established in laboratory to study the performance of semi-active control algorithms. The above-proposed semi-active algorithm with MR dampers is applied experimentally to the laboratory cable, and is compared to the passive control algorithm by using MR dampers tuned to a specific mode. The experimental study validate the semi-active algorithm is superior to the passive control tuned to a particular mode. The equivalently linear modal damping ratios experimentally obtained from semi-active control is slightly smaller than those theoretically obtained from semi-active control for all the three modes (78%, 89%, and 74%).
5. Field tests are implemented on a stay cable incorporated with AMP-MR dampers of Hongshan Bridge in Changsha, China to evaluate practical mitigation vibration performance of MR damper. A series of sinusoidal exciting tests is used to measure modal damping characteristic of cable-MR dampers system. The displacement, acceleration and force time history data is obtained, then the filter and the least squares algorithm are employed to obtain the first three equivalent modal damping ratios. Vibration mitigation performance of the cable using the APM-MR dampers are compared to that using oil damper, the result shows that the APM-MR damper can more significantly suppress cable vibration than oil dampers, and have an obvious increase in equivalently linear modal damping ratios. The displacement response reduces at the location of damper of the cable when the dampers are installed. The displacement reduction effecting is studied by displacement time history data of the cable. Relationships between the DRE and the amplitude and the mode of the cable vibration and the magnetic field intensity of the APM-MR dampers are established for future applications. The field experiment results are generally in accordance with those of theoretical study.
引文
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