VIBRATION CONTROL OF BRIDGES UNDER MOVING LOADS … · 2006/3 – 4 PAGES 1 — 4 VIBRATION CONTROL...
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1 INTRODUCTION One of the most important factors determining road design is the intensity of heavy trucks, which is often higher than originally assumed by the designers. According to the traffic forecasts in Europe and the USA, an annual increase in such vehicles will occur and new trucks with multiple axles or trails will appear. Additional costs for road repair and maintenance will be required. A world-wide reduction in the availability of funds for construction and maintenance of infrastructure, along with rapidly-expanding demands for freight transport, requires scientific and engineering responses to the issues of reducing pavement and bridge maintenance costs related to truck use and to a better, more-integrated design of vehicles, pavements and bridges. Despite the fact that the proper mechanisms of road damage are not yet precisely known, it has been proven that road damage significantly depends on the traffic of the heavy-duty vehicle fleet, which in turn is related to axle loads. It is also well known that construction and maintenance costs increase at a faster rate than axle loads. A higher level of scientific knowledge of the interaction between trucks and pavements and between trucks and bridges will open the way for regulations based on vehicle performance in terms of road-friendliness. The so-called road/bridge-friendly vehicle is one whose operation in a road/bridge system will bring about marginally less need for road/bridge maintenance, for a given level of axle load. 2 ROAD DAMAGE Vehicle-generated road damage is caused by forces between the road and tyres, the so-called road-tyre forces [1]. Road-tyre forces are affected by the design of a vehicle, such as total weight, axle J. MÁCA , M.VALÁŠEK VIBRATION CONTROL OF BRIDGES UNDER MOVING LOADS KEY WORDS • dynamics, bridge, • vibration, • control, • truck, • suspension ABSTRACT A truck with controlled semi-active suspensions traversing a bridge is examined for benefits to the bridge structure. The original concept of a road-friendly truck was extended to a bridge-friendly vehicle using the same optimization tools. The numerical integration in a MATLAB/SIMULINK environment re-solves the coupled dynamic equations of motion with optimized truck suspensions. A significant decrease in the contact road-tyre forces is observed when compared to commercial passive suspensions. Dr. Jiří Máca Research field: dynamics of structures, vibration control, interaction of bridges and vehicles Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics. Thákurova 7, CZ-166 29, Prague 6. +42024354500, [email protected]. Prof. Michael Valášek Research field: dynamics of structures, vibration control, interaction of bridges and vehicles Czech Technical University in Prague, Faculty of Mechanical Engineering, Department of Mechanics, Karlovo náměstí 13, CZ-121 35 Prague 2. +420224357361, [email protected]. 2006 SLOVAK UNIVERSITY OF TECHNOLOGY 2006/3 – 4 PAGES 1 – 4 RECEIVED 18. 9. 2006 ACCEPTED 27. 11. 2006 maca.indd 1 7. 5. 2007 11:27:59
Transcript of VIBRATION CONTROL OF BRIDGES UNDER MOVING LOADS … · 2006/3 – 4 PAGES 1 — 4 VIBRATION CONTROL...
1 INTRODUCTION
One of the most important factors determining road design is the intensity of heavy trucks, which is often higher than originally assumed by the designers. According to the traffic forecasts in Europe and the USA, an annual increase in such vehicles will occur and new trucks with multiple axles or trails will appear. Additional costs for road repair and maintenance will be required. A world-wide reduction in the availability of funds for construction and maintenance of infrastructure, along with rapidly-expanding demands for freight transport, requires scientific and engineering responses to the issues of reducing pavement and bridge maintenance costs related to truck use and to a better, more-integrated design of vehicles, pavements and bridges.Despite the fact that the proper mechanisms of road damage are not yet precisely known, it has been proven that road damage significantly depends on the traffic of the heavy-duty vehicle fleet,
which in turn is related to axle loads. It is also well known that construction and maintenance costs increase at a faster rate than axle loads.A higher level of scientific knowledge of the interaction between trucks and pavements and between trucks and bridges will open the way for regulations based on vehicle performance in terms of road-friendliness. The so-called road/bridge-friendly vehicle is one whose operation in a road/bridge system will bring about marginally less need for road/bridge maintenance, for a given level of axle load.
2 ROAD DAMAGE
Vehicle-generated road damage is caused by forces between the road and tyres, the so-called road-tyre forces [1]. Road-tyre forces are affected by the design of a vehicle, such as total weight, axle
J. MÁCA , M.VALÁŠEK
VIBRATION CONTROL OF BRIDGES UNDER MOVING LOADS
KEY WORDS
• dynamics, bridge, • vibration, • control, • truck, • suspension
ABSTRACT
A truck with controlled semi-active suspensions traversing a bridge is examined for benefits to the bridge structure. The original concept of a road-friendly truck was extended to a bridge-friendly vehicle using the same optimization tools. The numerical integration in a MATLAB/SIMULINK environment re-solves the coupled dynamic equations of motion with optimized truck suspensions. A significant decrease in the contact road-tyre forces is observed when compared to commercial passive suspensions.
Dr. Jiří MácaResearch field: dynamics of structures, vibration control, interaction of bridges and vehiclesCzech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics. Thákurova 7, CZ-166 29, Prague 6. +42024354500, [email protected].
Prof. Michael ValášekResearch field: dynamics of structures, vibration control, interaction of bridges and vehiclesCzech Technical University in Prague, Faculty of Mechanical Engineering, Department of Mechanics, Karlovo náměstí 13, CZ-121 35 Prague 2. +420224357361, [email protected].
2006 SLOVAK UNIVERSITY OF TECHNOLOGY
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configuration, tyre configuration and suspension configuration. The vertical road-tyre forces applied to the road by each vehicle tyre can be divided into two components: the static forces due to vehicle weight and the dynamic forces which are caused by the vibration of a vehicle excited by the road surface.Road damage can be reduced by decreasing road-tyre forces. Since static axle loads are already fixed, further investigations must be focused on the reduction of dynamic forces. Dynamic loads can be reduced by proper suspension design. Since the design of passive systems has been almost driven to its limits, additional improvements can be expected from controllable suspensions, active or semi-active, with suitable, road-friendly oriented control laws.Many evaluative criteria are based on the so-called fourth-power law, which originated in the AASHO (American Association of State Highway Officials) road tests. This law states that road damage generated by a wheel is proportional to the fourth power of the wheel force. Generally it should be noted that the validity of the fourth power law is questionable, and some recent studies have indicated that the damage exponent may take a wide range of values. Despite this fact, this approach to estimating road damage is widely used and has been also considered as a judging basis in our research. In order to quantify a road load due to dynamic road-tyre forces, Dynamic Load Stress Factor [2], (DLSF) is used. The dynamic load-stress factor is based on the fourth power law and is defined as follows:
DLSF = 1 + 6DLC2 + 3DLC4 ,
where DLC is the Dynamic Load Coefficient
,
where the RMS (Root Mean Square) value of the dynamic tyre force is the standard deviation of the probability distribution of the wheel force. Under normal operation conditions, DLC values of 0.1 to 0.4 are typical.Unevenness on a road surface generates, in addition from static, a dynamic contact force, which can be controlled and possibly reduced. In order to extend the useful service life of bridges, some efforts have been made to control the vibration of bridges. All these bridge control efforts are based on putting a special device such as a tuned mass damper or intelligent stiffener directly on the underside of a bridge deck [3]. An obvious disadvantage of this bridge control strategy is the reduction of the permitted height of vehicles passing under a bridge.
3 SUSPENSION CONTROL
When the direct reduction of bridge deflections was found to be too complicated, new trends in the development of vehicle suspensions follow the concept of tuning the vehicles to minimize the tyre-road contact forces – such vehicles are called bridge-friendly vehicles. In the development of road-friendly truck suspensions, passive, active and semi-active control systems have been considered.The control force in a passive control is developed as a result of the motion of the structure itself and does not require external power. It is inexpensive, simple and reliable, but it has a performance limitation. An active control system can provide better performance,
Figure 1. Skyhook and groundhook control systems
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but is more costly and less reliable and requires electrohydraulic or electromechanical actuators to generate the control force.Semi-active suspensions are a good compromise between performance and cost. The term ”semi-active control system” can be used to refer to any policy in which the damping can be adjusted between a minimum and a maximum level. The control system can be based on a skyhook or groundhook scheme.The control policy is designed to modulate the damping force by using a passive device to approximate the force that would be generated by a damper fixed to an inertial reference. The device can only absorb vibration energy by a actuator with a low power operation. It has the flexibility of active systems and the reliability of passive systems. A modification by combining a ground-hook with passive control was introduced to reduce road damage as well as riding comfort. A mechatronic solution combined with a controlled damper provides a tool for its optimization and the reduction of dynamic contact force. The concept of road-friendliness has been extended to bridge-friendliness by means of the optimization of the damper parameters on bridges, e.g. [4]. The aim of this work is to explore the benefits of bridge-friendly trucks on ordinary, simply supported bridges.
The results from previous studies with a quarter-car model were so promising that a more accurate model with a half-car and a slab bridge were brought together, e.g. [6]. A similar model was re-solved for a simply supported bridge with a specific road profile, traversed by a quarter-car model with a passive sky-hook and ground-hook control configuration. The effect of a semi-controlled damper is significant on the bridge response for close natural frequencies of the vehicle and the bridge [5].
4 HALF-CAR MODEL
The proposed half-car model is based on the parameters of the commercially available LIAZ truck, simplified to four DOF. Figure 3 displays the configuration of the truck together with a bridge. The front axle comprises two axles of a real car and the rear axle of the four axles, respectively.
A truck with a damper control optimised for road friendliness has been tested on a bridge. The addition of bridge friendliness demands into the EGH control law optimisation process will bring about further improvements (Figure 4). It has also been demonstrated that a bridge-friendly truck is no worse on a road than a road-friendly one.
Figure 2. Extended Ground Hook control system
Figure 3. Half-car model
Figure 4. Trucks on a bridge
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5 CONCLUSIONS
The paper describes the effect of a bridge-friendly truck on a road and bridge structure and proves that the concept of road-friendliness can be extended to bridges. A semi-active optimized damper, when compared to a passive one, reduces the local contact force in all cases and shifts the contact force peaks after the unevenness crossing. Bridge-friendly truck dampers are beneficial for a decrease in road damage, especially the rear axle that carries the prevailing
truck load. The dynamic contact force is mainly influenced by the uneven shape and the control strategy of the damper; the bridge span plays a minor role.
ACKNOWLEDGEMENTSThe authors gratefully acknowledge the support for this work by the Ministry of Education, Youth and Sports as a part of grant MSM 6840770003.
REFERENCES
[1] Cebon,D (1989) Vehicle-generated road damage. A review. Vehicle System Dynamics, 18, 1989, pp. 107-150
[2] DIVINE (1997), Proceedings of the European DIVINE Concluding Conference, Rotterdam, The Netherlands, 1997
[3] Kwon,H.C. – Kim,M.C. – Lee,I.W. (1998): Vibration Control of Bridges under Moving Loads. Computers & Structures, 66, 1998, pp. 473-480.
[4] Valášek, M. - Kejval, J. - Máca, J. (2002) Control of truck-suspension as bridge-friendly. In: H. Grundmann and G. I. Schueller (eds.) Structural Dynamics Eurodyn 2002, Munich, Balkema, 2002, pp. 1015-1020
[5] Chen Y., et al., (2002) Smart Suspension Systems for Bridge-Friendly Vehicles. In: Proceedings of 9th SPIE Annual International Symposium on Smart Structures and Materials, San Diego, 2002. Paper 4696-06.
[6] Máca J. - Šmilauer V. - Valášek M. (2005) Dynamic Bridge Response for Bridge-Friendly Truck. In: Proceedings of the 6th International Conference on Structural Dynamics. Rotterdam: Millpress Science Publishers, 2005, vol. 1, pp. 1051-1056.
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