The paper presents a theoretical evaluation on modal damping of hybrid fiber reinforced polymer (FRP)cable with smart damper design in long-span cable-stayed bridge. The principles and design consider-ation of smart dampers were first clarified. Based on the energy principle, the theoretical equations ofmodal damping were derived for in-plane and out-of-plane vibrations, respectively. The parameters thatinfluence the damping effect were further analyzed. Finally, an example of hybrid basalt and carbon FRPcable with smart dampers was selected to evaluate damping ratio in terms of the equations derived in thepaper.50960
The results show that (1) the smart dampers with discontinuous distribution benefit not only sta-tic and dynamic behavior of a cable but also optimization of damping; (2) the gap width, bonding, lengthand modulus of each smart damper can be optimized to obtain maximum of potential damping; (3) anexample of smart damper designed hybrid FRP cable demonstrates its effectiveness for mitigating largemagnitude of in-plane vibration, while more dominant damping effect is observed for suppressing out-of-plane vibration. 1. IntroductionFiber reinforced polymer (FRP) composites characterized by ahigh strength-to-weight ratio and superb corrosion resistance havebeen widely applied in structural retrofitting and strengthening aswell as new structural components [1,2]. They are always regardedas the most suitable materials for building long-span bridges dueto the outstanding mechanical properties in longitudinal directioncompared with conventional steel material. Thus, when used instay cables for long-span cable-stayed bridges, FRP compositescan exhibit essential advantages that address the deficiencies ofconventional steel cable such as large sag effect and durabilityproblems [3]. Carbon FRP (CFRP) cables were initially most inves-tigated to replace steel cables [4–6]. Although the superior staticand dynamic performance of long-span cable-stayed bridges withCFRP cables was verified by theoretical analysis and finite elementmethod (FEM) simulation, the consistently high cost of CFRP cablesrestricted their practical application in large number of cases.Moreover, CFRP cables are also sensitive to wind effects due totheir extremely high ratio of strength-to-weight [7]. Therefore, interms of preferable mechanical and chemical properties as wellas low cost of the newly developed basalt FRP (BFRP), hybrid basalt and carbon FRP (B/CFRP) cables were developed to replace steelcables and also overcome the limitations of CFRP cables in long-span cable-stayed bridges—not only were high static and dynamicperformances achieved, but the overall cost was also lowered [8–10]. To further explore the advantages of hybrid FRP cables, the po-tential ability of vibration control is studied in this paper empha-sizing the designable characteristic of hybrid FRP cables.Due to the general deficiency in the damping of long-length staycables, vibration should always be concerned for design and long-term monitoring and control. For conventional long cable, its lowernatural frequency will have a higher risk of resonance between thecables and the deck of bridge, and its enlarged dimensions will suf-fer more load effects [11]. Moreover, for FRP cables, their muchlighter weight compared with conventional steel cables will makethem more sensitive to different kinds of excitations. Thus, coun-termeasures should be seriously concerned for application of FRPcables.Up to present, various types of countermeasures have beenadopted to suppress potential cable vibration such as aerodynamic,structural and mechanical control. Aerodynamic control is usuallyrestricted by sectional configuration and only able to suppress cer-tain vibrations such as rain-wind induced [12]. Structural controlrequires the stay cables to be connected by minor cables that arealso limited by aesthetics. Therefore, most control efforts are fo-cused on the mechanical control of cable vibration,
which areachieved by installing dampers at certain positions along the cable. This can involve installation of external dampers (passive, active orsemiactive damper) and internal dampers (viscoelastic inserting orfriction materials). The passive damper is usually not effective forlong length of cable due to the limitation on its ratio of installinglocation to the cable length [11]. Although the active dampersare more effective than the passive dampers, they are usually re-stricted by extra power and potentially unfavorable actuating[13]. Semiactive dampers may integrate the advantages of passiveand active dampers, but much research and development stillneeds to be conducted [14]. It should be mentioned that all ofthe external dampers are required to be properly positioned ortuned; otherwise, the effectiveness will be reduced or even nega-tive [11]. Aside from external dampers, some researchers empha-size enhancing the internal damping of a cable, such as with alayer of viscoelastic material covering the cable [15], or an increaseof the internal friction among the tendons in the cable by adjustingthe rotating direction [16]. The internal dampers do not requireoptimization of position or proper tuning, which can effectivelysuppress different kinds of vibration due to fundamental improve-ment of the damping. However, in practice, internal dampers werenot found to be very effective due to the small magnitude of defor-mation of internal dampers in conventional steel cables [15]. Basedon the characteristic of the internal damper, a new type of internaldamper will be proposed and evaluated theoretically in this paperfor newly developed hybrid B/CFRP cables [17], which can dissi-pate vibration energy intelligently by the internal interaction be-tween the separately arranged inner and outer cables. Due to thisfeature, the damper will be called smart damper in the followingchapters.The following topics will be described in sequence: the designand optimization of hybrid B/CFRP cable with smart dampers, thetheoretical derivation of the modal damping based on energy prin-ciples, and the example analysis of smart dampers’ effectiveness.2. Smart damper design of hybrid FRP cable2.1. Principle and sectional structureIn general, a typical cable consists of paralleled steel wires ortwisted steel strands as shown in Fig. 1a and b. The usual FRPcables such as CFRP, BFRP and hybrid B/CFRP can also be similarlycomposed of paralleled wires or twisted strands, where inpidualwires or stands are made from CFRP, BFRP or B/CFRP in stead ofsteel. When constructed by this way, the damping properties ofFRP cables will be similar to those of steel cables from a structuralperspective. Although the material damping of FRP cable is proba-bly higher than that of steel due to the viscoelasticity of the matrix[18–20], it is still insufficient to enhance overall structural damp-ing substantially because of small amplitude of vibrational strainin the matrix.For hybrid B/CFRP cable, aside from the conventional structureof the cable, a special arrangement of tendons or strands can be de-signed to focus on enhancing the internal damping, as shown inFig. 1c. Here, a hybrid B/CFRP cable with a 25% volume proportionof carbon fibers (B/CFRP 25%) is adopted for explaining this design. The usual B/CFRP 25% cable is separated into two portions of FRPcables, the outer hybrid B/CFRP portion with a 50% volume propor-tion of carbon fibers (B/CFRP 50%) and an inner of complete BFRPportion, designed such that the entire cable has a 25% volume pro-portion of carbon fibers. In practical application, BFRP tendons arearranged inside the cable and form the inner cable, while B/CFRP50% tendons are arranged around the inner cable through an innersleeve as shown in Fig. 1c. A gap is left between the inner and outercable where the viscoelastic material can be inserted. 智能阻尼器对大跨度斜拉桥模态阻尼评估英文文献和中文翻译:http://www.youerw.com/fanyi/lunwen_54418.html