Vibration control of civil structures using piezoceramic smart materials: A review

Engineering Structures 28 (2006) 1513–1524 www.elsevier.com/locate/engstruct

Vibration control of civil structures using piezoceramic smart materials: A review G. Song a,∗ , V. Sethi b , H.-N. Li c a Department of Mechanical Engineering, University of Houston, 4800 Calhoun Road, Houston, TX 77204-4006, USA b Department of Engineering Technology, University of Houston, 4800 Calhoun Road, Houston, TX 77204-4020, USA c School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian, 116024, China

Received 26 June 2004; received in revised form 16 January 2006; accepted 2 February 2006 Available online 30 March 2006

Abstract A review is presented for vibration suppression of civil structures. Special emphasis is laid upon smart structures with piezoelectric control actuation. The last decade has seen spiraling efforts going on around the world into development of the smart structures field. The success of these smart structures is orchestrated by the materials, such as piezoceramics, shape memory alloys, controllable fluids such as magneto-rheological fluids and electro-rheological fluids, fiber-optic sensors and various other materials. Piezoceramics have been known as low-cost, lightweight, and easy-to-implement materials for active control of structural vibration. Piezoceramics are available in various forms such as rigid patch, flexible patch, stack, Macro-Fiber Composite (MFC) actuator, and piezoceramic friction dampers. Piezoelectric patch actuators can be surface bonded to high strain areas of the structure with minimal modification of the original structure or they can be embedded into such as composites structures. On the other hand, stack type actuators can be incorporated into the structures, which require high control forces and micron level displacements, with slight modifications. This paper first presents basics about piezoceramic materials, various actuation methods and types of piezoceramic actuators. Then this paper reviews research into the application of piezoceramic actuators in various civil structures such as beams, trusses, steel frames and cable-stayed bridges. c 2006 Elsevier Ltd. All rights reserved.  Keywords: Civil structural control; Piezoceramics; Active control

1. Introduction Structural vibration control has always received considerable research attention by the civil engineering community. In this regard, an excellent review of structural control applied to civil engineering was presented by Housner et al. [1]. This review was a tutorial/survey that provided special insight into the various needs of structural control for civil engineering and laid down the future research needs in this potentially growing field. Various methods to suppress vibrations have been investigated and these commonly include active, passive, semi-active and hybrid vibration control systems. Semi-active control devices that possess the advantages of active control devices and ∗ Corresponding author. Tel.: +1 713 743 4525; fax: +1 713 743 4503.

E-mail address: [email protected] (G. Song). c 2006 Elsevier Ltd. All rights reserved. 0141-0296/$ - see front matter  doi:10.1016/j.engstruct.2006.02.002

passive control have been proposed for structural control applications. These devices include controllable fluids, including electro-rheological (ER) fluid and magneto-rheological (MR) fluids. Yi and Dyke [2] in their research titled ‘Performance of smart structures’ discussed the results of studying a series of simulations conducted to compare the effectiveness of various control systems for earthquake hazard mitigation. They demonstrated the semi-active and active systems achieved similar performance levels, both of these generally surpassing the performance of the passive control system at the same force level. The improvement in performance of the semi-active case over the passive case was found to increase with the number of storeys and with the frequency of the system. Further, Dyke et al. [3] and Yi et al. [4] performed experimental verification of the use of magneto-rheological dampers for the control of civil engineering structures.

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Passive vibration control using tuned passive mass dampers has been used in buildings for improved structural performance. Active mass tuned dampers have also been installed in buildings [5] and TV towers [6]. Active mass tuned dampers have been successful because they can produce the tons of forces necessary for the structural response control of the buildings. However active/passive mass dampers have limitations too. They have high inherent costs and besides this the associated costs of the driving power source is also high. Thus in view of the limitations, it is a challenge to the scientific community to devise new structures that are capable of vibration control of large civil engineering structures [7,8]. In this paper, a review is presented for vibration suppression of civil structures, where special emphasis is laid upon smart structures with piezoelectric control actuation. The smart structures have the potential and offer remarkable capabilities for active control of large structures. Intelligent or smart or adaptive structures are a subset of active structures that have highly distributed actuator and senor systems with structural functionality and in addition distributed control function and computing architecture [9,10]. Based upon a comprehensive survey and research Spillman et al. [11] gave a formal definition of the field of smart materials and structures. Their definition emphasized three basic necessities for a smart structure: (1) the ‘purpose’ of the structure, (2) the means and the will to achieve that purpose i.e. the sensing and actuation, and (3) the integrated structural system acts in such a way so as to mimic the biological functioning i.e. the self-adaptation and diagnostic capabilities. A smart structure that fits into the above definition and has the capability to respond to a changing external and internal environment incorporates smart material actuators and sensors. A smart material changes its characteristics (such as Young’s modulus, free strain, viscosity) under external fields (such as electric, magnetic or thermal) [12]. Smart materials can be used as actuators and sensors and include piezoelectric materials, shape memory alloys, electro-strictive materials, magnetostrictive materials, electro-rheological and magneto-rheological fluids and fiber optics. Piezoceramics are the most popular amongst the smart materials. Piezoceramics materials have the advantages of being lightweight, low-cost, and easy-to-implement and offer the sensing and actuation capabilities that can be utilized for passive and active vibration control. Piezoceramics can be surface bonded in high strain areas to the structure with or without minimal modification of the original structure or they can be embedded such as in composites structures. Also, stack type piezoceramic actuators can be incorporated into the structures, with slight modifications and without significantly changing the structural stiffness of the system. In 1998 a US–Japan co-operative research group was established for development of smart systems for building structures [13]. Smart systems requirements for building structures were then classified as (1) sensing and monitoring technology, and (2) control and effector technology. The following review is towards the vibration control technology using piezoceramics in civil structures.

Fig. 1. Piezoceramic element.

2. Basics of piezoceramics materials Piezoceramic material refers to the substances that have the following unique property: an electric charge is produced when a piezoelectric substance is subjected to a stress or strain (direct effect), and conversely a mechanical deformation i.e. the stress or strain produced when an electric field is applied to a piezoelectric substance in its poled direction (converse effect). Hence, the direct piezoelectric effect is useful in sensors such as some microphones, accelerometers, sonar, and ultrasound transducers. The converse effect is useful in actuators such as ultrasonic welders and ultrasonic motors. The piezoelectric effect is formed in crystals that have no center of symmetry such as quartz and Rochelle salt. An important group of piezoelectric polycrystalline ceramics is ferroelectric materials with the perovskite crystal structure such as barium titanate and lead zirconate titanate (PZT). Ferroelectric ceramics become piezoelectric when poled. Lead zirconate titanate ceramics (PZT) and their modifications are solid solutions of lead titanate and lead zirconate. The relationship between the applied forces and resultant responses of piezoelectric material depend upon a number of parameters such as the piezoelectric properties of the material, its size and shape and the direction in which forces or electrical fields are applied relative to the material’s axis. Fig. 1 shows an element of piezoelectric element material. Three axes are used to identify directions in the piezoelectric element termed 1, 2 and 3 in respective correspondence with the x, y and zaxes of rectangular coordinates. These axes are set during the poling process, which induces the piezoelectric properties of the material by applying a large d.c. voltage to the element for an extended period of time. The z-axis is taken parallel to the poling direction. Piezoelectric coefficients are usually written in a form with double subscripts. Eq. (1) provides the relationship between electrical fields associated with the applied voltage and the charge produced. The second subscript gives the direction of the mechanical strain of the material. IEEE standards on piezoelectricity [14] provide definitions of several piezoelectric constants. The constitutive equations for a linear piezoelectric material when the applied electric field and the generated stress

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are not large can be written as εi = SiEj σ j + dmi E m , Dm = dmi σi + ξik E k ,

(1)

where the indices i, j = 1, 2, . . . , 6 and m, k = 1, 2, 3 refer to different directions within the material coordinate system. In (1) ε, σ , D and E are, respectively, the strain, stress, electrical displacement (charge per unit area) and the electrical field (volts per unit length). In addition S E , d and ξ are the elastic compliance (the inverse of elastic modulus), the piezoelectric strain constant, and the permittivity of the material, respectively. Piezoceramics have been known as a simple, low-cost, lightweight, and easy-to-implement material for passive and active control of structural vibration. Because of the piezoelectric nature of the material, it can transform mechanical vibration energy of the structure to electrical energy or vice versa. Piezoceramics are available in various forms such as stack actuators, patch actuators, flexible patch actuators, Macro-Fiber Composite actuators developed at the NASA Langley Research Center [15] and Active Fiber Composite actuators developed at the Continuum Control Corporation. Bent et al. [16] presented Active Fiber Composite (AFC) actuators that are comprised of piezoelectric fibers, polymer matrix, and electrodes. PZT fibers are unidirectionally aligned in order to sense and actuate in-plane stresses and strains for structural actuation applications. Horner [17] developed a new packaging technique for piezoceramic wafers in which encapsulation of the piezoceramic incorporates the electrical leads. Their technique for encapsulation produces a hermetically sealed package that also is flexible and can be surface mounted or embedded into composites. Commonly used piezoceramics in civil applications are stack type actuators, also known as multi-layered actuators. Multi-Layer piezoelectric Actuators (MLAs) offer many advantages, such as high energy density, compared to other active materials, and therefore they are increasingly used in various smart actuator applications [18]. Typically, a 100 mm long with a cross-section area of 1 cm2 provides a free stroke of 100 µm and a blocked force of about 3 kN. These MLAs do have some disadvantages because of the low tensile strength. This is a source of failure in bending conditions, in vibration environments and in dynamic applications where high transient stresses are present. Recently, Cedrat Technologies [18] introduced mechanically Amplified Piezoelectric Actuators (APAs), to overcome the tensile stress limitation of MLAs, by applying a compressive prestress on the ceramic, which, additionally, enhances the piezoelectric deformation. The APA actuator form shows significant improvement in terms of output energy per actuator mass or per actuator volume. In stack type piezoceramics the piezoelectric strain coefficient in d33 direction is utilized whereas in patch actuators the piezoelectric strain coefficient in d31 is used. Piezoelectric patch actuators can be surface bonded in high strain areas to the structure with or without minimal modification of

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the original structure or they can be embedded such as in composites structures. On the other hand, stack type actuators can be incorporated into the structures, which require high control forces and micron level displacements, with slight modifications. Thus, there exist a wide range of piezoceramics commercially available that can be utilized according to the application requirements. 3. Applications of piezoceramics in civil structures: Background information What developed as a technology to address the problem of exerting control on large or precision flexible structures for aerospace applications has now found usage in civil engineering applications. Hence, it is imperative to highlight some of the achievements smart structure technology has made in aerospace engineering by using piezoceramic materials. Pioneering research for space structures was contributed by Balas [19,20]. Bailey and Hubbard [21] in 1985 presented an active vibration damper for a cantilever beam of a satellite structure using the piezoelectric polymer polyvinylidene fluoride (PVDF) as the distributed parameter actuator. Later on, Crawley et al. [22,23] presented analytical techniques and experimental results for use with piezoelectric actuators as elements of intelligent structures. They presented the static analysis and complete analytic solutions for surface bonded cases of piezoceramic actuators. The flexural static models were integrated with the Euler–Bernoulli beam model which led to the dynamic model analysis and prediction of the behavior of the beam under piezoelectric actuation. The last decade has also witnessed publication of various books [24–29] and reviews on smart structures. Intelligent structures technology assessment and reviews were provided by Crawley [30], Rao and Sunar [31], Chandra et al. [32], Chopra [33], and Rao and Sana [34] wherein current research status was reviewed, research needs were assessed, identified and a vision for future was laid. Crawley [30] discussed the research needs in terms of better actuation materials, optimized sensors, distributed control, structural control algorithms, power conditioning and switching, large scale structurally robust integration, impact on host structure, embedded components, manufacturability, reliability and repairability. The review by Chopra [33] consisted mainly towards the development of models for the beams and plates with piezoceramic elements. In one of the recent publications by Flatau and Chong [35], some of the broad initiatives taken by the National Science Foundation for dynamic civil and mechanical infrastructural systems were presented. This paper gave an important direction where the current state-of-the-art research is headed in the development of the vibration control and health monitoring systems for infrastructures. Notable contributions have been made by various researchers for the vibration control of flexible structures using piezoceramics and implementation of this technology in aerospace engineering. These contributions have been in the development of induced strain actuation [33,36], finite element

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Fig. 2. 3.3 m long smart beam [51].

modeling [22], electro-mechanical modeling [23], control algorithms [34], digital signal processing, data acquisition and computational methods for real time implementation. Since each of the above areas represents an entire field, this review is therefore limited to the perspective of civil structural control. The aerospace industry has reached milestones in the development and demonstration of smart structures technologies by operating Vibration Isolation, Suppression, and Steering space experiment [37,38], the Middeck Active Control Experiment [38,39], Satellite Ultra-quiet Isolation Technology Experiment (SUITE) [38] and Miniature Vibration Isolation System (MVIS) [40] for space applications using piezoceramics. Seismic Isolation in civil structures was summarized and reviewed by Kelly [41] in 1986. This research characterized various implemented systems and their range of applicability. It was envisaged that future structures will have traditional passive and non-traditional active load resisting members. Since this concept was non-traditional for civil engineering real obstacles with respect to its acceptance existed at that time. Later, Soong [42] reviewed the importance and necessity of passive and active vibration control in civil engineering. This paper included a brief historical outline of the development and an assessment of the state-of-the-art and state-of-practice of the passive and active structural control systems. For civil engineering, the intelligent structures have made inroads following the leads of aerospace systems. Application of smart structures technology in civil engineering has been reviewed by Huston [43], Culshaw et al. [44], and Shakeri et al. [45]. Huston [43] reviewed the ‘sensing structures’ and the ‘sensing and reacting structures’. Huston [43] also envisaged the application of smart structure technology in cable-stayed bridges, reduction of wind and earthquake induced vibrations in large structures and resisting corrosion. The review by Culshaw et al. [44] focused on the application of fiber optics as sensing devices in civil engineering mainly for the purpose of health monitoring of structures. Shakeri et al. [45] gave a broad application based review covering the gamut of smart materials. American Society of Civil Engineers (ASCE) [46] also published ‘Intelligent Civil Engineering Material and Structures’ in 1997 which is an excellent collection of state-of-the-art papers in this field with applicability to civil engineering. The majority of the papers in this book reference the applications of fiber optics to civil structures. Therefore this provided us motivation for reviewing the applications of piezoceramics to civil engineering.

Fig. 3. Positive position feedback controlled response of the beam [51].

4. Implemented applications related to civil engineering 4.1. Cantilevered structures The control problem of cantilever flexible beams has been investigated by various researchers [47–50]. Sethi [51] also investigated the vibration suppression using piezoceramic patch actuators of a 3.3 m long pultruded fiber reinforced polymer Ibeam set up in cantilevered configuration as shown in Fig. 2. In this study, the structure to actuator weight ratio was 186, which is substantially higher than that of the lightweight flexible structures that also used piezoelectric patch actuators. Controllers such as positive position feedback, strain rate feedback, and pole placement control were implemented and a maximum damping increase of 1000% was achieved. The results of active vibration control with a positive position feedback controller are shown in Figs. 3 and 4. 4.2. Truss structures Another typical example of the application of piezoceramic stack actuators is truss experiments. Although these truss structures experiments were meant for space applications, however their applicability extends to civil structures. Fanson et al. [52] experimentally demonstrated piezoelectric active members in a space truss for its precision control. They developed in-house an active member consisting of nested

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Fig. 5. Active vibration control truss experimental setup [60].

Fig. 4. Power spectral density comparison plots for the beam [51].

thin walled three piezoelectric cylinders. This active member functioned as a load carrying structural member as well as an actuator or sensor. Thus this allowed them to implement collocated direct velocity feedback control of the large space truss. Anderson et al. [53] presented the design and development of a zero stiction active member using a piezoelectric and electrostrictive actuation motor for precision control of large space structures. Fanson et al. [54] studied a test bed structure with two active piezoceramic struts also called dial-a-strut. These struts had a collocated displacement and a force feedback. They found that local force feedback, accompanied by small phase shift, achieved nearly optimal damping performance. They also implemented bridge feedback circuit through the feedback of both force and velocity. The first and second mode response was reduced by 40 dB from initial damping 0.1%. Preumont et al. [55] investigated and developed an active bar element that consisted of a linear actuator collocated with a force transducer. They integrated this active bar element as a load carrying element in the truss structure and implemented a local force feedback control to actively damp the vibrations of the structure. They achieved a damping ratio of 0.10 on this lightly damped truss structure. O’Brien and Luire [56] also reported on the implementation of integral force feedback for control of a truss structure using a piezoelectric active strut member. Won and Sulla [57] also studied vibration suppression of a ten bay truss. They used PVDF film as sensors and two commercially available (from Physik Instrumente) piezoelectric struts as actuators to suppress the vibration of the ten bay truss. The linear quadratic regulator, second-order decentralized and direct rate feedback control law schemes were designed and implemented successfully on the truss structure. Other reported work on truss structures have been presented by McClelland et al. [58] and Zhang and Liu [59]. Song et al. [60] presented experimental results on active vibration suppression of a spacecraft truss using a lead zirconate titanate (PZT) stack actuator. To simulate the effects of a spacecraft

Fig. 6. The installed smart strut installed in truss [60].

Fig. 7. Power spectral density plot for truss experiment [60].

disturbance on the truss, a proof mass actuator was incorporated on the structure to excite the truss vibrational modes. By using the force transducer as a sensor and the PZT stack as an actuator, an integral plus double-integral force controller was designed to suppress vibration of the truss using one active strut. The experimental setup is depicted in Fig. 5 with the smart strut used for active control shown in Fig. 6. The active vibration control experiment, shown in Fig. 7, resulted in a power reduction of 14.8 dB.

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Preumont et al. [61,62] presented experimental results for active damping of a guyed truss with three active tendons. Each tendon consisted of a displacement piezoelectric actuator collocated with a force sensor. They presented a modeling technique for cable structures and then implemented the control algorithm of an integral force feedback on the guyed truss. 4.3. Frame structures Another demonstration of this technology has been in the area of frames and building structures. Seismic control of buildings is a challenging and large scale application of smart structures. Valliappan and Qi [8] reviewed the seismic vibration control using smart materials. However, their discussion was limited to the analytical and finite element methods for design of distributed sensors/actuators and optimum position of sensors and actuators. Experimental investigations on building structures have been done by Nishimura et al. [63]. The investigators subjected a structural model of a five-storey building about 2.5 m high to non-stationary random excitations such as earthquakes. Control was done through active braces using electromagnetic actuators for generation of the required control forces. Sensing was done through five accelerometers mounted on the structure and two were used for feedback control. As a result the damping of the system was increased to 20% from the initial few tenths of a percent. Kamada et al. [64,65] and Aizawa et al. [66] demonstrated the use of thirty two piezoelectric stack actuators for response control of a four-storey structural frame, 3.7 m in height and 2000 kg in total weight, by inserting the actuators into the bottom of a column. The experimental setup is demonstrated in Fig. 8 with the enlarged view of piezo stack actuators mounting shown in Fig. 9. In one paper, the investigators proposed to produce a bending moment force control of the columns and in another paper they proposed a combination of bending moment control and axial force control of columns for the control of flexural–shear deformation of building structures. They examined the model matching method and H∞ for the control application of this structure. As a result of the closed loop control, 10% first- and second-mode damping ratios were achieved. In another similar experiment, Fujita et al. [67] tested a smart structure for active micro vibration control of a twostorey 2500 kg steel frame building model, used in precision manufacturing semiconductor facilities. In semiconductor manufacturing, the steel frame structures can shorten the time for construction and make spaces with fewer columns and longer spans but they perform worse in a vibration environment than reinforced concrete frame structures. They envisaged that the active micro-vibration control can improve the performance and it will be applied to floors and even entire buildings to meet requirements for a more perfect vibration-free environment in the facilities. To demonstrate this, they used piezoelectric stack actuators attached to the columns and the beams for the microvibration control by bending moment. The control strategy was the same as adopted by Kamada et al. [64,65].

Fig. 8. Four-storey structural frame setup by Kamada et al. [64,65] and Aizawa et al. [66].

Fig. 9. Enlarged view of the bottom of the structure in Fig. 8 with piezoceramic stack actuators mounted [66].

Fig. 10. Experimental setup for building structure [68].

Sethi and Song [68] have also implemented multimodal vibration suppression for a scaled building model using piezoelectric patches as actuators and sensors. The experimental setup is shown in Figs. 10 and 11. Using a state feedback pole placement controller coupled with a state estimator a multimodal controller was implemented and the time response and

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Fig. 13. Power spectral density comparison for building structure [68]. Fig. 11. Close up view of the PZT patch actuator used in building structure [68].

Fig. 12. Time response comparison for building structure [68].

power spectral density results are plotted in Figs. 12 and 13 respectively. Substantial decibel reductions were achieved in the first three modes of the structure. The question whether the scaled model smart structure applications can be extended to large civil building structures depends on the development and performance of large scale piezoelectric actuators. In this regard Fujita et al. [69] tested a large scale piezoelectric actuator in their laboratory. This actuator consisted of 30 piezoceramic plates of 100 mm ∗ 100 mm ∗ 5 mm and they achieved a maximum displacement of 94 × 10−6 m under initial load, and the maximum force of 270 kN under zero displacement with a 3.0 kV voltage and initial compressive load of 196 kN. Using this actuator they simulated this large scale piezoelectric actuator for active vibration control on an actual nine-storey building of steel frame structure 31 m in height and 273 t total mass. They concluded that a smart structure with large scale piezoelectric

actuators could perform the same active control in stronger excitation than the hybrid mass damper could. Thus their research reinforces the point that we are not far from when these large scale piezoelectric actuators could be seen in action in large building structures. Piezoelectric friction damper is a type of new energy dissipation semi-active control device for civil engineering. Chen and Chen [70] proposed a conceptual piezoelectric friction damper installed between a floor of a building structure and the supporting bracket with the contact force regulated by piezoelectric stack actuators. They used the advantage that a piezoelectric friction damper takes of the slip mode at the friction surface to endure the large deformation in structures while the piezoelectric actuators regulate the clamped force on the damper on a single-storey structure. They analyzed analytically the free vibration and harmonic responses of a single-storey frame structure incorporating a piezoelectric friction damper and demonstrated that the piezoelectric friction damper can significantly reduce the response of the structure. Morita et al. [71] proposed a semi-active base isolation system with controllable friction damper using piezoelectric actuators for control of building structures. They demonstrated that by semi-active isolation, response displacement of the structure could be reduced to 50% of values of the passive isolation system without deteriorating the isolation efficiency. A new design for piezoelectric friction damper was presented by Li et al. [72]. This piezoelectric friction damper was developed by combining the existing slot bolted connector design and the piezoceramic actuator. The schematic of this design is shown in Fig. 14. It is composed of tube piezoceramic stack actuators, load cells, preload bolts, an upper plate, a sliding plate and a lower plate. The three plates are slotbolted together so that sliding takes place among the sliding plate, upper plate and lower plate. This type of semi-active piezoelectric friction damper can be connected to the beams or floors using chevron braces through the connecting plates. A preload is applied to the piezoceramic actuators to avoid slack and constraining the deformation of the actuators. This new

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Fig. 14. Schematic of a new piezoelectric friction damper proposed by Li et al. [72].

Fig. 16. Active stiffness control of out-plane (transverse) cable vibrations: Chen [88] and Fujino et al. [89].

Fig. 15. Schematic of the structure on which a semi-active piezoelectric friction damper was simulated by Li et al. [72].

design was numerically simulated on a three-storey building model, in which each storey unit is identically constructed. One piezoelectric friction damper is installed at the first storey as shown in Fig. 15. In their numerical simulations using the El Centro earthquake excitation, they achieved the reduction ratios of the relative acceleration on the second and third storey as 59.7% and 61.1%. In addition, the reduction ratios of the inter-storey drift of the first, second and third storey achieved were 86.1%, 70.0% and 64.5%, respectively. Thus their numerical simulations clearly demonstrate the effectiveness of the proposed method for vibration reduction during a seismic event. 4.4. Cable-stayed structures The cable-stayed bridge/structure is another area where smart materials are now being used for vibration suppression. The cable-stayed bridges are more sensitive to wind and traffic induced vibrations, deck and pylon vibrations and to flutter instability, because of their high flexibility, relatively small mass, low structural damping and steadily increasing moving loads. Cable vibrations studies were matured and developed by Irvine [73–75] and [76]. Subsequently, Yang

and Giannopoulos [77,78] demonstrated the feasibility and the advantage of applying active control to a cable-stayed bridge. They used active cables and showed the root mean square responses of the bridge can be reduced as much as 80% with active control systems. They concluded the feasibility of active control to cable-stayed bridges. Since cable-stayed bridges are highly flexible structures, cables are prone to vibrate locally in both in-plane and outplane motion (transverse vibrations). Furthermore, the cable vibrations can also be accompanied by the tower/pylon or the deck motions called global vibrations. The coupling between the local and global modes gives rise to parametric excitation. Therefore, Ghaffar and Khalifa [79] studied the importance of cable vibrations in cable-stayed bridges. To better understand the coupling effects, modeling of the cables’ motions dynamics, that include quadratic as well as cubic nonlinearities, and their application to cable-stayed bridges have been performed by Hagedorn and Schaffer [80], Takahashi and Konishi [81, 82], Mitsugi and Yasaka [83], Perkins [84], Perngjin and Nayfeh [85], Warnitchai et al. [86] and Desai and Punde [87]. Experimental studies on active cable vibration control using piezoceramic stack actuator have been conducted by several investigators. Chen [88] showed analytically active stiffness control on a string, by varying the in-plane tension for the control of out-of-plane response. Fig. 16 illustrates this concept. It was showed analytically/numerically that time variation in in-plane tension causes variation of the transverse stiffness which can thus produce damping effect on transverse vibrations. The concept of time varying stiffness demonstrated by Chen [88] has been used by most of the investigators. The time varying stiffness can be realized by the time varying boundary conditions, using the piezoelectric stack actuator. In a study conducted by Fujino et al. [89], they used the concept demonstrated by Chen for vibration suppression of transverse vibrations of the cable. They used optimal control and found that the instability occurs when the structure frequency is twice the natural frequency of the cable. It was also concluded that

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Fig. 17. Active sag induced control of in-plane cable vibrations: Fujino and Susumpow [90].

the dynamic force required for the active stiffness control was only a few percent of the static tension of the cable. In the last paragraph, we outlined the strategy used for controlling the out-plane (transverse) motions of the cable structure system. The cables also have in-plane motion (Fig. 17) for which active sag induced force control utilizing velocity feedback was suggested by Fujino and Susumpow [90]. The active sag induced force could be realized by the axial movement of the support, which in turn needs physically a piezoelectric stack actuator to change the tension in the cable. They experimentally confirmed active sag induced force control is applicable only for the symmetric modes of a sagged cable and that first in-plane mode can be controlled efficiently. To

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further this study, the same investigators [91] also conducted a multimodal cable vibration control by axial support motion. The justification for doing multimodal control was active sag induced control is effective for the first in-plane mode but this is true under the harmonic excitations only. In general the disturbances are random in nature, thus the authors suggested a bilinear controller for the nonlinear motion of the cable with movable support. The authors demonstrated its efficiency using numerical simulations. The above highlights some of the studies conducted for control of local vibrations of the cable structures. However, such structures do exhibit global vibrations for which active tendon control is proposed by investigators and is illustrated in Fig. 18. Warnitchai et al. [92] conducted an experimental study on active tendon control of cable-stayed bridges. In this experiment they used piezoelectric stack actuators to provide active tendon force and non-collocated strain gauges as sensors. They demonstrated that active tendon control using velocity feedback control is very effective for global vertical (pylon) dominated mode. In this case, the cable displacements are in quasi-static motions i.e. as an elastic tendon due to movement of the anchorages. However, they also showed that active tendon control is not very effective for local i.e. cable dominated modes. In this study problems due to spillover effect were also encountered. Achkire and Preumont [93] have also studied active tendon control of cable-stayed bridges. The difference between this study and one by Warnitchai et al. [92] lies in the collocated vs. non-collocated control. As said earlier Warnitchai et al. [92] encountered spillover problems, mainly due to non-collocated control. However, Achkire and Preumont [93] used a load sensor collocated with a piezoelectric stack actuator for the implementing of a force feedback controller. A collocated force

Fig. 18. Active tendon control of cable-stayed bridges for global vertical mode [92,93].

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feedback control guarantees stability, as demonstrated by the researchers, and thereby eliminating spillover problems. The controller produced active damping of the symmetric in-plane modes and of the coupled cable structure system. They achieved a damping of 0.018 for the cable and 0.04 ∼ 0.06 for the cable structure system. Subsequently, Bossens and Preumont [94] explored active tendon control on large scale demonstrations. They showed that parametric excitations can be controlled using an integral force feedback collocated control approach. The above discussed were some civil engineering application areas with piezoceramics actuators and sensors used for the effector technology. 5. Summary and conclusions An overview was presented for vibration suppression of civil structures with special emphasis laid upon smart structures with piezoelectric control actuation. The distributed sensing and induced strain actuation as proposed by several researchers offer a good opportunity for structural control application in civil engineering. Piezoceramics material that have the advantages of being lightweight, low-cost, and easyto-implement offer the sensing and actuation capabilities that can be utilized for active vibration control. A number of examples including the applications of piezoceramics to various kinds of civil engineering structures like truss, beams, buildings and cable structures were presented. Research activity going on around the world in terms of development and implementation of this technology in civil engineering structures was reviewed. Piezoceramics have limitations too. The current status of piezoceramic actuators provides small displacements. An innovative way to overcome this limitation for large structural configurations was implemented by Kamada et al. [64], where they included a number of actuators in the building structure for structural control. Thus, the present applications have found some ways to overcome the existing limitations. However, efforts in the direction of actuator development are already initiated [69] and it will not be long before we shall see the implementation of this technology into real world structures. The introduction of stack actuators in structures also causes some structural modifications. These have to be accommodated during the design phase of the structures. Another drawback when piezoceramics are used for active control is that they need a power source. During an earthquake or seismic activity, the power supply may be interrupted; in that case the reliance of these structures totally on active control may prove catastrophic. This is also one of the reasons that is prohibiting the adaptation of this technology to civil structures. However it is envisaged the community will see developments that shall reduce the power consumption and this may be in areas of the development of actuators or power efficient control algorithms. Although there exists some limitations the benefits of this technology far outweigh the problems of not using them. This is evident by the tremendous amount of contributions from the scientific community for introducing this technology into the mainstream of civil engineering. Thus, we will continue to see the manifestation of this technology in civil structures.

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