STRUCTURAL SEMI-ACTIVE CONTROL DEVICE

Transcription

1 STRUCTURAL SEMI-ACTIVE CONTROL DEVICE Ming-Hiang SHIH SUMMARY Method for vibration reduction of tructure under dynamic excitation uch a wind and earthquake were generally claified into active control and paive control. Both method have their pecific application field and limitation. Recently, epecially after Kobe Earthquake 995, reearcher gradually doubt about the feaibility of thee method by trong earthquake. Engineer and reearcher intend to find more efficient and more reliable method for vibration reduction under trong eimic excitation. Method uch a hybrid control and emi-active control are developed and have directed reearcher attention to development of control apparatu. One emi-active control apparatu that i invented and contructed by the author will be preented in thi report. Moreover, ome numerical reult are ued to examine the feaibility of thi control ytem. The emi-active control apparatu, which i introduced in thi report, include active joint and tiffener. Active joint are particularly connector that can releae the retraint in one of two pecific direction. The tiffener are ame a common tiffener improving the lateral tiffne of tructure uch a hear wall, bracing and pretreed tendon. They are fixed connected to the tructure at one ide, and indirectly connected via active joint to the tructure at the other ide. The tiffener have the function to tore the control energy by vibration of tructure. The tiffener in cooperation with active joint will diipate a large amount of mechanical energy of eimic excited tructure, even though the tiffener i elatically deformed. The mot noticeable feature of thi ytem i that there i no external energy required. Structural vibration under trong earthquake will be evidently and reliably reduced. The functional principle and contruction of active joint are in detail introduced at firt part of the text. An experimental reult of mall model and ome numerical analyi will be ued to how the efficiency of the new ytem. The reult conclude that thi emi-active control ytem will reduce more than 70% of maximal deflection without diadvantage to induce. INTRODUCTION Engineer have learned by catatrophic earthquake experience, that the afety of tructure i uually not guaranteed under economic conideration. For the ake improving the eimic reitant capacity of tructure, the trength of tructural member or the tiffne of tructure will be improved. But unfortunately, thi attempt i not alway ucceful and uually uneconomical. Moreover, the performance deign require in many cae reduction of diplacement and/or acceleration repone under pecific earthquake magnitude. Seimic reitant deign, which generally enhance the tructural ductility, can merely improve the tructural afety but can t reduce the eimic repone. Modern technologie were developed in recent year. They improve the tructural afety by mean of reducing repone. National Kaohiung Firt Univerity of Science and Technology, Taiwan. mhhih@ccm.nkfu.edu.tw

2 Technologie attempt to reduce the repone of tructure under dynamic excitation are generally claified into active control [Leipholz et al 986, Soong 990] and paive control [Aguirre et al. 992, Xia 992] method. Both method have their pecific application field and limitation. Recently, epecially after Kobe Earthquake 995, reearcher gradually doubt about the feaibility of thee method by trong earthquake. Engineer and reearcher intend to find more efficient and more reliable method for vibration reduction under trong eimic excitation. Method uch a hybrid control and emi-active control [Kurino et al. 998] are developed and have directed reearcher attention to the development of control apparatu. The mot important feature of emiactive control method are high reduction effect and minimal demand on control energy. Due to low energy demand, the emi-active control are abolutely table, which i generally a problem of active control. A emi-active control apparatu deigned by the author [Shih 997] will be introduced in thi paper. Key advance of the new propoed control method conit in the development of active joint, which are practically connector that can releae the retraint between main tructure and tiffener in one of two pecific direction. By utilizing the active joint, the ign of inner tre of tiffener can be changed without triking requirement on external energy upply. The direction of reultant of tiffener act on tructure are then revered, and it i poible, that the reultant alway oppoe againt the motion of the tructure. Mechanical energy of tructure i diipated, even though the tiffener deform elatically. FUNDAMENTAL PRINCLPLE Stiffener uch a bracing and hear wall are believed to be available for diipating tructural mechanical energy only when they practice platic deformation or vicoe effect i preent. Elatic deformed member are generally acknowledged to be incapable of energy diipation. Thi viewpoint wa not alway correct. We can ue the relation between work, force and diplacement to declare it. Baic equation indicate the relation of work; force and diplacement vector take the form: dw = F dx () In equation (a) dw i not real differential of work but the work done by a contant force by infiniteimal motion of tructure. Vector F i the reultant vector of tiffener acting on main tructure and dx i the infiniteimal diplacement vector of point ubjected to force F. Divide both ide of equation () by infiniteimal time interval dt, we obtain the following equation: dw dt dx = F or (2) dt W = F x. (3) It i clear from equation (3) that the change rate of work depend on magnitude of vector F and x, and alo on the angle between thee two vector. In cae, that the force F and velocity x are collinear, tiffener can perform negative work, if the force act oppoite to the motion of tructure. In general cae that tiffener alway connect with main tructure, there i a fixed relation between the vector F and x. The change rate of work done by elatic tiffener i negative when magnitude of diplacement increae, but i poitive when magnitude of diplacement decreae. Total work done by tiffener in every half cycle of ocillation i zero. Thi i the reaon why elatic deformed tiffener can t diipate energy. On the contrary, elatic deformed tiffener can perform energy diipation if the tiffener i not fixed connected to main tructure. In cae, that tiffener i decoupled at on end, the tiffener vibrate freely after the decoupling in natural frequency of tiffener. The interaction force between tiffener and tructure uddenly become zero. Thi tate hold until the tiffener i again coupled with the tructure. If the tiffener i coupled again before the free vibration top, an interaction force exit between tiffener and tructure. The magnitude lie between zero and the magnitude before decoupling, and the direction can be either oppoite or identical to the original one, depend on deformation tate of the tiffener. Becaue we can alway elect a reaction force oppoing to the motion of tructure, negative change rate of work can be guaranteed. Thi feature make it poible that the 2

3 elatic deformed tiffener are alo capable of energy diipation. Energy diipation by mean of decoupling and re-coupling action in equence i the baic principle of thi new propoed control method. An apparatu that make it poible will be preented in next ection. ACTIVE JOINT To perform the required function above, active joint, that connect the tiffener and main tructure, mut act fat and preciely. Relative to re-coupling, the fat and precie decoupling i relative imple to achieve. The major difficulty conit in the accurate re-coupling action. According to the illutration in lat ection, the optimal intant of re-coupling i that moment about half natural period of the tiffener after the decoupling, ince the maximal negative change rate of work can be achieved at thi moment. Thi time interval i uually le than econd. No literature decribe an apparatu that i enough precie to do it. Figure how an active joint propoed by the author. The active joint conit eentially of two ingledirectional connector. Both connector allow relative motion between tiffener and main tructure in one pecific direction (left or right). In cae that the hydraulic mechanim for decoupling i till, the tiffener and tructure are practice coupled together, and relative motion in both direction i prevented. If the hydraulic cylinder act on one connector (ay the right one), relative motion in direction left i free, while the relative motion in the other direction remain prevented. Thi property reult in automatic re-coupling at the optimal intant. It i alo to emphaize that the force neceary to releae the one-ide connector i little. The operation of the active joint require only tiny energy. Hydraulic Mechanim for Decoupling To Stiffener Connect to Structure Figure : Contruction of Active Joint Tranducer Active Joint Stiffenerer Deciion Making U it Control Command Figure 2: Setup of Semi-Active Control Sytem with Active Joint 3

4 Figure 2 how the etup of emi-active control ytem with active joint. Tranducer are needed for every active joint to detect the direction of motion at related tory. When the direction of motion change, the Deciion Making Unit end a control ignal to the aociate active joint. The interaction force between tiffener and main tructure i then revered. Figure 3 how the typical time hitory of interaction force F. In thi figure, it i found that the magnitude after decoupling and re-coupling action reduce ome. Thi i a reult of friction and damping effect in active joint and tiffener. The reaonable ratio between thee two magnitude lie between 0.7 and 0.95, which depend on the natural frequency of tiffener and quality of active joint. The ratio i called retoring-coefficient (denoted by α) and defined a following equation. α = F F,,0 (4) Where F, 0 and F, are magnitude of reaction force before and after control action, repectively. Diplacement/Control Force Diplacement Control Force Control Command Figure 3: Typical Hitory of Control Force and Control Command EXPERIMENTAL STUDIES Experiment on caled down ingle degree of freedom model were performed for the purpoe verifying the vibration reduction effect of the control ytem with active joint. Three group of experiment were proceeded, they are: Group I, free vibration tet; Group II, harmonic excited vibration tet at reonant frequency; group III, excited vibration tet. The repone hitorie will avail againt qualitative verification of control effect. To keep the identity of the dynamical propertie of controlled and uncontrolled ytem, ame tiffener were ued in all tet. The ytem parameter for all experiment model are hown in Table. Model Ma (kg) Table : Sytem parameter of experiment model Structural Stiffener Structural Active Joint Stiffne(N/m Stiffne(N/M Damping preent ) ) Ratio(%) Retoring- Coefficient (α) Without Control With Control NO YES

5 A indicated in Table, the ratio of tiffener' tiffne to total tiffne i Relative to the ratio of common paive ytem uch a ADAS ytem, thi value i very little [Xia 992]. The major advantage of thi feature i that the natural frequency of controlled ytem will not be apparently increaed, o that the acceleration repone will alo be reduced. The retoring-coefficient wa etimated by experimental data prior to the tet. Becaue of large influence of friction effect on mall model, thi value i little. Although the condition impair the control effect, the time hitorie of diplacement repone indicate a noticable reduction effect. Reult of Free Vibration Tet Repone time hitorie are hown in Figure 4. Reult of free vibration tet indicate a rapid elimination of vibration. Eential diplacement diappear in about one ocillation. The tiny vibration after firt period cannot be eliminated from control ytem, becaue the remaining interaction force between tiffener and main tructure cannot overcome the friction in active joint. Free Vibration Repone Diplacement (cm) with control w/o control Figure 4: Repone time hitory of free vibration Harmonic excited vibration tet In thee tet, tructure were excited by harmonic loading with the natural frequency of tructure (.05Hz). Reult were hown in Figure 5. The repone of ytem with control i a expected lower than that without control. An equivalent damping ratio of 25% can be concluded from the time hitory in Fig. 5. Harmonic Excited (Reonanat) Repone Diplacement (cm) with control w/o control Figure 5: Diplacement repone under harmonic (reonant) excitation Seimic excited vibration tet Record of ground motion of earthquake EL Centro in 940 wa caled down and imulated to excite the model. Both controlled and uncontrolled repone time hitorie are hown in Figure 6. It can be concluded from the 5

6 time hitory that the maximum diplacement of ytem with control equal about 50% of ytem without control. Main reaon for the poor reduction effect i the low retoring coefficient. A mentioned earlier, the influence of friction i eriou for mall model. Experiment on larger model will be performed in thi year. The fact that there i no evident change in natural frequency i alo worthy to emphaize, beide the reduction of diplacement. The acceleration repone i alo reduced under thi condition. It i reaonable that the maximal diplacement occurred when the eential ground motion arrive. Thi can be a key point to improve the control method. Thi problem could be overcome by mean of pretreing the tiffener prior to the earthquake. An even better control effect i expected. Seimic Vibration (EL Centro 940) Diplacement (cm) wth control w/o control Figure 6: Diplacement repone under eimic excitation (EL Centro940) CONCLUSION A emi-active control device, namely active joint, wa preented. The active joint conit merely of elementary machine element. A high reliable control i achieved, becaue no precie control i needed for the propoed control method. Reult of numerical tudie in another work of the author [Shih 996] indicate following important concluion:. 80% of maximal diplacement can be reduced by ue of active joint. 2. A high equivalent damping ratio of 40% can be achieved. 3. The control effect will only lightly affect by malfunction of everal active joint. Further experimental tudie on larger model are planned and will be performed at National Center of Reearch on Earthquake Engineering (Taiwan) at the end of thi year. Effect of friction and control algorithm will be tudied. REFERENCE Aguirre, M., Sánchez, A.R. (992), "Structural Seimic Damper", ASCE, Journal of Structural Engineering, Vol. 08, No. 5. Kurino, H. and Kobori, T. (998), "Semi-Active Structural Repone Control by Optimizing the Forcedeformation Loop of Variable Damper", Second World Conference on Structural Control, Kyoto. Leipholz, H.H.E., Abdel-Rohman, M. (986), Control of Structure, Martinu Nijhoff Publiher. Shih, M.-H. (996), Eine active Regelung zur Schwingungreduzierung von Bauwerken unter eimichen Beanpruchungen, Diertation, RWTH Aachen, Germany. Shih, M.-H. (997), "Active Control Apparatu and Method for Vibration Reduction", American Patent, Application No. 08/ Soong, T. T. (990), Active Structural Control - Theory and Practice, Longman, London and Wiley, NewYork. Xia, C., Hanon, R.D. (992), "Influence of ADAS Element Parameter on Building Seimic Repone", ASCE, Journal of Structural Engineering", Vol. 8, No. 7, July. 6