مقایسه ای از روش های جاگذاری میراگر ویسکوز برای بهبود طراحی لرزه ای ساختمان A Comparison of Viscous Damper Placement Methods for Improving Seismic Building Design

Supplemental damping is becoming an increasingly tested and reliable seismic design strategy, and with it has come the evolution of building guidelines to include supplementally damped structures. The placement of dampers is a critical design concern, as the distribution of damping may greatly affect a building’s dynamic response and the necessary damping cost [Soong and Dargush, 1997]. However, building codes and guidelines do not prescribe a particular method for optimally placing dampers. While the 2003 NEHRP Provisions [BSSC, 2004] offers a methodology for determining a total damping value corresponding to a desired effective damping ratio, it does not address an optimal distribution of dampers. A large variety and quantity of damper placement methods have been proposed. Some of the earlier research efforts include Constantinou and Tadjbakhsh [1983], Ashour and Hanson [1987], Gürgöze and Müller [1992], and Hahn and Sathiavageeswaran [1992]. A novel heuristic placement method was the adaptation of the controllability index (previously used to determine optimal actuator locations for active structural control; Cheng and Pantelides, 1988) to sequentially place dampers where their effects are maximised [Zhang and Soong, 1992].Considered an advancement because ofits practicality,it was verified for a shear-frame model [Shukla and Datta, 1999] and a three-dimensional model [Wu et al., 1997]. An evolution of the sequential method was the Simplified Sequential Search Algorithm (SSSA) [Lopez-Garcia, 2001], which sought to further simplify the method for passive devices by decreasing the computational-effort of optimal location indices and simulated ground motions. For linear structures with linear viscous dampers, the method was as efficient as more complex placement methods, such as Takewaki [1997] and Gluck et al. [1996], in terms of interstory drifts [Lopez-Garcia, 2001]. Lopez-Garcia and Soong [2002] demonstrated the SSSA’s efficiency for a recommended number of procedural steps (damper sizes) based on building height. Limitations of the study include the use of few ground motions, small unrealistic effective damping ratios (less than 10% with dampers) for comparing SSSA to other methods, and the use of example structures and damper placement distributions from previous researchers, implying that the placement methods compared to SSSA were not followed in full and usability cannot be adequately compared. The method’s dependency on specific ground motions (particularly sensitive to ground motion characteristics for small damping ratios; Lopez-Garcia and Soong, 2002) and proven effectiveness limited to linear structures are two limitations of the technique. Many analytical optimal placement methods have been proposed, including methods based on the principles of active control theory [Gluck et al., 1996] and gradient-based search methods, including Takewaki [1997, 2000], Singh and Moreschi [2001], and Lavan and Levy [2006]. In particular, the Optimum for Minimum Transfer Functions [Takewaki, 1997] damper placement technique (abbreviated in this article as the “Takewaki” method) is a gradient-based optimization method with the objective of minimising the sum of the interstory drifts of the transfer function, evaluated at the structure’s undamped fundamental frequency. The method has since been developed further for more-complex structures, multiple performance objectives, and optimal sensitivity design to optimize total damping and distribution [Takewaki, 2009]. Since the damper placement schemes are based on the dynamic behavior of the structure alone, the Takewaki method claims independence from ground motions. Takewaki [1997] showed the efficiency of the method for two shear buildings and assumed stationary ground motions. Limitations of the technique include the objective of minimizing the sum of a performance indicator as opposed to the peak value, which is a more appropriate damage indicator, and the exclusion of design objectives in the method. The lack of verification of the 1997 method for realistic building designs and ground motion scenarios, the method’s status as an early benchmark method for optimal damper placement, and its claimed independence from ground motion characteristics warrants further investigation. Another notable analytical placement method is the Fully-stressed Analysis/Redesign procedure (abbreviated in this article as the “Lavan A/R” method), which uses engineering knowledge and a simple numerical approach for damper placement [Levy and Lavan, 2006]. Based on the principle of fully stressed design of truss members, the Lavan A/R method uses a recurrence relationship to maximize (“fully-stress”’) the dampers’ influence on the building performance parameter (i.e., drift allowance) and minimize the total adding damping necessary [Levy and Lavan, 2006]. A slight alteration of the original Fully Stressed Analysis/Redesign procedure may be used to constrain the total damping [Lavan and Levy, 2009]. The method has been verified by formal gradient-based optimization and applied to shear-frames, industrial frames [Levy and Lavan, 2006], and 3D irregular frames [Lavan and Levy, 2006]. Levy and Lavan [2009] showed the Lavan A/R method to be more effective than active control approaches such as Gluck et al. [1996] in terms of interstory drifts for multiple structures and ground motions. However, to the authors’ knowledge, the Lavan A/R method has not been compared to any other available advanced damper placement techniques, evaluated in terms of additional performance objectives, nor employed by other researchers from the ground-up to assess usability.Computationally-intensive evolutionary methods have notably included genetic algorithms, such as Singh and Moreschi [2002] and Apostolakis and Dargush [2010]. Recent methods consider multi-objective optimization [Lavan and Dargush, 2009] and structural softening incorporated with a strategic damper placement [Cimellaro and Retamales, 2007]. Takewaki [2009] presented a more comprehensive list of contributions to the field of damper placement and concludes that despite the large quantity of information, structural engineers lack tools necessary for placing dampers optimally in a structure. Comparisons of practical, existing placement methods may provide insight into the effectiveness of certain methods and their usability for practicing engineers, but few comparisons exist for realistic design scenarios. The purpose of this article is to present a thorough comparison of three advanced methods and two standard methods for realistic design scenarios and performance levels. The standard damper placement methods selected are Uniform damping and Stiffness Proportional damping methods, and the advanced damper placement methods are the Simplified Sequential Search Algorithm (SSSA) [Lopez-Garcia, 2001], the Optimal Damper Placement for Minimum Transfer Functions (Takewaki) [Takewaki, 1997], and the Fully Stressed Analysis/Redesign method (Lavan A/R) [Levy and Lavan, 2006]. The three advanced techniques were selected because they cover a range of methodologies and avoid the pitfalls of computationally-intensive methods. The comparison is made in terms reductions in peak interstory drifts, absolute accelerations, and residual drifts. The performance of the placement techniques are evaluated statistically for two steel moment resisting frames under varying seismic hazards levels. In addition, the usability and time efficiency of each damper placement method is assessed.