Takewaki method

Takewaki Method The aim ofthe Takewaki (1997) method is to minimise an objective function given by the sum of the amplitudes ofthe interstory drifts ofthe transfer function, evaluated atthe undamped natural frequency of the structure, subject to a constraint on the total amount of added viscous damping. Initially the added damping is uniformly distributed and the optimum distribution is then achieved using a gradient-based search algorithm, that is, the damping distribution... 

Takewaki (1997) proposed a stiffness-damping simultaneous optimization procedure where the sum of mean square responses to stationary random excitations is minimized subjected to the constraints on total stiffness and damping capacity. It is a two-step optimization method where, in the first step, the optimal design is found for a specified value of total stiffness and damping, while in the second step the procedure is repeated for a set of total stiffiiess and damping capacity. 

While all methods investigated were effective, the three optimal placement techniques studied, the SSSA, Takewaki and Lavan methods, all offered greater reductions in interstory drifts than the uniform and stiffness-proportional schemes. It is therefore evident that there is benefit to be gained from the additional effort of implementing an iterative scheme, in terms of further response reductions for a given outlay. It is notable that this benefit of the advanced schemes is not so evident when considering peak absolute floor accelerations, which do not reveal large differences between any of the added damper schemes, apart from consistently smaller acceleration distributions in the upper floors for the standard placement methods. 

In the last decade, there have been several studies on optimal damper positioning. Aydin et al (2007) presented an alternative to Takewaki s method by considering the transfer function... 

Takewaki, I. (1997b). Efficient redesign of damped structural systems for target transfer functions. Computer Methods in Applied Mechanics and Engineering, 747(3-4), 275-286. doi 10.1016/ S0045-7825(97)00022-4... 

Takewaki, 1. (2000c). A new probabilistic critical excitation method. Journal of Structural and Construction Engineering, 533, 69-74. 

Takewaki, 1. (2001b). Nonstationary random critical excitation for nonproportionally damped structural systems. Computer Methods in Applied Mechanics and Engineering, 190(31), 3927-3943. doi 10.1016/S0045-7825(00)00354-6... 

Takewaki, 1. (2007). Critical excitation methods in earthquake engineering. Netherlands Elsevier. 

Takewaki, . (1998). Optimal damperpositioning in beams for minimum dynamic compliance. Computer Methods in AppliedMechanics and Engineering, 755(1-4), 363-373. doi 10.1016/80045-7825(97)00221-1... 

Takewaki and Ben-Haim 2005 Takewaki 2006, 2013 Takewaki et al. 2012 Kanno and Takewaki 2006 Elishakoff and Ohsaki 2010). It is well understood and accepted that the interval analysis is a representative of the reliable uncertainty analysis methods. It seems that the concept of interval analysis was introduced by Moore (1966). Alefeld and Herzberger (1983) have then conducted the pioneering work. They treated... 

In this section, the URP (updated reference-point) method proposed originally for stochastic input is explained (Fujita and Takewaki 2011a). This method can be used as an efficient uncertainty analysis to obtain the robustness function a explained in the previous section. Since the URP method takes full advantage of an approximation of first- and second-order Taylor series expansion in the interval analysis, the formulation of Taylor series expansion in the interval analysis and the achievement of second-order Taylor series expansion proposed by Chen et al. (2009) are explained briefly. 

This is the same as Eq. 12. The evaluation of first- and second-order sensitivities/ x- and/ x-Xi is made at the nominal model (reference point). It should be noted that the correlation among interval parameters is not taken into account. Here a method called the lIRP (updated reference-point) method (Fujita and Takewaki 2011a) is used. This method changes the reference point step by step. The flowchart for finding the upper bound of the objective function is shown in Fig. 17a. 

Robust Control of Building Structures Under Uncertain Conditions, Fig. 21 Comparison of maximum interstory drift of base-isolation story derived by URP method with MCS (Fujita and Takewaki 2012a)... 

Takewaki I, Conte IP, Mahin SA, Pister KS (1991) A unified earthquake-resistant design method for steel frames using ARMA models. Earthq Eng Struct Dyn 20(5) 483-501... 

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