PSI - Issue 64

Amir Shamsaddinlou et al. / Procedia Structural Integrity 64 (2024) 360–367 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

365

6

Real ( ) −33.67931 −31.45189 −27.96010 −23.51421 −18.50924 −13.38992 −8.61111 −4.59744 −1.70554 −0.19236

Imaginary ( ) ±76.9902 ±74.8701 ±71.2800 ±66.1625 ±59.4843 ±51.2667 ±41.6101 ±30.7057 ±18.8336 ±6.3479

Pole −33.67931 ± 76.9902 −31.45189 ± 74.8701 −27.96010 ± 71.2800 −23.51421 ± 66.1625 −18.50924 ± 59.4843 −13.38992 ± 51.2667 −8.61111 ± 41.6101 −4.59744 ± 30.7057 −1.70554 ± 18.8336 −0.19236 ± 6.3479

No.

1 2 3 4 5 6 7 8 9

10 −163.61111 The control performance is evaluated through a series of performance indices obtained from the ratio between the controlled and uncontrolled responses. Six criteria are used: the first three are the maximum values, and the other three are the norm values of structural response. These criteria are briefly presented in Table 3. These criteria, , ̈ and are maximum uncontrolled inter-story drift, absolute roof acceleration, and base shear force. ( ) and ̈ ( ) are controlled inter-story drift and absolute acceleration of the − ℎ level. is the seismic mass of the − ℎ level. Also, ‖.‖ is the normed operator. Table 3. Performance criteria for controlled building. Peak inter-story drift: 1 = { . (| ( )| ) } Peak level acceleration: 2 = { . { ̈ ̈ ( ) } } Peak base shear force: 3 = { | ∑ ̈ ( ) | } Normed inter-story drift: 4 = { . (‖ ( )‖ ) ‖ ‖ } Normed level acceleration: 5 = { . ‖ ̈ ‖ ̈ ( ) ‖ ‖ } Normed base shear force: 6 = { ‖ ∑ ̈ ( ) ‖ ‖ ‖ } 7. Result and Discussion This section presents the results obtained from the optimal design of the TMD in terms of different objective functions and using the CGO optimization algorithm. Then, the seismic performance of the building structure equipped with the designed TMD is evaluated and compared for each objective function. Table 4 shows the results of solving the TMD design optimization problem according to each objective function. This table presents the optimal value of the objective function and the values obtained for the damper's mechanical characteristics. In the following, the structure's performance equipped with each of these dampers is evaluated. Table 4. The results of the optimum design of three objective functions. Method Objective Function OF1 OF2 OF3 Cost of Design 4.8925 7.6772 -165.6192 Figure 2 compares the transfer function of the acceleration response for the first floors and roof of the structure in uncontrolled and controlled cases with the TMD designed based on the transfer function of the acceleration response. The effect of this TMD can be seen in reducing the value of the transfer function of acceleration response in the frequency range of the structure. Figure 3 compares the geometric location of the system poles for the shear frame structure in uncontrolled and controlled cases with the TMD designed based on the system pole location. According to the figure, the effect of the damper is evident in the displacement of the poles of the system towards the left area of the s space and more stability. ∑ Parameter 1 ( ) 1 ( ⁄ ) 1 ( . ⁄ ) 143.98 4961.5 285.61 99.17 4964.6 119.97 128.87 4999.9 425.29