- Email: [email protected]
Response of discussion “Estimating optimum parameters of tuned mass dampers using harmony search”
Engineering Structures xxx (2013) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Discussion
Response of discussion ‘‘Estimating optimum parameters of tuned mass dampers using harmony search’’ Gebrail Bekdasß ⇑, Sinan Melih Nigdeli Department of Civil Engineering, Istanbul University, 34320 Avcılar, Istanbul, Turkey
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Tuned Mass Damper (TMD) Optimization Harmony Search (HS) Earthquake excitation
a b s t r a c t In the discussion of Miguel et al., the analyses results of Harmony Search (HS) approach were investigated but the exact results could not be found. In this response, the possible reasons of differences between the results of discussion and original paper were illustrated. The differences may be originated by the analysis method and content of the earthquake excitation. Ó 2013 Elsevier Ltd. All rights reserved.
1. The analysis method used in the original paper of Bekdas and Nigdeli [1] The analyses of multiple degree of freedom (MDOF) structure were performed by transforming the coupled equations of motion into generalized coordinates from geometric coordinates. After the solutions of all modes were obtained, the solutions were transformed back into geometric coordinates. The equation of motions and transformation can be seen in the original paper [1]. The dynamic analysis of a mode was obtained by using Matlab with Simulink [2]. The Simulink block diagram of Eq. (8) given in original paper [1] is shown in Fig. 1. The block diagram was constructed by using continuous state blocks. Runge–Kutta method with 0.001 s time step was chosen for solver. Matlab with Simulink uses a fourth order Runge–Kutta method. For the analyses of El-Centro record, north–south component of seismic record downloaded from ‘‘http://www.vibrationdata.com/ elcentro.htm’’ was used. In Tables 1 and 4 given in original paper [1], the maximum displacement results of structure without TMD and HS approach were directly obtained by using the employed program. The other results were directly taken from the paper of Hadi and Arfiadi [3]. The solution method of the discussion results was not clearly explained. A different method with different time step and con-
⇑ Corresponding author. Tel.: +90 212 4737070; fax: +90 212 4737176. E-mail addresses: [email protected] (G. Bekdasß), [email protected] (S.M. Nigdeli).
tent of earthquake data (time step, time period of data or filtering) may be effective on the results. A small difference can be also seen for the results of Hadi and Arfiadi [3] and Lee et al. [4] with the discussion results, so the analysis method of Hadi and Arfiadi [3], discussion and original paper are different. In the second session of this response, the results were investigated for the example 1 of the original paper by using the tuned mass damper (TMD) parameters of Hadi and Arfiadi [4]. Different methods with different time steps were used.
2. Investigation of results for different solvers The maximum absolute displacement respect to the ground under El-Centro excitation was inspected for the TMD parameters (md = 108 t, cd = 151.5 kN s/m and kd = 3750 kN/m) proposed by Hadi and Arfiadi [3]. The analyses were done for both continuous and discrete state methods with different time steps.
2.1. Continuous state analyses In the continuous state analyses, two methods were used for 0.001 s and 0.01 s time steps. These methods are Runge–Kutta and extrapolation. The results are given in Table 1. As seen from the results of Table 1, the difference of the method and time step is not effective on the results for continuous state. In Fig. 2, the time history of the displacement of the 10th floor is given. The time history is quite different with the time histories gi-
0141-0296/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2013.03.043
Please cite this article in press as: Bekdasß G, Nigdeli SM. Response of discussion ‘‘Estimating optimum parameters of tuned mass dampers using harmony search’’. Eng Struct (2013), http://dx.doi.org/10.1016/j.engstruct.2013.03.043
2
G. Bekdasß, S.M. Nigdeli / Engineering Structures xxx (2013) xxx–xxx
Fig. 1. Block diagram of the equation of a mode.
Table 1 Continuous state results for maximum absolute displacement respect to the ground. Floor
Runge–Kutta (0.01 s)
Runge–Kutta (0.001 s)
Extrapolation (0.01 s)
Extrapolation (0.001 s)
1 2 3 4 5 6 7 8 9 10 TMD
0.015 0.030 0.043 0.056 0.066 0.077 0.086 0.093 0.098 0.100 0.332
0.015 0.030 0.043 0.056 0.066 0.077 0.086 0.093 0.098 0.100 0.332
0.015 0.030 0.043 0.056 0.066 0.077 0.086 0.093 0.098 0.100 0.332
0.015 0.030 0.043 0.056 0.066 0.077 0.086 0.093 0.098 0.100 0.332
0.15 Table 2 Discrete state results for maximum absolute displacement respect to the ground.
x 10 (m)
0.1 0.05
Floor
0
1 2 3 4 5 6 7 8 9 10 TMD
-0.05 -0.1
0
5
10
15
20
Time (s)
Time step (s) 0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.016 0.031 0.044 0.056 0.067 0.078 0.087 0.094 0.099 0.102 0.340
0.016 0.031 0.045 0.057 0.069 0.080 0.089 0.097 0.102 0.104 0.349
0.016 0.032 0.046 0.059 0.071 0.083 0.092 0.100 0.105 0.108 0.357
0.017 0.033 0.047 0.061 0.074 0.085 0.095 0.103 0.108 0.111 0.368
0.017 0.033 0.048 0.062 0.076 0.088 0.098 0.106 0.112 0.115 0.381
0.018 0.034 0.049 0.064 0.078 0.091 0.101 0.110 0.116 0.119 0.395
0.018 0.035 0.050 0.066 0.081 0.094 0.105 0.114 0.120 0.124 0.410
0.019 0.036 0.052 0.067 0.083 0.097 0.109 0.119 0.125 0.129 0.425
Fig. 2. Displacement of the 10th floor with respect to ground (Runge–Kutta method with 0.001 s time step).
ven in the discussion. This reason may be resulted by the different content of the excitation. 2.2. Discrete state analyses The first numerical example was also analyzed in discrete state for TMD parameters of Hadi and Arfiadi [3]. The analysis results for difference fixed step sizes were given in Table 2.
As seen in Table 2, time step is effective on the maximum results of time displacements. For 0.007 s and 0.008 s time step values, the results are near to values given in discussion. These results clearly show that the maximum results of dynamic analyses can be different from each other for discrete state. The 10th floor time histories for discrete state analyses with 0.001 s, 0.005 s and 0.008 s time steps were given in Fig 3a, b and c, respectively.
Please cite this article in press as: Bekdasß G, Nigdeli SM. Response of discussion ‘‘Estimating optimum parameters of tuned mass dampers using harmony search’’. Eng Struct (2013), http://dx.doi.org/10.1016/j.engstruct.2013.03.043
G. Bekdasß, S.M. Nigdeli / Engineering Structures xxx (2013) xxx–xxx
0.15
3. Conclusion According to the analyses given in Section 2, the results may vary for the analyses in discrete state with different time steps. Since the solution method was not clearly given in both discussion and original paper, the difference of the results between discussion and original paper may be originated because of this reason. Also, the time histories are quite different in the discussion. For that reason, the excitation may have different content. Especially, the time step of the excitation may be different.
0.1
x 10 (m)
0.05 0 -0.05
References
-0.1
0
3
5
10
15
20
15
20
15
20
Time (s)
(a)
0.15
[1] Bekdasß G, Nigdeli SM. Estimating optimum parameters of tuned mass dampers using harmony search. Eng Struct 2011;33:2716–23. [2] The MathWorks Inc. MATLAB R2010a. Natick, MA, USA; 2010. [3] Hadi MNS, Arfiadi Y. Optimum design of absorber for MDOF structures. J Struct Eng (ASCE) 1998;124:1272–80. [4] Lee CL, Chen YT, Chung LL, Wang YP. Optimal design theories and applications of tuned mass dampers. Eng Struct 2006;28:43–53.
0.1
x 10 (m)
0.05 0
-0.05 -0.1
0
5
10
Time (s)
(b)
0.15 0.1
x 10 (m)
0.05 0 -0.05 -0.1
0
5
10
Time (s)
(c) Fig. 3. Displacement of the 10th floor with respect to ground (discrete state analyses).
Please cite this article in press as: Bekdasß G, Nigdeli SM. Response of discussion ‘‘Estimating optimum parameters of tuned mass dampers using harmony search’’. Eng Struct (2013), http://dx.doi.org/10.1016/j.engstruct.2013.03.043
Contents lists available at SciVerse ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Discussion
Response of discussion ‘‘Estimating optimum parameters of tuned mass dampers using harmony search’’ Gebrail Bekdasß ⇑, Sinan Melih Nigdeli Department of Civil Engineering, Istanbul University, 34320 Avcılar, Istanbul, Turkey
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Tuned Mass Damper (TMD) Optimization Harmony Search (HS) Earthquake excitation
a b s t r a c t In the discussion of Miguel et al., the analyses results of Harmony Search (HS) approach were investigated but the exact results could not be found. In this response, the possible reasons of differences between the results of discussion and original paper were illustrated. The differences may be originated by the analysis method and content of the earthquake excitation. Ó 2013 Elsevier Ltd. All rights reserved.
1. The analysis method used in the original paper of Bekdas and Nigdeli [1] The analyses of multiple degree of freedom (MDOF) structure were performed by transforming the coupled equations of motion into generalized coordinates from geometric coordinates. After the solutions of all modes were obtained, the solutions were transformed back into geometric coordinates. The equation of motions and transformation can be seen in the original paper [1]. The dynamic analysis of a mode was obtained by using Matlab with Simulink [2]. The Simulink block diagram of Eq. (8) given in original paper [1] is shown in Fig. 1. The block diagram was constructed by using continuous state blocks. Runge–Kutta method with 0.001 s time step was chosen for solver. Matlab with Simulink uses a fourth order Runge–Kutta method. For the analyses of El-Centro record, north–south component of seismic record downloaded from ‘‘http://www.vibrationdata.com/ elcentro.htm’’ was used. In Tables 1 and 4 given in original paper [1], the maximum displacement results of structure without TMD and HS approach were directly obtained by using the employed program. The other results were directly taken from the paper of Hadi and Arfiadi [3]. The solution method of the discussion results was not clearly explained. A different method with different time step and con-
⇑ Corresponding author. Tel.: +90 212 4737070; fax: +90 212 4737176. E-mail addresses: [email protected] (G. Bekdasß), [email protected] (S.M. Nigdeli).
tent of earthquake data (time step, time period of data or filtering) may be effective on the results. A small difference can be also seen for the results of Hadi and Arfiadi [3] and Lee et al. [4] with the discussion results, so the analysis method of Hadi and Arfiadi [3], discussion and original paper are different. In the second session of this response, the results were investigated for the example 1 of the original paper by using the tuned mass damper (TMD) parameters of Hadi and Arfiadi [4]. Different methods with different time steps were used.
2. Investigation of results for different solvers The maximum absolute displacement respect to the ground under El-Centro excitation was inspected for the TMD parameters (md = 108 t, cd = 151.5 kN s/m and kd = 3750 kN/m) proposed by Hadi and Arfiadi [3]. The analyses were done for both continuous and discrete state methods with different time steps.
2.1. Continuous state analyses In the continuous state analyses, two methods were used for 0.001 s and 0.01 s time steps. These methods are Runge–Kutta and extrapolation. The results are given in Table 1. As seen from the results of Table 1, the difference of the method and time step is not effective on the results for continuous state. In Fig. 2, the time history of the displacement of the 10th floor is given. The time history is quite different with the time histories gi-
0141-0296/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2013.03.043
Please cite this article in press as: Bekdasß G, Nigdeli SM. Response of discussion ‘‘Estimating optimum parameters of tuned mass dampers using harmony search’’. Eng Struct (2013), http://dx.doi.org/10.1016/j.engstruct.2013.03.043
2
G. Bekdasß, S.M. Nigdeli / Engineering Structures xxx (2013) xxx–xxx
Fig. 1. Block diagram of the equation of a mode.
Table 1 Continuous state results for maximum absolute displacement respect to the ground. Floor
Runge–Kutta (0.01 s)
Runge–Kutta (0.001 s)
Extrapolation (0.01 s)
Extrapolation (0.001 s)
1 2 3 4 5 6 7 8 9 10 TMD
0.015 0.030 0.043 0.056 0.066 0.077 0.086 0.093 0.098 0.100 0.332
0.015 0.030 0.043 0.056 0.066 0.077 0.086 0.093 0.098 0.100 0.332
0.015 0.030 0.043 0.056 0.066 0.077 0.086 0.093 0.098 0.100 0.332
0.015 0.030 0.043 0.056 0.066 0.077 0.086 0.093 0.098 0.100 0.332
0.15 Table 2 Discrete state results for maximum absolute displacement respect to the ground.
x 10 (m)
0.1 0.05
Floor
0
1 2 3 4 5 6 7 8 9 10 TMD
-0.05 -0.1
0
5
10
15
20
Time (s)
Time step (s) 0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.016 0.031 0.044 0.056 0.067 0.078 0.087 0.094 0.099 0.102 0.340
0.016 0.031 0.045 0.057 0.069 0.080 0.089 0.097 0.102 0.104 0.349
0.016 0.032 0.046 0.059 0.071 0.083 0.092 0.100 0.105 0.108 0.357
0.017 0.033 0.047 0.061 0.074 0.085 0.095 0.103 0.108 0.111 0.368
0.017 0.033 0.048 0.062 0.076 0.088 0.098 0.106 0.112 0.115 0.381
0.018 0.034 0.049 0.064 0.078 0.091 0.101 0.110 0.116 0.119 0.395
0.018 0.035 0.050 0.066 0.081 0.094 0.105 0.114 0.120 0.124 0.410
0.019 0.036 0.052 0.067 0.083 0.097 0.109 0.119 0.125 0.129 0.425
Fig. 2. Displacement of the 10th floor with respect to ground (Runge–Kutta method with 0.001 s time step).
ven in the discussion. This reason may be resulted by the different content of the excitation. 2.2. Discrete state analyses The first numerical example was also analyzed in discrete state for TMD parameters of Hadi and Arfiadi [3]. The analysis results for difference fixed step sizes were given in Table 2.
As seen in Table 2, time step is effective on the maximum results of time displacements. For 0.007 s and 0.008 s time step values, the results are near to values given in discussion. These results clearly show that the maximum results of dynamic analyses can be different from each other for discrete state. The 10th floor time histories for discrete state analyses with 0.001 s, 0.005 s and 0.008 s time steps were given in Fig 3a, b and c, respectively.
Please cite this article in press as: Bekdasß G, Nigdeli SM. Response of discussion ‘‘Estimating optimum parameters of tuned mass dampers using harmony search’’. Eng Struct (2013), http://dx.doi.org/10.1016/j.engstruct.2013.03.043
G. Bekdasß, S.M. Nigdeli / Engineering Structures xxx (2013) xxx–xxx
0.15
3. Conclusion According to the analyses given in Section 2, the results may vary for the analyses in discrete state with different time steps. Since the solution method was not clearly given in both discussion and original paper, the difference of the results between discussion and original paper may be originated because of this reason. Also, the time histories are quite different in the discussion. For that reason, the excitation may have different content. Especially, the time step of the excitation may be different.
0.1
x 10 (m)
0.05 0 -0.05
References
-0.1
0
3
5
10
15
20
15
20
15
20
Time (s)
(a)
0.15
[1] Bekdasß G, Nigdeli SM. Estimating optimum parameters of tuned mass dampers using harmony search. Eng Struct 2011;33:2716–23. [2] The MathWorks Inc. MATLAB R2010a. Natick, MA, USA; 2010. [3] Hadi MNS, Arfiadi Y. Optimum design of absorber for MDOF structures. J Struct Eng (ASCE) 1998;124:1272–80. [4] Lee CL, Chen YT, Chung LL, Wang YP. Optimal design theories and applications of tuned mass dampers. Eng Struct 2006;28:43–53.
0.1
x 10 (m)
0.05 0
-0.05 -0.1
0
5
10
Time (s)
(b)
0.15 0.1
x 10 (m)
0.05 0 -0.05 -0.1
0
5
10
Time (s)
(c) Fig. 3. Displacement of the 10th floor with respect to ground (discrete state analyses).
Please cite this article in press as: Bekdasß G, Nigdeli SM. Response of discussion ‘‘Estimating optimum parameters of tuned mass dampers using harmony search’’. Eng Struct (2013), http://dx.doi.org/10.1016/j.engstruct.2013.03.043