Optimal Tuned Mass Damper for Nonlinear Structure under Different Earthquakes
Authors
Abstract
Since there is no closed-form formula for designing TMD (Tuned Mass Damper) for nonlinear structures, some researchers have proposed numerical optimization procedures such as a genetic algorithm to obtain the optimal values of TMD parameters for nonlinear structures. These methods are based on determining the optimal values of TMD parameters to minimize the maximum response (e.g. inter story drift) of the controlled structure subjected to a specific earthquake record. Therefore, the performance of TMD that has been designed using a specific record strongly depends on the characteristics of the earthquake record. By changing the characteristics of the input earthquake record, the efficiency of TMD is changed and in some cases, it is possible that the response of the controlled structure is increased. To overcome the shortcomings of the previous researches, in this paper, an efficient method for designing optimal TMD on nonlinear structures is proposed, in which the effect of different ground motion records is considered in the design procedure. In the proposed method, the optimal value of the TMD parameters are determined so that the average maximum response (e.g. inter story drift) resulting from different records in the controlled structure is minimized. To illustrate the procedure of the propose method, the method is used to design optimal TMD for a sample structure. The results of numerical simulations show that the average maximum response of controlled structure resulting from different records is reduced significantly. Hence, it can be concluded that the proposed method for designing optimal TMD under different earthquakes is effective.
Keywords
1. Frahm, H., “Device for Damping Vibrations of Bodies”, US patent, No.989958, 1909.
2. Den Hartog, J. P., Mechanical Vibration, McGraw-Hill, New York, 4th edition, pp. 86-93, 1956.
3. Warburtun, G. B., “Optimum Absorbers Parameters for Various Combinations of Response and Excitation” Earthquake Engineering and Structural Dynamics, Vol.10, Issue 3, pp. 381-401, 1982.
4. Villaverde, R., “Reduction in Seismic Response with Heavily-Damped Vibration Absorbers” Earthquake Engineering and Structural Dynamics, Vol. 13, Issue 1, pp. 33–42, 1985.
5. Villaverde, R., and Koyama, L. A.,“Damped Resonant Appendages to Increase Inherent Damping in Buildings” Earthquake Engineering and Structural Dynamics, Vol. 22, Issue 6, pp. 491-507, 1993.
6. Hadi, M., N. S., Arfiadi, Y., “Optimum Design of Absorber for MDOF Structures”, Journal of Structural Engineering, Vol. 124, Issue 11,
pp. 1272-1280, 1998.
7. Kaynia, A. M., Veneziano, D., and Biggs, J. M., “Seismic Effectiveness of Tuned Mass Dampers”, Journal of the Structural Division, Vol.107, pp. 1466-1483, 1981
8. Bernal, D., “Influence of Ground Motion Characteristics on the Effectiveness of Tuned Mass Dampers”, Proceedings of the 11th World Conference on Earthquake Engineering, Acapulco, Mexico, pp.1455, 1996
9. Soto-Brito, R., and Ruiz, S. E., “Influence of Ground Motion Intensity on the Effectiveness of Tuned Mass Dampers”, Earthquake Engineering and Structural Dynamics, Vol. 28, Issue 11, pp. 1255-1271, 1999.
10. Joghataie, A., and Mohebi, M., “Design and Assesment of Optimal TMDs for Nonlinear Structures Under Earthquakes”, 10th World Conference on Seismic Isolation, Energy Dissipation and Active Vibrations Control of Structures, Istanbul, Turkey, 2007.
11. Mohebbi, M., and Joghataie, A., “Designing Optimal Tuned Mass Dampers for Nonlinear Frames by distributed genetic algorithms”, Design of Tall and Special Buildings, Vol. 21, Issue 1, pp. 57-76, 2012.
12. Bagley, J. D., “The Behaviour of Adaptive Systems Which Employ Genetic and Correlation Algorithms” Ph.D. Thesis, University of Michigan, 1967.
13. Goldberg, D. E., and Samtani, M. P., “Engineering Optimization via Genetic Algorithm”, Proceedings of the 9th Conference on Electronic Computation, ASCE, New York, N.Y., pp. 471-482, 1986.
15. McCulloch, W., and Pitts, W., “A Logical Calculus of Ideas Immanentin Nervous Activity”, Bulletin of Mathematical Biophysics, Vol. 5,
pp. 115-133, 1943.
17. Broomhead, D.vS., and Lowe, D., “Multivariable Functional Interpolation and Adaptive Networks”, Complex Systems, Vol. 2, pp. 321-355, 1988.
18. Han, H., Chen, Q., and Qiao, J., “ Research on an Online Self-Organizing Radial Basis Function Neural Network ”, Neural Computing and Applications, Vol. 19., Issue 5, pp. 667-676, 2010.
19. Sadek, F., Mhraz, B., Taylor, A.W., and Chung, R. M., “A Metod of Estimating the Parameters of Tuned Mass Dampers for Seismic Applications”, Earthquake Engineering and Structural Dynamics, Vol. 26, Issue 6, pp. 617-635, 1997.
20. Gupta, A., and Krawinkler, H., “Seismic Demands for Performance Evaluation of Steel Moment Resisting Frame Structures”, The John A. Blume Earthquake Engineering Center, Stanford University, Report no. 132, pp.342-359, 1999.
21. McKenna, F., Fenves, G. L., and Scott, M. H., Open System for Earthquake Engineering Simulation (OpenSees), Pacific Earthquake Engineering Research Center, University of California, Berkeley, 2006.
22. FEMA 356, NEHRP Guidelines for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency, Washington DC, 2000.
24. Somerville, P.G., Smith, N., Punyamurthula, S., and Sun, J., “Development of Ground Motion Time Histories for Phase 2 of the FEMA/SAC Steel Project”, SAC Background Document, Report No. SAC/BD 97/04, 1997.
2. Den Hartog, J. P., Mechanical Vibration, McGraw-Hill, New York, 4th edition, pp. 86-93, 1956.
3. Warburtun, G. B., “Optimum Absorbers Parameters for Various Combinations of Response and Excitation” Earthquake Engineering and Structural Dynamics, Vol.10, Issue 3, pp. 381-401, 1982.
4. Villaverde, R., “Reduction in Seismic Response with Heavily-Damped Vibration Absorbers” Earthquake Engineering and Structural Dynamics, Vol. 13, Issue 1, pp. 33–42, 1985.
5. Villaverde, R., and Koyama, L. A.,“Damped Resonant Appendages to Increase Inherent Damping in Buildings” Earthquake Engineering and Structural Dynamics, Vol. 22, Issue 6, pp. 491-507, 1993.
6. Hadi, M., N. S., Arfiadi, Y., “Optimum Design of Absorber for MDOF Structures”, Journal of Structural Engineering, Vol. 124, Issue 11,
pp. 1272-1280, 1998.
7. Kaynia, A. M., Veneziano, D., and Biggs, J. M., “Seismic Effectiveness of Tuned Mass Dampers”, Journal of the Structural Division, Vol.107, pp. 1466-1483, 1981
8. Bernal, D., “Influence of Ground Motion Characteristics on the Effectiveness of Tuned Mass Dampers”, Proceedings of the 11th World Conference on Earthquake Engineering, Acapulco, Mexico, pp.1455, 1996
9. Soto-Brito, R., and Ruiz, S. E., “Influence of Ground Motion Intensity on the Effectiveness of Tuned Mass Dampers”, Earthquake Engineering and Structural Dynamics, Vol. 28, Issue 11, pp. 1255-1271, 1999.
10. Joghataie, A., and Mohebi, M., “Design and Assesment of Optimal TMDs for Nonlinear Structures Under Earthquakes”, 10th World Conference on Seismic Isolation, Energy Dissipation and Active Vibrations Control of Structures, Istanbul, Turkey, 2007.
11. Mohebbi, M., and Joghataie, A., “Designing Optimal Tuned Mass Dampers for Nonlinear Frames by distributed genetic algorithms”, Design of Tall and Special Buildings, Vol. 21, Issue 1, pp. 57-76, 2012.
12. Bagley, J. D., “The Behaviour of Adaptive Systems Which Employ Genetic and Correlation Algorithms” Ph.D. Thesis, University of Michigan, 1967.
13. Goldberg, D. E., and Samtani, M. P., “Engineering Optimization via Genetic Algorithm”, Proceedings of the 9th Conference on Electronic Computation, ASCE, New York, N.Y., pp. 471-482, 1986.
15. McCulloch, W., and Pitts, W., “A Logical Calculus of Ideas Immanentin Nervous Activity”, Bulletin of Mathematical Biophysics, Vol. 5,
pp. 115-133, 1943.
17. Broomhead, D.vS., and Lowe, D., “Multivariable Functional Interpolation and Adaptive Networks”, Complex Systems, Vol. 2, pp. 321-355, 1988.
18. Han, H., Chen, Q., and Qiao, J., “ Research on an Online Self-Organizing Radial Basis Function Neural Network ”, Neural Computing and Applications, Vol. 19., Issue 5, pp. 667-676, 2010.
19. Sadek, F., Mhraz, B., Taylor, A.W., and Chung, R. M., “A Metod of Estimating the Parameters of Tuned Mass Dampers for Seismic Applications”, Earthquake Engineering and Structural Dynamics, Vol. 26, Issue 6, pp. 617-635, 1997.
20. Gupta, A., and Krawinkler, H., “Seismic Demands for Performance Evaluation of Steel Moment Resisting Frame Structures”, The John A. Blume Earthquake Engineering Center, Stanford University, Report no. 132, pp.342-359, 1999.
21. McKenna, F., Fenves, G. L., and Scott, M. H., Open System for Earthquake Engineering Simulation (OpenSees), Pacific Earthquake Engineering Research Center, University of California, Berkeley, 2006.
22. FEMA 356, NEHRP Guidelines for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency, Washington DC, 2000.
24. Somerville, P.G., Smith, N., Punyamurthula, S., and Sun, J., “Development of Ground Motion Time Histories for Phase 2 of the FEMA/SAC Steel Project”, SAC Background Document, Report No. SAC/BD 97/04, 1997.
)