- Volume 9 Issue 6
A frequency-domain method is developed for evaluating the earthquake input energy to two building structures connected by viscous dampers. It is shown that the earthquake input energies to respective building structures and viscous connecting dampers can be defined as works done by the boundary forces between the subsystems on their corresponding displacements. It is demonstrated that the proposed energy transfer function is very useful for clear understanding of dependence of energy consumption ratios in respective buildings and connecting viscous dampers on their properties. It can be shown that the area of the energy transfer function for the total system is constant regardless of natural period and damping ratio because the constant Fourier amplitude of the input acceleration, relating directly the area of the energy transfer function to the input energy, indicates the Dirac delta function and only an initial velocity (kinetic energy) is given in this case. Owing to the constant area property of the energy transfer functions, the total input energy to the overall system including both buildings and connecting viscous dampers is approximately constant regardless of the quantity of connecting viscous dampers. This property leads to an advantageous feature that, if the energy consumption in the connecting viscous dampers increases, the input energies to the buildings can be reduced drastically. For the worst case analysis, critical excitation problems with respect to the impulse interval for double impulse (simplification of pulse-type impulsive ground motion) and multiple impulses (simplification of long-duration ground motion) are considered and their solutions are provided.
earthquake input energy;frequency-domain analysis;time-domain analysis;energy transfer function;connected buildings;passive structural control;impulsive ground motion;long-duration ground motion;critical excitation
- Zahrah, T.F. and Hall, W.J. (1984), "Earthquake energy absorption in SDOF structures", J. Struct. Eng., ASCE, 110(8) 1757-1772.
- Zhu, H.P., Ge, D.D. and Huang, X. (2011), "Optimum connecting dampers to reduce the seismic responses of parallel structures", J. Sound Vib., 330(9), 1931-1949. https://doi.org/10.1016/j.jsv.2010.11.016
- Murase, M., Tsuji, M. and Takewaki, I. (2013), "Smart passive control of buildings with higher redundancy and robustness using base-isolation and inter-connection", Earthq. Struct., 4(6), 649-670. https://doi.org/10.12989/eas.2013.4.6.649
- Ok, S., Song, J. and Park, K. (2008), "Optimal design of hysteretic dampers connecting adjacent structures using multiobjective genetic algorithm and stochastic linearization method", Eng. Struct., 30(5), 1240-1249. https://doi.org/10.1016/j.engstruct.2007.07.019
- Ordaz, M., Huerta, B. and Reinoso, E. (2003), "Exact computation of input-energy spectra from Fourier amplitude spectra", Earthq. Eng. Struct. Dyn., 32(4), 597-605. https://doi.org/10.1002/eqe.240
- Richardson, A., Walsh, K.K. and Abdullah, M.M. (2013a), "Closed-form design equations for controlling vibrations in connected structures", J. Earthq. Eng., 17(5), 699-719. https://doi.org/10.1080/13632469.2013.771590
- Richardson, A., Walsh, K.K. and Abdullah, M.M. (2013b), "Closed-form equations for coupling linear structures using stiffness and damping elements", J. Struct. Control Hlth. Monit., 20(3), 259-281. https://doi.org/10.1002/stc.490
- Roh, H., Cimmellaro, G.P. and Lopez-Garcia, D. (2011), "Seismic response of adjacent steel structures connected by passive device", Adv. Struct. Eng., 14(3), 499-517. https://doi.org/10.1260/1369-43220.127.116.119
- Seto, K. (1994), "Vibration control method for flexible structures arranged in parallel", Proceedings of the 1st World Conference on Structural Control, Pasadena, California.
- Takewaki, I. (2001), "A new method for nonstationary random critical excitation", Earthq. Eng. Struct. Dyn., 30(4), 519-535. https://doi.org/10.1002/eqe.21
- Takewaki, I. (2002), "Critical excitation method for robust design: A review", J. Struct. Eng., ASCE, 128(5), 665-672. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:5(665)
- Takewaki, I. (2004a), "Bound of earthquake input energy", J. Struct. Eng., ASCE, 130(9), 1289-1297. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:9(1289)
- Takewaki, I. (2004b), "Frequency domain modal analysis of earthquake input energy to highly damped passive control structures", Earthq. Eng. Struct. Dyn., 33(5), 575-590. https://doi.org/10.1002/eqe.361
- Takewaki, I. (2005a), "Frequency domain analysis of earthquake input energy to structure-pile systems", Eng. Struct., 27(4), 549-563. https://doi.org/10.1016/j.engstruct.2004.11.014
- Takewaki, I. (2005b), "Bound of earthquake input energy to soil-structure interaction systems", Soil Dyn. Earthq. Eng., 25(7-10), 741-752. https://doi.org/10.1016/j.soildyn.2004.11.017
- Takewaki, I. (2007a), Critical excitation methods in earthquake engineering, Elsevier, Second edition in 2013.
- Takewaki, I. (2007b), "Earthquake input energy to two buildings connected by viscous dampers", J. Struct. Eng., ASCE, 133(5), 620-628. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:5(620)
- Takewaki, I. and Fujita, K. (2009), "Earthquake input energy to tall and base-isolated buildings in time and frequency dual domains", J. Struct. Des. Tall Spec. Build., 18(6), 589-606. https://doi.org/10.1002/tal.497
- Uang, C.M. and Bertero, V.V. (1990), "Evaluation of seismic energy in structures", Earthq. Eng. Struct. Dyn., 19(1), 77-90. https://doi.org/10.1002/eqe.4290190108
- Xu, Y.L., He, Q. and Ko, J,M. (1999), "Dynamic response of damper-connected adjacent buildings under earthquake excitation", Eng. Struct., 21(2), 135-148. https://doi.org/10.1016/S0141-0296(97)00154-5
- Christenson, R.E., Spencer, B.F. and Johnson, E.A. (2007), "Semiactive connected control method for adjacent multi-degree-of freedom buildings", J. Eng. Mech., ASCE, 133(3), 290-298. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:3(290)
- Cimellaro, G.P. and Lopez-Garcia, D. (2011), "Algorithm for design of controlled motion of adjacent structures", J. Struct. Control Hlth. Monit., 18(2), 140-148. https://doi.org/10.1002/stc.357
- Drenick, R.F. (1970), "Model-free design of aseismic structures", J. Eng. Mech. Div., ASCE, 96(EM4), 483-493.
- Housner, G.W. (1959), "Behavior of structures during earthquakes", J. Eng. Mech. Div., ASCE, 85(4), 109-129.
- Kalkan, E. and Kunnath, S.K. (2006), "Effects of fling step and forward directivity on seismic response of buildings", Earthq. Spectra, 22(2), 367-390. https://doi.org/10.1193/1.2192560
- Khaloo, A.R., Khosravi1, H. and Hamidi Jamnani, H. (2015), "Nonlinear interstory drift contours for idealized forward directivity pulses using "Modified Fish-Bone" models", Adv. Struct. Eng., 18(5), 603-627. https://doi.org/10.1260/1369-4318.104.22.1683
- Akiyama, H. (1985), Earthquake Resistant Limit-State Design for Buildings, University of Tokyo Press, Tokyo, Japan.
- Basili, M. and Angelis, M.D. (2007), "Optimal passive control of adjacent structures interconnected with nonlinear hysteretic devices", J. Sound Vib., 301(1-2), 106-125. https://doi.org/10.1016/j.jsv.2006.09.027
- Kim, K., Rye, J. and Chung, L. (2006), "Seismic performance of structures connected by viscoelastic dampers", Eng. Struct., 28(2), 83-195.
- Kojima, K., Fujita, K. and Takewaki, I. (2015a), "Critical double impulse input and bound of earthquake input energy to building structure", Frontier. Built Envir., 1(5), doi: 10.3389/fbuil.2015.00005. https://doi.org/10.3389/fbuil.2015.00005
- Kojima, K. and Takewaki, I. (2015b), "Critical input and response of elastic-plastic structures under longduration earthquake ground motions", Frontier. Built Envir., 1(15), doi: 10.3389/fbuil.2015.00015. https://doi.org/10.3389/fbuil.2015.00015
- Kuwamura, H., Kirino, Y. and Akiyama, H. (1994), "Prediction of earthquake energy input from smoothed Fourier amplitude spectrum", Earthq. Eng. Struct. Dyn., 23(10), 1125-1137. https://doi.org/10.1002/eqe.4290231007
- Leger, P. and Dussault, S. (1992), "Seismic-energy dissipation in MDOF structures", J. Struct. Eng., ASCE, 118(5), 1251-1269. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:5(1251)
- Luco, J.E. and Barros, F.C.P. (1998), "Optimal damping between two adjacent elastic structures", Earthq. Eng. Struct. Dyn., 7(7), 649-659.
- Lyon, R.H. (1975), Statistical Energy Analysis of Dynamical Systems, The MIT Press, Cambridge, MA.
- Mavroeidis, G.P. and Papageorgiou, A.S. (2003), "A mathematical representation of near-fault ground motions", Bull. Seism. Soc. Am., 93(3), 1099-1131. https://doi.org/10.1785/0120020100
- Mitsuda, E., Ohbuchi, M., Tsuji, M. and Takewaki, I. (2014), "Fundamental properties on eigenvibration and damping in connected building structures", J. Constr. Struct. Eng., Archi. Inst. of Japan, 696, 227-236. (in Japanese)
- Investigation of earthquake angle effect on the seismic performance of steel bridges vol.22, pp.4, 2016, https://doi.org/10.12989/scs.2016.22.4.855
- Innovative Seismic Response-Controlled System with Shear Wall and Concentrated Dampers in Lower Stories vol.3, 2017, https://doi.org/10.3389/fbuil.2017.00057
- Effect of Non-linearity of Connecting Dampers on Vibration Control of Connected Building Structures vol.1, 2016, https://doi.org/10.3389/fbuil.2015.00025
- Dual Control High-rise Building for Robuster Earthquake Performance vol.3, 2017, https://doi.org/10.3389/fbuil.2017.00012
Supported by : Japan Society for the Promotion of Science