### Citations

144 |
Random Variables and Stochastic Processes”, McGraw-Hill, 3rd edition,
- Papoulis, “Probability
- 1991
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Citation Context ...ally observed in recorded ground motions. To do this, it is :rst noted that the entropy rate of a stationary, zero mean, Gaussian random process Mwg(t), in terms of its psd function S(!), is given by =-=[17]-=- SHW = loge √ 2$e+ 1 2(!c −!0) ∫ !c !0 loge S(!) d! (21) This equation can be used to estimate entropy rate from samples of Gaussian random processes. In the context of development of critical excitat... |

20 |
Simulation of non-stationary random processes.
- Shinozuka, Sato
- 1967
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Citation Context ...c). The envelope function e(t) is assumed to be of the form e(t)=A0[exp(−t)− exp(−t)]; ¿¿0 (5) Here and are parameters that impart the observed transient trends in the recorded ground motions =-=[14]-=-. In our study, we take these parameters to be known and speci:cally it is assumed that =0:13 and =0:50. This choice represents the earthquake duration to be about 30 s that is considered typical of... |

13 |
Maximum structural response to seismic excitations
- Shinozuka
- 1970
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Citation Context ...tudy by Drenick [1], in which he showed that critical excitations for linear systems are given by their impulse response functions reversed in time, is an example for non-parametric models. Shinozuka =-=[7]-=- solved the same problem by introducing an upper bound on the Fourier amplitude spectrum of the critical excitation. Similarly, the studies on determination of stochastic critical excitations reported... |

10 |
Critical earthquake input power spectral density function models for engineering structures." Earthquake Engrg
- Manohar, Sarkar
- 1995
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Citation Context ...x and hi(t) the ith impulse response function. It may be noted that, in this model, the ground acceleration Mug(t) is taken to be deterministic and is assumed to be represented by Mug(t)= e(t) Mwg(t) =-=(3)-=- Copyright ? 2002 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2002; 31:813–832 816 A. M. ABBAS AND C. S. MANOHAR Here e(t) is an enveloping function that imparts transient nature to the inpu... |

6 |
A new method for nonstationary random critical excitation." Earthquake Engrg
- Takewaki
- 2001
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Citation Context ...he critical excitation. Similarly, the studies on determination of stochastic critical excitations reported by Iyengar and Manohar [8], Manohar and Sarkar [3], Sarkar and Manohar [9; 10] and Takewaki =-=[11; 12]-=- provide examples of nonparametric models within the probabilistic framework. In these studies, the input processes are taken to be Gaussian and the functional form of the critical psd function=matrix... |

4 |
Model-free design of aseismic structures
- RF
- 1970
(Show Context)
Citation Context ...ble for the main shock for these earthquakes. The method of critical excitation has its roots in the :eld of electrical engineering and was introduced to the :eld of earthquake engineering by Drenick =-=[1; 2]-=-. A brief chronology of selected literature published prior to 1995 has been presented by Manohar and Sarkar [3]. The central idea of this method consists of optimizing the missing information in the ... |

4 |
Manohar CS. Critical seismic vector random excitations for multi-supported structures
- Sarkar
- 1998
(Show Context)
Citation Context ...plitude spectrum of the critical excitation. Similarly, the studies on determination of stochastic critical excitations reported by Iyengar and Manohar [8], Manohar and Sarkar [3], Sarkar and Manohar =-=[9; 10]-=- and Takewaki [11; 12] provide examples of nonparametric models within the probabilistic framework. In these studies, the input processes are taken to be Gaussian and the functional form of the critic... |

4 |
Optimal damper placement for critical excitation." Probabilistic Engrg
- Takewaki
- 2000
(Show Context)
Citation Context ...he critical excitation. Similarly, the studies on determination of stochastic critical excitations reported by Iyengar and Manohar [8], Manohar and Sarkar [3], Sarkar and Manohar [9; 10] and Takewaki =-=[11; 12]-=- provide examples of nonparametric models within the probabilistic framework. In these studies, the input processes are taken to be Gaussian and the functional form of the critical psd function=matrix... |

4 |
Dynamics of structures, 2nd edn
- RW, Penzien
- 1993
(Show Context)
Citation Context ...equation of motion for the relative displacement u(t) of a discretized N -degree-of-freedom linear structure driven by a single component horizontal ground acceleration Mug(t) at its base is given by =-=[13]-=- M Mu(t) +Cu̇(t) +Ku(t)=−M{1} Mug(t) (1) Here M;C;K are, respectively, the mass, damping and stiKness matrices of the discretized structure, and {1} represents a column vector of ones. Assuming the da... |

3 |
Manohar CS. Nonstationary random critical excitations
- RN
- 1987
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Citation Context ... by introducing an upper bound on the Fourier amplitude spectrum of the critical excitation. Similarly, the studies on determination of stochastic critical excitations reported by Iyengar and Manohar =-=[8]-=-, Manohar and Sarkar [3], Sarkar and Manohar [9; 10] and Takewaki [11; 12] provide examples of nonparametric models within the probabilistic framework. In these studies, the input processes are taken ... |

3 |
Manohar CS. Critical cross power spectral density functions and the highest response of multisupported structures to multi component earthquake excitations. Earthquake Engineering and Structural Dynamics
- Sarkar
- 1996
(Show Context)
Citation Context ...plitude spectrum of the critical excitation. Similarly, the studies on determination of stochastic critical excitations reported by Iyengar and Manohar [8], Manohar and Sarkar [3], Sarkar and Manohar =-=[9; 10]-=- and Takewaki [11; 12] provide examples of nonparametric models within the probabilistic framework. In these studies, the input processes are taken to be Gaussian and the functional form of the critic... |

3 |
A generalization of the Drenick-Shinozuka model for bounds on the seismic response of a single-degree-of-freedom system." Earthquake Engrg. and Struct
- Baratta, Elishakoff, et al.
- 1998
(Show Context)
Citation Context ...omputed using the FFT algorithm. It may be noted that the idea of introducing an upper bound on the Fourier amplitude of the ground motion has been considered earlier by Shinozuka [7], Baratta et al. =-=[16]-=- and, also, in a probabilistic setting, by Takewaki [11; 12]. These authors, however, have not considered introducing the lower bound on the Fourier amplitude spectra. It may also be remarked here tha... |

2 |
Corotis R, Ellingwood B. Generation of critical stochastic earthquakes. Earthquake Engineering and Structural Dynamics
- Srinivasan
- 1992
(Show Context)
Citation Context ...e, since there is no reason why past records need to form a complete set. Therefore, the questions on convergence of the series representation become di=cult to answer. The study by Srinivasan et al. =-=[6]-=- is representative of parametric critical excitation models. These authors modelled the earthquake acceleration as a non-stationary :ltered shot noise and optimized the parameters of this model such t... |

2 |
Random vibration of a beam column
- Shinozuka, Henry
- 1965
(Show Context)
Citation Context ... Nf∑ n=1 ∫ t 0 e( )[An cos!n + Bn sin!n ] d + C1 (7) ug(t) = Nf∑ n=1 ∫ t 0 e( )(t −s)[An cos!n + Bn sin!n ] d + C1t + C2 (8) The constants of the integrations C1 and C2 are found using the conditions =-=[15]-=- ug(0)=0; lim t→∞ u̇g(t)→ 0 (9) Copyright ? 2002 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2002; 31:813–832 CRITICAL EARTHQUAKE LOAD MODELS 817 This leads to C2 = 0; C1 =− Nf∑ n=1 ∫ ∞ 0 e(... |

2 |
Huang MJ. Standard tape format for CSMIP strong-motion data tapes. California strong motion instrumentation program
- AF
- 1985
(Show Context)
Citation Context ...ation of the methods outlined in Sections 2 and 3 require, as a :rst step, quanti:cation of the various constraints. To achieve this, a set of ten recorded earthquake ground motions has been selected =-=[18; 19]-=- (see Table I). The available records contain digitized information on acceleration, velocity and displacement. All these records are reported to have been measured on :rm soil. Also, these ground mot... |

2 |
The Strong Motion Databased. http:==smdb.crustal.ucsb.edu
- SMDB
(Show Context)
Citation Context ...ation of the methods outlined in Sections 2 and 3 require, as a :rst step, quanti:cation of the various constraints. To achieve this, a set of ten recorded earthquake ground motions has been selected =-=[18; 19]-=- (see Table I). The available records contain digitized information on acceleration, velocity and displacement. All these records are reported to have been measured on :rm soil. Also, these ground mot... |

1 |
Aseismic design by way of critical excitation
- RF
- 1973
(Show Context)
Citation Context ...ble for the main shock for these earthquakes. The method of critical excitation has its roots in the :eld of electrical engineering and was introduced to the :eld of earthquake engineering by Drenick =-=[1; 2]-=-. A brief chronology of selected literature published prior to 1995 has been presented by Manohar and Sarkar [3]. The central idea of this method consists of optimizing the missing information in the ... |

1 |
Site-dependent critical design spectra. Earthquake Engineering and Structural Dynamics
- PC, CB
- 1979
(Show Context)
Citation Context ...t) is an enveloping function that imparts transient nature to the inputs and Mwg(t) is a steady-state function that admits a Fourier representation of the form Mwg(t)= Nf∑ n=1 [An cos!nt + Bn sin!nt] =-=(4)-=- where An and Bn are unknown constants, and the frequencies !n, n=1; 2; : : : ; Nf , are selected such that they span satisfactorily the frequency range (!0; !c). The envelope function e(t) is assumed... |

1 |
Barbela M, Drenick RF, Tsirk A. Critical excitation method for calculating earthquake eKects on nuclear plant structures: An assessment study
- Bedrosian
- 1980
(Show Context)
Citation Context ...ncies !n, n=1; 2; : : : ; Nf , are selected such that they span satisfactorily the frequency range (!0; !c). The envelope function e(t) is assumed to be of the form e(t)=A0[exp(−t)− exp(−t)]; ¿¿0 =-=(5)-=- Here and are parameters that impart the observed transient trends in the recorded ground motions [14]. In our study, we take these parameters to be known and speci:cally it is assumed that =0:13... |

1 |
Reinforced Concrete Chimneys and Towers
- GM
- 1975
(Show Context)
Citation Context ...) ] ¿U SHW ;s2n¿0 (25) Copyright ? 2002 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2002; 31:813–832 CRITICAL EARTHQUAKE LOAD MODELS 821 Figure 1. Example structures considered: (a) chimney =-=[20]-=-, (b) Earth dam [21]. This problem, again, constitutes a constrained non-linear optimization problem. As in the previous case, the optimal solutions are computed using ‘CONSTR’ program of the MATLAB O... |

1 |
Earthquake stress analysis in earth dams
- RW, AK
(Show Context)
Citation Context ...5) Copyright ? 2002 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2002; 31:813–832 CRITICAL EARTHQUAKE LOAD MODELS 821 Figure 1. Example structures considered: (a) chimney [20], (b) Earth dam =-=[21]-=-. This problem, again, constitutes a constrained non-linear optimization problem. As in the previous case, the optimal solutions are computed using ‘CONSTR’ program of the MATLAB Optimization Toolbox.... |