• Structural Engineering and Mechanics
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• 제21권3호
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• pp.255-273
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• 2005

Based on the random vibration theory, a response spectrum method is developed for seismic response analysis of linear, multi-degree-of-freedom structures under multi-support excitations is developed. Various response quantities, including the mean and variance of the peak response, the response mean frequency, are obtained from proposed combination rules in terms of the mean response spectrum. This method makes it possible to apply the response spectrum to the seismic reliability analysis of structures subjected to multi-support excitations. Considering that the tedious numerical integration is required to compute the spectral parameters and correlation coefficients in above combination rules, this paper further offers simplified procedures for their computation, which enhance dramatically the computational efficiency of the suggested method. The proposed procedure is demonstrated for tow numerical examples: (1) two-span continuous beam; (2) two-tower cabled-stayed bridge by using Monte Carlo simulation (MC). For this purpose, this paper also presents an approach to simulation of ground motions, which can take into account both mean and variation properties of response spectrum. Computed results based on the response spectrum method are in good agreement with Monte Carlo simulation results. And compared with the MSRS method, a well-developed multi-support response spectrum method, the proposed method has an incomparable computational efficiency.

• 한국전산구조공학회논문집
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• 제12권3호
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• pp.437-445
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• 1999

본 논문에서는 다지지점 가진에 의한 구조물의 동적응답을 구하기 위하여 유한요소모형을 수정하고 등가하중을 도입하는 간단한 기법을 제안하였다. 제안방법은 다지지점 입력에 대한 해석기능이 있는 기존의 범용구조해석 S/W를 이용한 선형 및 비선형 해석결과와 비교하여 검증하였다. 이 기법은 다지지점 입력에 대한 해석기능이 없는 범용유한요소해석 S/W 및 비선형 구조해석을 위하여 특별히 개발되었던 전산프로그램을 이용하여 다지지점 입력에 대한 지진응답해석을 수행할 때 유용하게 활용될 수 있을 것으로 기대된다.

• Structural Engineering and Mechanics
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• 제65권5호
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• pp.633-644
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• 2018

This paper presents the results of an assessment of the seismic fragility of a long, curved multi-frame bridge under multi-support earthquake excitations. To achieve this aim, the numerical model of columns retrofitted with elliptical steel jackets was developed and validated using existing experimental results. A detailed nonlinear numerical model of the bridge that can capture the inelastic response of various components was then created. Using nonlinear time-history analyses for a set of stochastically generated spatially variable ground motions, component demands were derived and then convolved with new capacity-based limit state models to obtain seismic fragility curves. The comparison of failure probabilities obtained from uniform and multi-support excitation analyses revealed that the consideration of spatial variability significantly reduced the median value of fragility curves for most components except for the abutments. This observation indicates that the assumption of uniform motions may considerably underestimate seismic demands. Moreover, the spatial correlation of ground motions resulted in reduced dispersion of demand models that consequently decreased the dispersion of fragility curves for all components. Therefore, the spatial variability of ground motions needs to be considered for reliable assessment of the seismic performance of long multi-frame bridge structures.

• Earthquakes and Structures
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• 제15권2호
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• pp.193-202
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• 2018

This paper studied the probability of pounding occurred between decks and abutments of a long span high-pier continuous rigid fame bridge subjected to ground motions with local soil effect. A pounding probability analysis methodology has been proposed using peak acceleration at bedrock as intensity measure (IM) for multi-support seismic analysis. The bridge nonlinear finite element (FE) models was built with four different separation distances. Effect of actual site condition and non-uniform spatial soil profiles on seismic wave propagating from bedrock to ground surface is modelled. Pounding probability of the high-pier bridge under multi-support seismic excitations (MSSE) is analyzed based on the nonlinear incremental dynamic analysis (n-IDA). Pounding probability results under uniform excitations (UE) without actual local site effect are compared with that under MSSE with site effect. The study indicates that the required design separation length between deck and abutment under uniform excitations is larger than that under MSSE as the peak acceleration at bedrock increases. As the increase of both separation distance between deck and abutment and the peak acceleration, the probability of pounding occurred at a single abutment or at two abutments simultaneously under MSSE is less than that under UE. It is of great significance considering actual local site effect for determining the separation distance between deck and abutment through the probability pounding analysis of the high-pier bridge under MSSE.

• Structural Engineering and Mechanics
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• 제64권2호
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• pp.259-270
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• 2017

The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.

• Smart Structures and Systems
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• 제19권1호
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• pp.21-31
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• 2017

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

• Earthquakes and Structures
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• 제9권5호
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• pp.1115-1132
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• 2015

The study considers earthquake shake table testing of bending-torsion coupled structures under multi-component stationary random earthquake excitations. An experimental procedure to arrive at the optimal excitation cross-power spectral density (psd) functions which maximize/minimize the steady state variance of a chosen response variable is proposed. These optimal functions are shown to be derivable in terms of a set of system frequency response functions which could be measured experimentally without necessitating an idealized mathematical model to be postulated for the structure under study. The relationship between these optimized cross-psd functions to the most favourable/least favourable angle of incidence of seismic waves on the structure is noted. The optimal functions are also shown to be system dependent, mathematically the sharpest, and correspond to neither fully correlated motions nor independent motions. The proposed experimental procedure is demonstrated through shake table studies on two laboratory scale building frame models.

• Earthquakes and Structures
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• 제13권2호
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• pp.193-200
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• 2017

To overcome the difficulty of performing multi-point response spectrum analysis for engineering structures under spatially varying ground motions (SVGM) using the general finite element code such as ANSYS, an approach has been developed by improving the modelling of the input ground motions in the spectral analysis. Based on the stochastic vibration analyses, the cross-power spectral density (c-PSD) matrix is adopted to model the stationary SVGM. The design response spectra are converted into the corresponding PSD model with appropriate coherency functions and apparent wave velocities. Then elements of c-PSD matrix are summarized in the row and the PSD matrix is transformed into the response spectra for a general spectral analysis. A long-span high-pier bridge under multiple support excitations is analyzed using the proposed approach considering the incoherence, wave-passage and site-response effects. The proposed approach is deemed to be an efficient numerical method that can be used for seismic analysis of large engineering structures under SVGM.

• Smart Structures and Systems
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• 제23권6호
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• pp.641-651
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• 2019

The stochastic stability control of the parameter-excited vibration of an inclined stay cable with multiple modes coupling under random and periodic combined support disturbances is studied by using the direct eigenvalue analysis approach based on the response moment stability, Floquet theorem, Fourier series and matrix eigenvalue analysis. The differential equation with time-varying parameters for the transverse vibration of the inclined cable with control under random and deterministic support disturbances is derived and converted into the randomly and deterministically parameter-excited multi-degree-of-freedom vibration equations. As the stochastic stability of the parameter-excited vibration is mainly determined by the characteristics of perturbation moment, the differential equation with only deterministic parameters for the perturbation second moment is derived based on the $It{\hat{o}}$ stochastic differential rule. The stochastically and deterministically parameter-excited vibration stability is then determined by the deterministic parameter-varying response moment stability. Based on the Floquet theorem, expanding the periodic parameters of the perturbation moment equation and the periodic component of the characteristic perturbation moment expression into the Fourier series yields the eigenvalue equation which determines the perturbation moment behavior. Thus the stochastic stability of the parameter-excited cable vibration under the random and periodic combined support disturbances is determined directly by the matrix eigenvalues. The direct eigenvalue analysis approach is applicable to the stochastic stability of the control cable with multiple modes coupling under various periodic and/or random support disturbances. Numerical results illustrate that the multiple cable modes need to be considered for the stochastic stability of the parameter-excited cable vibration under the random and periodic support disturbances, and the increase of the control damping rather than control stiffness can greatly enhance the stochastic stability of the parameter-excited cable vibration including the frequency width increase of the periodic disturbance and the critical value increase of the random disturbance amplitude.

• 한국구조물진단유지관리공학회 논문집
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• 제23권7호
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• pp.137-144
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• 2019

근단층 지역에 위치한 교량은 근단층지반운동에 대한 내진안전성을 확보하는 것이 중요하다. 본 연구에서는 연약지반이 두껍고 다양한 지층으로 구성된 지역에 건설되는 단일형 현장타설말뚝 교량의 지진거동특성과 내진안전성을 분석하였다. 근단층지반운동을 생성하고 지반해석을 수행하여 각 지층에서의 지반가속도이력을 산정하였다. 이 가속도이력을 이용하여 각 지층의 지반을 등가스프링으로 모델화하고, 각 지층에서의 가속도시간이력을 입력지반운동으로 하는 다지점 가진 지진해석을 수행하였다. 근단층지반운동의 특성으로 인하여 교량은 탄성영역 내에서 거동하였지만 최대모멘트의 발생 위치 등이 설계지반운동을 고려할 때와는 상이한 특성을 보였다.