Stochastic response of bridges seismically isolated by friction pendulum system

Stochastic response of bridges seismically isolated by the friction pendulum system (FPS) is investigated. The earthquake excitation is modeled by a nonstationary random process (i.e., uniformly modulated broadband excitation). The stochastic response of the isolated bridge is obtained using the time dependent equivalent linearization technique due to nonlinear force-deformation behavior of the FPS. The nonstationary response of the isolated bridge is compared with the corresponding stationary response in order to study the influence of nonstationary characteristics of earthquake excitation. An optimum value of the friction coefficient of FPS for which the root mean square absolute acceleration of the bridge deck attains a minimum value was observed. The influence of system parameters such as isolation period of the FPS, frequency content, and intensity of an earthquake on the optimum friction coefficient of FPS is investigated. It was observed that the above parameters have significant effects on the optimum friction coefficient of FPS. A closed form expression for the optimum friction coefficient of FPS and corresponding response of the isolated bridge system are proposed. These expressions were derived based on the model of the bridge with rigid deck and pier conditions subjected to stationary white-noise excitation. It was concluded that there is a good comparison between the proposed closed form expressions and actual optimum parameters and the response of the isolated bridge system. The maximum difference observed was about 10-15% percent and these expressions may be used for initial optimal design of the FPS for bridges

DYNAMIC CHARACTERISTICS OF STRUCTURES WITH MULTIPLE TUNED MASS DAMPERS

Effectiveness of multiple tuned mass dampers (MTMD) in suppressing the dynamic response of base excited structure for first mode vibration is investigated. The effectiveness of the MTMD is expressed by the ratio of the root mean square (RMS) displacement of the structure with MTMD to corresponding displacement without MTMD. The frequency content of base excitation is modelled as a broad-band stationary random process. The MTMD's with uniformly distributed natural frequencies are considered for this purpose. A parametric study is conducted to investigate the fundamental characteristics of the MTMD's and the effect of important parameters on the effectiveness of the MTMD's. The parameters include: the fundamental characteristics of the MTMD system such as damping, mass ratio, total number of MTMD, tuning frequency ratio, frequency spacing of the dampers and frequency content of the base excitation. It has been shown that MTMD can be more effective and more robust than a single TMD with equal mass and damping ratio

Optimum friction pendulum system for near-fault motions

The analytical seismic response of multi-story buildings isolated by the friction pendulum system (FPS) is investigated under near-fault motions. The superstructure is idealized as a linear shear type flexible building. The governing equations of motion of the isolated structural system are derived and the response of the system to the normal component of six recorded near-fault motions is evaluated by the step-by-step method. The variation of top floor absolute acceleration and sliding displacement of the isolated building is plotted under different system parameters such as superstructure flexibility, isolation period and friction coefficient of the FPS. The comparison of results indicated that for low values of friction coefficient there is significant sliding displacement in the FPS under near-fault motions. In addition, there also exists a particular value of the friction coefficient of FPS for which the top floor absolute acceleration of the building attains the minimum value. Further, the optimum friction coefficient of the FPS is derived for different system parameters under near-fault motions. The criterion selected for optimality is the minimization of both the top floor acceleration and the sliding displacement. The optimum friction coefficient of the FPS is found to be in the range of 0.05 to 0.15 under near-fault motions. In addition, the response of a bridge seismically isolated by the FPS is also investigated and it is found that there exists a particular value of the friction coefficient for which the pier base shear and deck acceleration attain the minimum value under near-fault motions.© Elsevie

Optimum damping in a non-linear base isolation system

Optimum isolation damping for minimum acceleration of a base-isolated structure subjected to earthquake ground excitation is investigated. The stochastic model of the El-Centro 1940 earthquake, which preserves the non-stationary evolution of amplitude and frequency content of ground motion, is used as an earthquake excitation. The base isolated structure consists of a linear flexible shear type multi-storey building supported on a base isolation system. The resilient-friction base isolator (R-FBI) is considered as an isolation system. The non-stationary stochastic response of the system is obtained by the time dependent equivalent linearization technique as the force-deformation behaviour of the R-FBI system is non-linear. The optimum damping of the R-FBI system is obtained under important parametric variations: i.e., the coefficient of friction of the R-FBI system, the period and damping of the superstructure; the effective period of base isolation. The criterion selected for optimality is the minimization of the top floor root mean square (r.m.s.) acceleration. It is shown that the above parameters have significant effects on optimum isolation damping. (C) 1996 Academic Press Limite

Computational numerical models for seismic response of structures isolated by sliding systems

The problem of sliding structures is discontinuous one as different sets of equations of motion with varying forcing functions are required for the sliding and non-sliding phases. This is inconvenient for the numerical integration of the governing equations for the response of sliding structures. To overcome such difficulties continuous hysteretic models of the sliding systems have been presented in the past. In the present study, a comparison of the response of structures (i.e. multi-storey buildings and bridges) isolated by sliding systems with conventional and hysteretic models of the frictional force of the sliding system is carried out to investigate the comparative performance and computational efficiency of the two models. The seismic response of isolated structures is obtained by solving the governing equations of motion using a step-by-step method under single and two horizontal components of real earthquake motions. For comparative study, the seismic response of a multi-storey building obtained by the conventional model is compared with the corresponding response by the hysteretic model under different sliding isolation systems, numbers of storeys and values of the fundamental time period of the superstructure. It is found that the conventional and hysteretic models of sliding systems predict a similar seismic response for isolated structures. However, the difference in the response between the two models is relatively more for the pure friction system as compared with the sliding systems with restoring force. Further, the conventional model is relatively more computationally efficient as compared with the hysteretic model. Copyright (c) 2004 , Ltd

Optimum frictional elements in sliding isolation systems

The optimum friction coefficient of a sliding system with a restoring force for the minimum acceleration response of a base-isolated structure under earthquake ground motion is investigated. The stochastic model of El-Centro 1940 earthquake which preserves the non-stationary evolution of amplitude and frequency content of the original record is used for the model of earthquake. The base-isolated structure consists of a linear flexible multi-storey structure supported on the sliding system. The sliding system is modelled to provide a friction force (ideal Coulomb-friction type) and a linear restoring force. The non-stationary stochastic response of the isolated structure is obtained using the time dependent equivalent linearisation technique as the force-deformation behaviour of the sliding system is highly non-linear. The response of the system is analysed for the optimum friction coefficient of the sliding base isolation system. The criterion selected for optimality is the minimisation of the root mean square top floor absolute acceleration. The optimum friction coefficient of sliding isolation system is obtained under important parametric variations such as: period and damping of the superstructure, ratio of the base mass to the superstructure floor mass, the damping ratio of the isolation system, the period of base isolation system and the intensity of earthquake excitation. It has been shown that the above parameters have significant effects on optimum friction coefficient of the sliding base isolation system.© Elsevie

Response of sliding structures to bi-directional excitation

Dynamic response of structures supported on the sliding systems to bi-directional (i.e. two horizontal components) earthquake and harmonic ground motion is investigated. The superstructure is assumed to be rigid acid the frictional forces mobilized at the interface of sliding system are assumed to have the ideal Coulomb-friction characteristics. Coupled differential equations of motion of the structure with sliding system in two orthogonal horizontal directions are solved in the incremental form using Newmark's method with iterations. The iterations are required due to dependence of the frictional forces on the response of the system. The response of the system with bi-directional interaction is compared with those without interaction (i.e., two-dimensional idealization in two directions) in order to investigate the effects of bi-directional interaction of frictional forces. These effects are investigated under important parametric variations. The important parameters considered include the isolator properties (i.e., period, damping and friction coefficient) and the characteristics of the harmonic excitation (namely excitation frequency, amplitude ratio and phase difference). it is shown that if the effects of hi-directional interaction of frictional forces are neglected then the sliding base displacements will be underestimated which can be crucial from the design point of view. Further, the hi-directional interaction effects are found to be more severe for the sliding systems without restoring force in comparison with the systems with restoring force

Response of SDOF system to non-stationary earthquake excitation

Earthquake excitation is often modelled by non-stationary random process (i.e. uniformly modulated broad-band excitation) for analysis of structural safety subjected to seismic hazards. In this paper, the non-stationary response of a single-degree-of-freedom (SDOF) system to non-stationary earthquake motion is investigated for different shapes of modulating functions. The evolutionary power-spectral density function (PSDF) of the displacement of the SDOF system is obtained using the time-varying frequency response function and the PSDF of the earthquake excitation. The close form expressions for time-varying frequency response function are derived for different shapes of the modulating functions. In order to study the effects of the shape of the modulating function, a comparison of the non-stationary earthquake response of the SDOF system is also made for different modulating functions having the same energy content. Copyright (C) 2004 John Wiley Sons, Ltd

Response of pure-friction sliding structures to bi-directional harmonic ground motion

The response of structures with sliding support to bi-directional (i.e. two horizontal components) harmonic ground motion is investigated. The frictional forces mobilized at the sliding support are assumed to have the ideal coulomb-friction characteristics. The coupled differential equations of motion of the sliding structure in two orthogonal directions are solved in the incremental form using Newmark's method with iterations. The iterations are required due to dependence of the frictional forces on the response of the system. The responses of the system with bi-directional interaction are compared with those without interaction (2D idealization in two orthogonal directions) in order to investigate the effects of bi-directional interaction of frictional forces at the sliding supports. It has been shown that effects of bi-directional interaction are significant and should be included for the effective design of sliding structures. Further, if the effects of bi-directional interaction of frictional forces are neglected then the sliding base displacement will be underestimated which is crucial from the design point of view. In addition to harmonic ground motion the significant effects of bi-directional interaction are also observed for selected real earthquake ground excitations. Copyright (C) 1996

Optimum multiple tuned mass dampers for base-excited undamped system

Optimum parameters of Multiple Tuned Mass Dampers (MTMD) for an undamped system to harmonic base excitation are investigated using a numerical searching technique. The criteria selected for the optimality is the minimization of steady-state displacement response of the main system. The explicit formulae for the optimum parameters of MTMD (i.e. damping ratio, bandwidth and tuning frequency) are then derived using curve-fitting scheme that can readily be used for engineering applications. The error in the proposed explicit expressions is investigated and found to be quite negligible. The optimum parameters of the MTMD system are obtained for different mass ratios and number of dampers. Copyright (C) 1999 , Ltd