Mode‐acceleration approach to seismic response of multiply‐supported secondary systems

A mode‐acceleration approach has been proposed for estimating the seismic response of a linear, classically‐damped, multiply‐supported secondary system within the framework of a power spectral density function (PSDF)‐based stochastic approach, while the primary system is linear and classically‐damped. Response transfer functions have been formulated in terms of chosen numbers of fixed‐base modes of the primary and secondary systems. The proposed approach does not involve the determination of combined system properties, and is applicable to the secondary systems with high mass ratios also. Through a few example primary–secondary systems and an example band‐limited white noise excitation, it has been shown that this approach leads to reasonably accurate results when only a few primary and secondary modes are to be considered. The proposed formulation has been used to obtain input data for a decoupled response spectrum analysis of secondary systems. This data accurately accounts for the effects of interaction between the primary and secondary systems. It is shown to lead to substantial reductions in the errors associated with the envelope spectrum method in the case of moderately heavy to heavy secondary systems and when the spatial coupling does not play a major role. Copyright © 2002 John Wiley & Sons, Ltd.     

Stochastic seismic response of multiply-supported secondary systems in flexible-base structures

A formulation has been proposed for the transfer function of a secondary system response while the primary system is supported on a compliant soil and the excitation comprises of translational ground motion at its base. For this purpose, the earlier formulation of the authors for the fixed-base case, which exactly considers the interaction between the two sub-systems and is based on the use of their individual modal properties, has been extended. Also, the concept of modifying the input excitation for the interaction accelerations (associated with the soil–structure interaction) has been used. An example P–S system and three example earthquake excitations have been considered to illustrate the proposed formulation and to estimate the expected response peak amplitudes in the secondary system. This study shows that ‘detuning’ of the tuned systems may occur in case of significant soil–structure interaction. Further, for the reasons of both safety and economy, ignoring the interaction effects in designing the secondary systems may not always be justified. Copyright © 1999 John Wiley & Sons, Ltd.     

A response‐based decoupling criterion for multiply‐supported secondary systems

It is often infeasible to carry out coupled analyses of multiply‐supported secondary systems for earthquake excitations. ‘Approximate’ decoupled analyses are then resorted to, unless the response errors due to those are significantly high. This study proposes a decoupling criterion to identify such cases where these errors are likely to be larger than an acceptable level. The proposed criterion is based on the errors in the primary system response due to decoupling and has been obtained by assuming (i) the input excitation to be an ideal white noise process, (ii) cross‐modal correlation to be negligible, and (iii) the combined system to be classically damped. It uses the modal properties of the undamped combined system, and therefore, a perturbation approach has been formulated to determine the combined system properties in case of light to moderately heavy secondary systems. A numerical study has been carried out to illustrate the accuracy achieved with the proposed perturbation formulation. The proposed decoupling criterion has been validated with the help of two example primary‐secondary systems and four example excitation processes. Copyright © 2002 John Wiley & Sons, Ltd.     

A method for the transfer function matrix of combined primary–secondary systems using classical modal decomposition

An iterative method is presented to compute the transfer function matrix of combined primary–secondary systems for seismic response analysis. It accounts for non‐proportional damping and dynamic interaction of the combined system. A closed form sequence is developed for the iterative computation of the transfer function matrix. Such sequence is assembled using independently the real classical mode frequencies, shapes and damping ratios of the primary system, and the natural frequency and critical damping ratio of the SDOF secondary system. The necessary and sufficient condition for convergence of the sequence is given in the paper. The method is illustrated through a couple of examples, including one of an appendix connected to a multi‐storey shear building. Convergence of the method is thoroughly analysed and peak responses are obtained using a spectral density function approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic analysis of multiply supported secondary systems with dynamic interaction effects

For a proper response spectrum analysis of a secondary system with multiple supports, the seismic inputs are required to be defined in terms of the auto and cross floor response spectra. If no feed-back or interaction effect from the secondary system to its supporting primary structure is suspected, these inputs can be developed by a direct analysis of the supporting structure alone. However, sometimes the effect of the interaction on the secondary system response can be quite significant. Herein, a method is developed to incorporate the feed-back effect, through proper modification of the interaction-free floor spectrum inputs. The interaction coefficients are used to effect such modifications in different floor spectral quantities. A procedure for the calculation of the interaction coefficients is proposed. The modified floor spectra when used as inputs to the secondary system do introduce the interaction effect in the secondary system response. A successful application of this method is demonstrated by numerical examples of secondary systems with three different secondary-to-primary system mass ratios.     

Combined dynamic response of primary and multiply connected cascaded secondary subsystems

A method is proposed for the deterministic and stochastic non-stationary analysis of linear composite systems with cascaded secondary subsystems subjected to a seismic input. This method makes it possible to evaluate, by means of a unitary formulation, the deterministic and non-stationary stochastic response of both classically and non-classically damped subsystems and of secondary subsystems multiply supported on the primary one, as well as the ground. The proposed procedure is very efficient from a computational point of view, because of the Kronecker algebra systematically employed. Indeed, by using this algebra, it is possible to obtain in a very compact and elegant form the eigenproperties of the composite system as a function of the eigenproperties of the two subsystems taken separately. Moreover, it is possible to write the first order differential equations governing the evolution of the second order moments of the response and to solve them in a simple way.     

A dynamic stiffness formulation for the analysis of secondary systems

Formulation of a frequency-domain substructure approach for the analysis of secondary systems is presented. The total system contemplated includes the primary structure, the secondary system, and the foundation medium, which is also treated as a substructure. A dynamic stiffness matrix in physical co-ordinates characterizes each one of the substructures. Elimination of the internal degrees of freedom of the primary structure prior to assembly of the equations for the coupled system is carried out with the aid of a truncated set of unconstrained normal modes. Accounting for the residual static flexibility of the truncated modes obviates potential problems of rank deficiency resulting from modal truncation. The formulation contemplates an arbitrary multi-component scattered motion at the soil–structure interface and imposes no limitations on the configuration of the primary or the secondary system. Connectivity between the systems is treated as an arbitrary linear relation between selected co-ordinates in each substructure. This feature is shown to be useful for modelling the commonly encountered situation where secondary systems are attached to torsionally eccentric structures. Copyright © 1999 John Wiley & Sons, Ltd.     

Non-equilibrium alcohol flooding model for immiscible phase remediation: 2. Model development and application

A non-equilibrium, two-phase, three-component compositional model for the simulation of alcohol flooding has been developed and tested. Inter-phase mass transfer algorithms allow for transfer of all three components at high concentrations and high mass flux rates using a two-film model. The model has been used to simulate alcohol floods where the alcohol has an affinity for either the water-rich phase, or the organic-rich phase. Calibration, using experimental effluent data from an alcohol flood which used a 2-propanol (IPA)-water-tetrachlorethene (PCE) ternary system, indicates that inter-phase mass transfer parameters can be non-unique. Sensitivity studies, completed using the non-equilibrium model for the IPA-water-PCE system, indicate that experimentally derived organic-rich phase composition data should lead to better estimates of the non-wetting phase film thickness. For alcohol flooding experiments where the primary mechanism of non-aqueous phase liquid (NAPL) removal is enhanced dissolution, near-equilibrium conditions may be achieved with NAPL recovery similar for conditions of near-equilibrium and equilibrium. However, for systems where remobilization is the primary mechanism of NAPL recovery, it is expected that although local conditions may approach equilibrium, the resulting NAPL recovery can be significantly lower than would be attained if equilibrium conditions persisted.     

Wavelet‐based non‐stationary response analysis of a friction base‐isolated structure

A wavelet‐based stochastic formulation has been presented in this paper for the seismic analysis of a base‐isolated structural system which is modelled as a two‐degree‐of‐freedom (2‐DOF) system. The ground motion has been modelled as a non‐stationary process (both in amplitude and frequency) by using modified Littlewood–Paley basis wavelets. The proposed formulation is based on replacing the non‐linear system by an equivalent linear system with time‐dependent damping properties. The expressions of the instantaneous damping and the power spectral density function (PSDF) of the superstructure response have been obtained in terms of the functionals of input wavelet coefficients. The proposed formulation has been validated by simulating a ground motion process. The effect of the frequency non‐stationarity on the non‐linear response has also been studied in detail, and it has been clearly shown how ignoring the frequency non‐stationarity in the ground motion leads to inaccurate non‐linear response calculations. Copyright © 2000 John Wiley & Sons, Ltd.     

Asynchronous driving principle and its application to vibration control

The vibration control of megaframes with suspension systems is developed in this paper. The interaction between the megaframe and the suspension systems is first analysed, then asynchronous driving principle is proposed for vibration control of such structures. A numerical example is presented to show the application of asynchronous driving principle in the design of vibration control. The response of the megaframe with suspension systems under evolutionary random excitation indicates the feasibility and effectiveness of the proposed method. The vibration control method, though studied in a special case of the megaframe with suspension systems, is also applicable to the vibration control of combined structures with large secondary‐to‐primary mass ratio. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimal design of SDOF envelope systems for the responses of MDOF dynamic systems

The concept of envelope system for a given dynamic system is proposed in this paper which refers to those systems whose module of transfer function in the whole range of frequency domain is always bigger than that of a given system. This concept opens a new way to study the problems of robust design and modelling for dynamic systems. The condition that an envelope system has to satisfy is rendered as the determination of the positiveness of a real polynomial function and Sturm's sequence method is used to establish an easily implemented criterion for evaluating the positiveness of the polynomial in terms of its coefficients. The optimization for the envelope system is expressed as the minimization of the 2-norm of its transfer function and simplex method is employed to search for the optimal solution. Two dynamic systems are used to illustrate the optimal design for the envelope systems of some of their responses. © 1998 John Wiley & Sons, Ltd.     

Reduction of steady-state forced vibrations of structures with dynamic absorbers

In the paper the problem of reduction of the steady-state response of a lightly damped structure to periodic excitation is considered. The primary structure, which has arbitrary distributions of mass, stiffness and damping, is subjected to periodic load with the fundamental frequency varying in a wide range that may include several resonant peaks of the amplitude-frequency response. A number of passive absorbers are applied simultaneously to the main structure. A general formulation of the dynamic absorber design methodology is presented, based on independent design of conventional absorbers, taking into account the selected modal systems of the original structure and the selected harmonic components of the excitation. In order to cover the losses in the vibration reduction, resulting from the couplings in the primary structure–the set of absorbers system and from the remaining harmonic components of the excitation, the mass of modal dynamic absorbers is increased properly. The methodology developed was verified on several numerical examples; one of them is presented in the study.     

Stochastic response of combined primary-secondary structures under seismic input

A technique for non-stationary stochastic analysis of linear combined primary and secondary subsystems subjected to a zero-mean Gaussian base excitation is presented. The proposed technique, based on the use of the Taylor's expansion in evaluating the operators which appear in the step-by-step procedure, does not require the evaluation of the complex eigenproperties of the combined system. Operating in this way, even though the numerical procedure is a conditionally stable one, appears to be more efficient than existing methods to evaluate the dynamic response of such composite systems. It is also shown that the proposed procedure is available whether the seismic input is idealized as a filtered white noise or it is defined by means of its autocorrelation function.     

主次结构减震特性研究

本文探讨了主次结构的减震特性以及土－结构相互作用对减震效果的影响，在一定条件下，次结构对主结构有减震作用，其减震效果与主次结构的刚度比和质量比、次结构的阻尼和输入地震动的特性有关，对于多层建筑，次结构既可能减小主结构的加速度，也可能减小其相对位移，对于高层建筑、则主要是减小主结构的相对位移，对于中软至弱地基条件，ＳＳＩ效应明显降低高层建筑的加速度反应；对于中等地基条件，ＳＳＩ效应显著降低次结构对高     

The influence of biogeochemical conditions and level of model complexity when simulating cometabolic biodegradation in sorbent-water systems

Eighteen models with different levels of complexity for representing sorption, mass transfer, and biodegradation are used to simulate the biodegradation of toluene (primary substrate) and TCE (cometabolic substrate). The simulations are conducted for hypothetical completely mixed systems of various scenarios with regard to sorbent, microbial composition, and solute concentrations. The purpose of the suite of simulations is to investigate the sensitivity of different modeling approaches in simulating the bio-attenuation of co-existing solutes in sorbent-water systems. The sensitivity of results to the modeling approach depends on the biogeochemical conditions of the system. For example, the results are insensitive to the type of sorption model in systems with low sorption strength and slow biodegradation rates, and insensitive to the biodegradation rate model if mass transfer controlled. Differences among model results are generally greater when evaluated in terms of total mass removal rather than aqueous phase concentration reduction. The fate of the cometabolite is more sensitive to the proper consideration of co-solute effects than is the fate of the primary substrate. For a given system, graphical comparison of a characteristic mass transfer rate coefficient (α_mt) versus a characteristic biodegradation rate coefficient (α_bio) provides an indication of how sensitivity to the different processes may be expected to change with time and can guide the selection of an appropriate level of model complexity.     

Application of semi‐active tuned mass dampers to base‐excited systems

A continuously variable semi‐active damper is used in a tuned mass damper (TMD) to reduce the level of vibration of a single‐degree‐of‐freedom system subjected to harmonic base excitations. The ground hook dampers as have been used in the auto‐industry are being studied here. Using these dampers a new class of tuned mass dampers, named as ground hook tuned mass dampers (GHTMD) is being introduced. In order to generalize the design properties of the GHTMDs, they are defined in terms of non‐dimensional parameters. The optimum design parameters of GHTMDs for lightly damped systems are obtained based on the minimization of the steady‐state displacement response of the main mass. These parameters are computed for different mass ratios and main system damping ratios. Frequency responses of the resulting systems are compared to that of equivalent TMDs using passive dampers. In addition, other characteristics of this system as compared to the passive TMDs are discussed. A design guide to obtain the optimum parameters of GHTMD using the developed diagrams in this paper based on non‐dimensional values is presented. Copyright © 2001 John Wiley & Sons, Ltd.     

考虑耦联影响的二次结构体系减震分析

建立了基础隔震的主次结构体系耦联运动方程,开发了动力分析程序PS—BASE．FOR,对一典型结构的二次结构绝对加速度反应谱与相对位移反应谱计算分析表明,主体结构隔震或同时增大二次结构阻尼,是取得二次结构较好抗震性能的有效途径,增大主体结构的隔震阻尼对二次结构略有不利影响。     

Dynamic soil–structure interaction effects on the seismic response of suspension bridges

A stochastic approach has been formulated for the linear analysis of suspension bridges subjected to earthquake excitations. The transfer functions of various responses have been formulated while including the effects of dynamic Soil–Structure Interaction (SSI) via the use of the fixed-base modes of the structure. The excitation has been characterized by the ‘equivalent stationary’ processes corresponding to the free-field motions at each support and by an assumed coherency function between these motions. The proposed formulation considers the non-stationarity in the structural response due to sudden application of excitation by considering (i) the time-dependent frequency response functions, and (ii) the order statistics formulation for the peak factors in evolutionary response processes. The formulation has been illustrated by analysing the seismic response of the Golden Gate Bridge at San Francisco for two example excitations conforming to USNRC-specified design spectra. The significance of various governing parameters on the dynamic soil–structure interaction effects on the seismic response of suspension bridges has also been studied. It has been found that the contribution of the vertical component of ground motion to the bridge response increases with increasing soil compliance. Also, the extent to which the spatial variation of ground motion affects the bridge response depends on how significant the SSI effects are. Copyright © 1999 John Wiley & Sons Ltd.     

Multi‐objective optimal design of FLC driven hybrid mass damper for seismically excited structures

Structural vibration control using active or passive control strategy is a viable technology for enhancing structural functionality and safety against natural hazards such as strong earthquakes and high wind gusts. Both the active and passive control systems have their limitations. The passive control system has limited capability to control the structural response whereas the active control system depends on external power. The power requirement for active control of civil engineering structures is usually quite high. Thus, a hybrid control system is a viable solution to alleviate some of the limitations. In this paper a multi‐objective optimal design of a hybrid control system for seismically excited building structures has been proposed. A tuned mass damper (TMD) and an active mass driver (AMD) have been used as the passive and active control components of the hybrid control system, respectively. A fuzzy logic controller (FLC) has been used to drive the AMD as the FLC has inherent robustness and ability to handle the non‐linearities and uncertainties. The genetic algorithm has been used for the optimization of the control system. Peak acceleration and displacement responses non‐dimensionalized with respect to the uncontrolled peak acceleration and displacement responses, respectively, have been used as the two objectives of the multi‐objective optimization problem. The proposed design approach for an optimum hybrid mass damper (HMD) system, driven by FLC has been demonstrated with the help of a numerical example. It is shown that the optimum values of the design parameters of the hybrid control system can be determined without specifying the modes to be controlled. The proposed FLC driven HMD has been found to be very effective for vibration control of seismically excited buildings in comparison with the available results for the same example structure but with a different optimal absorber. Copyright © 2002 John Wiley & Sons, Ltd.     

Sensitivity of Indian Monsoon to Entrainment and Detrainment in Mass Flux Schemes

A new analytical formulation of entrainment and detrainment in the Tiedtke's mass flux cumulus parameterization is presented here in which cloud height is one of the key parameters. The proposed analytical profiles of entrainment and detrainment are tested in GCM for long-term simulation and are evaluated in the light of the results from the original Tiedtke's scheme and another mass flux scheme due to Emanuel. The variations of Indian monsoon rainfall have been examined with these schemes in a general circulation model. Evaluation of the simulated rainfall against observations is done by empirical orthogonal function (EOF) analysis for the Indian Monsoon region. It is noted that the spatial and temporal variations of the all-India monsoon rainfall are sensitive to the formulation of entrainment and detrainment in a mass flux scheme, and that the new formulation can effectively represent the increased dilution with height in deep clouds.