Maximum Structural Response Research Articles

Optimization of non-uniformly distributed multiple tuned mass damper

A gradient-based method for optimizing non-uniformly distributed multiple tuned mass damper (MTMD) is presented in this paper. By solving an optimization problem with multiple objectives, optimized non-uniformly distributed MTMDs are obtained. Then the dynamic characteristics, effectiveness, robustness and redundancy of MTMDs are investigated in detail. Without restrictive assumptions such as uniformly distributed frequency, identical damping ratio, the optimized non-uniformly MTMDs obtained here can be considered as the “true” optimal ones. Unlike the references [L. Zuo, S.A. Nayfeh, Optimization of the individual stiffness and damping parameters in multiple-tuned-mass–damper system, Journal of Vibration and Acoustics—Transactions of the ASME 127(1) (2005) 77–83; N. Hoang, P. Warnitchai, Design of multiple tuned mass damper by using a numerical optimizer, Earthquake Engineering and Structural Dynamics 34(2) (2005) 125–144], the maximum displacement or frequency response of the main structure is chosen as the objective function in the present paper, because the maximum displacement is more concerned than the root-mean-square response sometimes. Using the presented method, the errors of estimate of the parameters of the structure and the MTMD can be taken into account quantitatively in the design procedure of the MTMD. It is demonstrated that the MTMDs designed in this paper are more effective than the traditional optimal uniformly distributed MTMDs whose frequency spacing, stiffness or mass and damping are under some restrictions for simplicity. And the MTMDs designed by accounting for possible errors of estimate are more robust than those without consideration of errors.

Energy density spectra in actively controlled inelastic structures—application

An accurate method of predicting peak structural responses and energy forms in actively controlled structures using generated response spectra and energy density spectra developed in the first part of this research is proposed for both elastic and inelastic structures. The accuracy of the predicted responses is compared with that obtained using inelastic time history analysis. Conventional analysis of controlled structures generally uses structural models that are simplified to a significant extent such that the results usually do not represent the actual behaviour of real moment resisting frames. In this research, inelastic structural control analysis based on force analogy method is extended to analyse real moment-resisting frames with plastic hinges offsets from the member ends. By using static condensation, additional degrees of freedom in real moment resisting frames are condensed out, and thereby the procedure of force analogy method in analysing inelastic structural response remains unchanged. Numerical simulation is performed using the modified 1940 El Centro earthquake time history and response spectra for both elastic and inelastic structural models to study the controlled responses using both optimal linear control and ad hoc control algorithms. Results show that the proposed method of predicting the maximum structural responses gives very accurate results for both elastic and inelastic structural systems. Copyright © 2005 John Wiley & Sons, Ltd.

エネルギースペクトルと速度応答スペクトルの対応

The maximum response of structure under an earthquake is closely related to the maximum response spectrum (S_V-spectrum). The cumulative plastic deformation is related to the energy spectrum (V_E-spectrum). The relationship between S_V-spectrum and V_E-spectrum is influenced by the scale of an earthquake or the time of duration of an earthquake. On the simple assumption that an earthquake consists of the repetition of a single elemental earthquake with the number of repetition of f, the relationship between S_V and V_E spectra is clearly described with the relationship of that in the elemental earthquake and f.

Cross-Polarized Reflected Light Measurement of Fast Optical Responses Associated with Neural Activation

We developed an optical probe for cross-polarized reflected light measurements and investigated optical signals associated with electrophysiological activation in isolated lobster nerves. The cross-polarized baseline light intensity (structural signal) and the amplitude of the transient response to stimulation (functional signal) measured in reflected mode were dependent on the orientation of the nerve axis relative to the polarization plane of incident light. The maximum structural signal and functional response amplitude were observed at 45 degrees , and the ratio of functional to structural signals was approximately constant across orientations. Functional responses were measured in single trials in both transmitted and reflected geometries and responses had similar waveforms. Both structural and functional signals were an order of magnitude smaller in reflected than in transmitted light measurements, but functional responses had similar signal/noise ratios. We propose a theoretical model based on geometrical optics that is consistent with experimental results. In the model, the cross-polarized structural signal results from light reflection from axonal fibers and the transient functional response arises from axonal swelling associated with neural activation. Polarization-sensitive reflected light measurements could greatly enhance in vivo imaging of neural activation since cross-polarized responses are much larger than scattering signals now employed for dynamic functional neuroimaging.

Critical orientation of three correlated seismic components

Analytical formulae are developed for the determination of the critical angle of seismic incidence and the corresponding maximum value of a response quantity of structures subjected to three seismic correlated components: two horizontal components applied along arbitrary directions and a vertical component of earthquake ground motion. The developed analytical formulae, which are derived assuming that the structure behaves linearly, are simple and require the solution of two specific time history loading cases for the horizontal components and one for the vertical component. The application and the accuracy of analytical formulae are illustrated by means of response history analysis of an asymmetric multistory building due to several earthquake records. Also the same asymmetric structure is analyzed by using several earthquake records for different incident angles in order to illustrate the variation of the maximum structural response with the incident angle. The analyses results show that, for the earthquake records used, the critical value of a response quantity can be up to 80% larger than the usual response produced when the seismic components are applied along the structural axes.

Jack-up response to wave-in-deck loads during extreme storms

This paper presents the methodology and key findings of a study into the wave loads generated on a typical jack-up structure, if the air-gap provision is eroded, and its resulting dynamic response to storm loading when inundation occurs. The effects of structural response to previous waves, foundation modelling complexity and hull inundation levels on maximum structural response to wave-in-deck loading were assessed by performing a number of short-duration time-domain analyses. A principal finding of the study was that large horizontal and vertical wave-in-deck loads are generated during inundation, and that the jack-up effectively reacts statically to the vertical loading. In addition, the complexity of the foundation modelling technique used has a very significant effect on predicted response, with coupled, non-linear foundation springs increasing horizontal response by 50% over the linear foundation case.

瞬間吸収エネルギーに基づく粘性系制振補強構造の入力低減率

A simplified method to assess the seismic performance of structures with added viscous or viscoelastic dampers is proposed. It is based on the momentary energy dissipated in structures with/without additional dampers and evaluates the reduction ratio of maximum acceleration of earthquake ground motions. The changes in structural stiffness, damping factor and seismic momentary induced energy are considered to relate the proposed method to the maximum displacement response of damped structures. Extensive time history analyses on the single-degree-of-freedom system with additional viscous or viscoelastic dampers are performed and results have shown a good agreement with those predicted by the proposed method.

Instantaneous optimal method for vibration control of linear sampled-data systems with time delay in control

In an actively controlled system, time delay exists inevitably. Neglecting time delay may cause degradation of control performance or even induce instability to the dynamic system. In this paper, instantaneous optimal control method for vibration control of linear sampled-data systems with time delay in control is investigated. By a peculiar integral transformation, the first order state equation with time delay is transformed into the standard first order state equation, which contains no time delay. Then the optimal controller is designed based on the numerical algorithm of the regular fourth order Runge–Kutta method. Since the obtained controller contains integral term, which is not practical for control implementation, the numerical algorithm for this integral term is investigated too. Since the controller is deduced directly from the time-delay differential equation, the control method presented is prone to guarantee system stability. Thus the presented control method can be applicable to the case of large time delay. The performance of the control method is demonstrated by numerical simulation. Simulation results indicate that this control method is feasible and is an attractive strategy for dealing with the time delay in vibration control systems and is effective in suppressing maximum structural responses. Instability in structural responses may occur if the systems with time delay are controlled using the controller designed in the case of no time delay.

Response characteristics of structures subjected to blasting-induced ground motion

This paper presents a conceptual discussion on structural response to ground shocks. Numerical parametric analyses are performed on a simplified linear structural model to investigate the special features of structural response brought by short duration, large amplitude and high frequency excitations, which are the basic characteristics of ground shocks induced by blasting. Nonlinear finite element analyses on a two-storey RC frame subjected to ground shocks are carried out to qualitatively understand building response to blasting. This study shows that maximum structural response to blasting depends primarily on the amount of impulse, and it generally occurs after the major ground shock has ceased. To capture the maximum response, it is hence necessary to consider additional time duration beyond the major ground shock period in blasting analysis. It is found that the response in the forced-vibration phase includes high frequency vibration modes with small displacement but large acceleration, thus inducing high inertial shear force. However, the free-vibration response is dominated by lower frequency modes with larger displacement but smaller acceleration. Hence, buildings subjected to strong ground shocks might experience a sudden shear failure of its components. Nevertheless, if a building's strength is enough to avoid the sudden shear failure during the major shock, it may be damaged after the ground shock during the free vibration, and the extent of damage depends on the ground shock magnitude.

RESPUESTA ACOPLADA DE TRASLACIÓN Y TORSIÓN DE ESTRUCTURAS ASIMÉTRICAS INCLUYENDO LA INTERACCIÓN CON EL SUELO

Considerando los efectos de interacción suelo-estructura, se estudia la respuesta acoplada de traslación y torsión de estructuras asimétricas desplantadas sobre un estrato de suelo ante excitación sísmica. El sistema investigado consiste en un oscilador simple torsionalmente acoplado con cimentación enterrada en un estrato blando sobre un semiespacio elástico, sometido a ondas SH condiferentes ángulos de incidencia. Se calculan soluciones numéricas para varias configuraciones del sistema, tomando como movimiento de control el gran temblor de Michoacán de 1985 registrado en tres sitios representativos de las zonas blanda y de transición en el Valle de México. Se evalúan la amplificación dinámica de la excentricidad y la relación entre las fuerzas cortantes acopladas y desacopladas, y se comparan con las actuales recomendaciones reglamentarias para estructuras de edificios (Normas Técnicas Complementarias para Diseño por Sismo del RCDF, Gaceta Oficial Del Distrito Federal, 1995). Se muestra que, al menos para comportamiento lineal de la estructura, lasespecificaciones de diseño por torsión pueden subestimar la máxima respuesta estructural cuando los efectos de interacción son de excepcional importancia, como sucede en la Ciudad de México.

Damaging properties of ground motions and prediction of maximum response of structures based on momentary energy response

AbstractDynamic damaging potential of ground motions must be evaluated by the response behaviour of structures, and it is necessary to indicate what properties of ground motions are most appropriate for evaluation. For that purpose, the behaviour of energy input process and hysteretic energy dissipation are investigated in this study. It is found that the momentary input energy that is an index for the intensity of input energy is related to the characteristics of earthquakes such as cyclic or impulsive, and to the response displacement of structures immediately.On the basis of these results, a procedure is proposed to predict inelastic response displacement of structures by corresponding earthquake input energy to structural dissipated damping and hysteretic energy. In this procedure the earthquake response of structures is recognized as an input and dissipation process of energy, and therefore structural properties and damaging properties of ground motions can be taken into account more generally.Lastly, the studies of the pseudodynamic loading test of reinforced concrete structure specimens subjected to ground motions with different time duration are shown. The purpose of this test is to estimate the damaging properties of ground motions and the accuracy of the proposed prediction procedure. Copyright © 2002 John Wiley & Sons, Ltd.

Effects of wave passage on the relevant dynamic properties of structures with flexible foundation

AbstractAn evaluation of the wave passage effects on the relevant dynamic properties of structures with flexible foundation is presented. A simple soil–structure system similar to that used in practice to take into account the inertial interaction effects by the soil flexibility is studied. The kinematic interaction effects due to non‐vertically incident P, SV and Rayleigh waves are accounted for in this model. The effective period and damping of the system are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free‐field ground motion. In this way, the maximum structural response could be estimated from standard free‐field response spectra using the period and damping of the building modified by both the soil flexibility and the travelling wave effects. Also, an approximate solution for the travelling wave problem is examined over wide ranges of the main parameters involved. Numerical results are computed for a number of soil–structure systems to identify under which conditions the effects of wave passage are important. It comes out that these effects are generally negligible for the system period, but they may significantly change the system damping since the energy dissipation within the soil depends on both the wave radiation and the diffraction and scattering of the incident waves by the foundation. Copyright © 2001 John Wiley & Sons, Ltd.

Response to three‐component seismic motion of arbitrary direction

AbstractThis paper presents a response spectrum analysis procedure for the calculation of the maximum structural response to three translational seismic components that may act at any inclination relative to the reference axes of the structure. The formula GCQC3, a generalization of the known CQC3‐rule, incorporates the correlation between the seismic components along the axes of the structure and the intensity disparities between them. Contrary to the CQC3‐rule where a principal seismic component must be vertical, in the GCQC3‐rule all components can have any direction. Besides, the GCQC3‐rule is applicable if we impose restrictions to the maximum inclination and/or intensity of a principal seismic component; in this case two components may be quasi‐horizontal and the third may be quasi‐vertical. This paper demonstrates that the critical responses of the structure, defined as the maximum and minimum responses considering all possible directions of incidence of one seismic component, are given by the square root of the maximum and minimum eigenvalues of the response matrix R, of order 3×3, defined in this paper; the elements of R are established on the basis of the modal responses used in the well‐known CQC‐rule. The critical responses to the three principal seismic components with arbitrary directions in space are easily calculated by combining the eigenvalues of R and the intensities of those components. The ratio rmax/rSRSS between the maximum response and the SRSS response, the latter being the most unfavourable response to the principal seismic components acting along the axes of the structure, is bounded between 1 and √(3γa2/(γa2 + γb2 + γc2)), where γa⩾γb⩾γc are the relative intensities of the three seismic components with identical spectral shape. Copyright © 2001 John Wiley & Sons, Ltd.

Performance-Based Design Approach for Seismic Rehabilitation of Buildings with Displacement-Dependent Dissipators

A performance-based approach for seismic retrofitting of buildings with energy dissipating devices is presented. The approach may be seen as an algorithm useful for converging to a preliminary design of a system to be analyzed according to the time history approach recommended in the NEHRP Guidelines for the Seismic Rehabilitation of Buildings (FEMA 273). The algorithm is based on the analysis of equivalent single-degree-of-freedom models with added parallel elements that represent the dissipating devices. The combined systems are analyzed under sets of accelerograms associated with different return intervals. The acceptance criteria are intended to control the peak drift of the rehabilitated structure and the maximum ductility demand of the dissipating devices. It is required that these maximum structural responses, for a given seismic intensity, be equal to or smaller than those associated with a given probability of exceedance. The approach is successfully applied to a ten-story, three-bay frame rehabilitated with U-shaped steel dissipators.

Structural response for stochastic kinematic interaction

The influence of stochastic kinematic interaction (SKI) on structural response is investigated in this paper. The SKI is evaluated through a computational model based on the boundary element method (BEM) formulated in the frequency domain. The singular integrals required in the computation of BEM are evaluated in a closed form. It is assumed that the foundation input motion (FIM) is the result of the superposition of many plane, stationary, correlated stochastic SH-, P- and SV-waves travelling within a homogeneous viscoelastic soil at different angles. The results obtained indicate that the effect of SKI on the foundation response is qualitatively similar to that of wave passage. Both effects involve a reduction of translational components of the response at intermediate and high frequencies and creation of a rotational response component at intermediate frequencies, which decreases at high frequencies. While, it is found that the SKI decreases the maximum response of structures built on embedded rigid strip foundations excited by SH- and P-waves, it increases the maximum response for SV-waves, except when the natural frequency of the structure is less than 0.5 Hz and for short structures excited by shallowly incident SV-waves. Copyright © 2001 John Wiley & Sons, Ltd.

Seismic effectiveness of tuned mass dampers considering soil–structure interaction

This paper presents how soil–structure interaction affects the seismic performance of Tuned Mass Dampers (TMD) when installed on flexibly based structures. Previous studies on this subject have led to inconsistent conclusions since the soil and structure models employed considerably differ from each other. A generic frequency-independent model is used in this paper to represent a general soil–structure system, whose parameters cover a wide spectrum of soil and structural characteristics. The model structure is subjected to a stationary random excitation and the root-mean-square responses of engineering interest are used to measure the TMD's performance. Extensive parametric studies have shown that strong soil–structure interaction significantly defeats the seismic effectiveness of TMD systems. As the soil shear wave velocity decreases, TMD systems become less effective in reducing the maximum response of structures. For a structure resting on soft soil, the TMD system can hardly reduce the structural seismic response due to the high damping characteristics of soil–structure systems. The model structure is further subjected to the NS component of the 1940 El Centro, California earthquake to confirm the TMD's performance in a more realistic environment. Copyright © 1999 John Wiley & Sons Ltd.

Seismic effectiveness of tuned mass dampers considering soil-structure interaction

This paper presents how soil–structure interaction affects the seismic performance of Tuned Mass Dampers (TMD) when installed on flexibly based structures. Previous studies on this subject have led to inconsistent conclusions since the soil and structure models employed considerably differ from each other. A generic frequency-independent model is used in this paper to represent a general soil–structure system, whose parameters cover a wide spectrum of soil and structural characteristics. The model structure is subjected to a stationary random excitation and the root-mean-square responses of engineering interest are used to measure the TMD's performance. Extensive parametric studies have shown that strong soil–structure interaction significantly defeats the seismic effectiveness of TMD systems. As the soil shear wave velocity decreases, TMD systems become less effective in reducing the maximum response of structures. For a structure resting on soft soil, the TMD system can hardly reduce the structural seismic response due to the high damping characteristics of soil–structure systems. The model structure is further subjected to the NS component of the 1940 El Centro, California earthquake to confirm the TMD's performance in a more realistic environment. Copyright © 1999 John Wiley & Sons Ltd.

The application of actuator performance limits to aeroservoelastic compensation

An interaction between an aircraft's structural dynamics, unsteady aerodynamics and flight control system can have serious effects on the aircraft both in terms of structural integrity and rigid body stability. The effects of such an interaction, known as aeroservoelasticity, are poorly understood and as a result, very conservative flight control system design methods are used in order to achieve flight clearance. This paper demonstrates how the use of nonlinear actuation system models predicts a maximum boundary for the amplitude of the structural response as a result of the performance limits of the nonlinear actuation system. This envelope of maximum structural response can then be used to allow relaxation of the current design criteria for the structural mode filters. The procedure is demonstrated using a representative aircraft system model. Finally, the results of single input frequency response tests of a representative actuation system are presented in support of the earlier results.

The critical angle of seismic incidence and the maximum structural response

SUMMARY A simple method which can be applied in seismic codes to determine the critical angle of seismic incidence and the corresponding peak response of structures subjected to two horizontal components applied along any arbitrary directions and to the vertical component of earthquake ground motion, is proposed in this paper. The seismic components are given in terms of response spectra that may be equal or have di⁄erent spectral shapes. The structures are discrete, linear systems with viscous damping. The method, which is based on the response spectrum method of analysis, requires the solution of standard cases of seismic analysis and therefore can be easily implemented in standard computer programs. For the general case of three arbitrary response spectra, the method requires the solution of five seismic loading cases, two for each horizontal component and one for the vertical component. If the horizontal response spectra have the same shape or if there is only one horizontal component, it is then required to solve just two seismic loading cases for the horizontal components and one for the vertical component. It can be shown that the formulas derived for the critical angles and the peak response are essentially identical to the ones obtained earlier by Smeby and Der Kiureghian using random vibration theory. The application and the accuracy of the method is illustrated by means of numerical analysis of buildings, comparing the results with those obtained using other proposed methods. For the specific case of two horizontal spectra with identical shape and an arbitrary vertical spectra, the critical angle neither depends on the spectral ratio of the two horizontal components nor on the vertical spectrum. For the special case of equal horizontal spectra, the structural response does not vary with the angle of incidence and it is an upper bound for all possible responses. ( 1997 by John Wiley & Sons, Ltd.

A NEW TWIST ON AN OLD MODEL FOR VORTEX-EXCITED VIBRATIONS

A new twist on an old model for predicting the vortex-excited vibrations of flexible cylindrical structures is developed. A van der Pol equation, driven by the local transverse motion of the cylinder, is taken as the governing equation for one component of the fluctuating lift force on the cylinder. The second component of the lift force is represented by a stall term which is linearly proportional to the local transverse velocity of the cylinder. In previous models, the van der Pol equation has been employed as the governing equation for the entire fluctuating lift force on the cylinder. The new model preserves the modal scaling principle for the structural response, as initially predicted by the previous models and since verified experimentally. The empirical parameters in the model are related to the physical mass and damping parameters that define the structural properties so that the maximum structural response and the reduced velocity at which it occurs agree with experimental observations. Because of the stall term, the new model provides for an asymptotic, self-limiting structural response at zero structural damping. This asymptotic, self-limiting behavior was not captured by the previous models.