Optimum absorber parameters for minimizing vibration response

Optimum parameters are determined for absorbers, which, when attached to one mass of a main system with two degrees of freedom, minimize the harmonic response of that mass. Comparison is made with the absorber parameters that are determined by treating the main system as an equivalent one degree-of-freedom system and using classical results. Close agreement is obtained if the ratio of the two natural frequencies of the main system is reasonably large. This is in agreement with the author's recent work on optimum absorber parameters which minimize the response of elastic bodies. The extension of the method to multi degree-of-freedom main systems is outlined. The conditions for which different values of these parameters are predicted when the response is minimized over narrow and broad frequency bands are determined.     

Optimum absorber parameters for simple systems

In the classical problem a damped one degree-of-freedom absorber system is attached to a main system, which has one degree of freedom and is undamped. The optimum values of absorber stiffness and damping, which will minimize the resonant response of the main mass, are well known. In this paper the effect on these optimum conditions of light damping in the main system is studied. The authors show that optimum parameters for absorbers, which are attached to beams and plates, can be obtained simply and accurately from those for an equivalent one degree-of-freedom main system. This depends upon the concept of an effective mass for the elastic body and the representation of its response by the single relevant mode. It will be shown in a later paper that for more complex elastic bodies such as cylindrical shells, for which the natural frequencies are more closely spaced, these simple concepts do not predict accurately optimum absorber parameters.     

Minimal structural response under random excitation using the vibration absorber

The equations of motion are derived for the first mode response of a linear multistorey structure having a linear vibration absorber attached to the roof. Furthermore, the variance of the first mode response to a gaussian white noise lateral base acceleration (as a model of earthquake excitation) is determined. Smallest possible values of the variance of the response along with corresponding absorber parameters are established using an optimization program. It is demonstrated that the absorber is quite effective in reducing first mode response for 5- and 10-storey structures even with relatively small values of the absorber mass. Moreover, minimal responses for the randomly excited single-degree-of-freedom system have been determined, and a design example is presented. The absorber system has potential application not only in earthquake engineering but also in aerospace and terrestrial vehicle design.     

Optimum placement and characteristics of velocity-dependent dampers under seismic excitation

In this study,through novel drift-based equations of motion in the frequency domain,optimum placement and characteristics of linear velocity-dependent dampers are investigated.In this study,the sum of the square of the absolute values of transfer matrix elements for interstory drifts is considered as the optimization index.Optimum placement and characteristics of dampers are simultaneously obtained by minimizing the optimization index through an incremental procedure.In each step of the procedure,a predefined value is considered as the damper characteristic.The optimum story for this increment is selected such that it leads to a minimum value for the optimization index.The procedure is repeated for the next increments until the optimization index meets its target value,which is obtained according to the desired damping ratio for the overall structure.In other words,the desired overall damping ratio is the input to the proposed procedure,and the optimal placement and characteristics of the dampers are its output.It is observed that the optimal placement of a velocitydependent damper depends on the damping coefficient of the added damper,frequency of the excitation,and distribution of the mass,stiffness,and inherent damping of the main structure.     

Optimum tuned-mass dampers for minimizing steady-state response of support-excited and damped systems

A numerical searching procedure to find the optimum tuning frequency and damping ratio of the tuned-mass damper which can reduce the steady-state response of damped main systems to a minimum level is developed and applied to the two different harmonic excitation sources, support motion of fixed-displacement amplitude and support motion of fixed-acceleration amplitude. The explicit formulae for these optimum parameters are then derived through a sequence of curve-fitting schemes. It has been found that, as the error of the explicit formulae is negligible, they provide a convenient tool to compute the optimum parameters in engineering applications. The numerical results show that the tuned-mass damper is less effective in reducing the system's response when there is a high level of damping incorporated into the system. It is also found that the optimum tuning frequency is strongly influenced by the damping level of a system, especially in regard to the fixed-acceleration support motion, but the optimum damping ratio of the tuned-mass damper is not sensitive to the damping level of a system. The response of the damped system using the undamped optimum value as the damping of the tuned-mass damper is not much different from the response using the damped optimum value.     

Optimum geometry of tuned liquid column-gas damper for control of offshore jacket platform vibrations under seismic excitation

In this study, the effectiveness of a tuned liquid column-gas damper, TLCGD, on the suppression of seismic-induced vibrations of steel jacket platforms is evaluated. TLCGD is an interesting choice in the case of jacket platforms because it is possible to use the structural elements as the horizontal column of the TLCGD. The objective here is to find the optimum geometric parameters, namely orientation and configuration of vertical columns, length ratio, and area ratio of the TLCGD, considering nonlinear damping of the TLCGD and water-structure interaction between the jacket platform and sea water. The effects of different characteristics of ground motion such as PGA and frequency content on the optimum geometry are also investigated and it is observed that these features have some influence on the optimum area ratio. Finally it is observed that pulse arrangement of ground acceleration is one of the most important parameters affecting the efficiency of a TLCGD. In other words, it is found that the TLCGD’s capability to reduce the RMS responses depends only on the frequency content of the ground acceleration, but its capability to reduce the maximum responses depends on both the frequency content and the pulse arrangement of the ground acceleration.     

Sliding-uplifting response of rigid blocks to base excitation

In the present paper a two-degree-of-freedom system is considered which allows the simulation of rigid blocks uplifting and sliding on frictional foundations; the monolateral constraint between block and base is schematized by means of a joint model, which allows the contact problem to be discretized. The joint model is governed by normal and shear constitutive laws, which have been derived by the phenomenological behaviour of stone blocks and rock joints, as given by rock mechanics. Furthermore, a numerical procedure has been developed in order to solve the non-linear equations governing the motion of the block-base system, and to analyse the dynamic response of this system under seismic excitation; particular attention has been paid to the influence of the vertical displacement on the slip response.     

Critical response of structures to multicomponent earthquake excitation

This paper aims to develop an improved understanding of the critical response of structures to multicomponent seismic motion characterized by three uncorrelated components that are defined along its principal axes: two horizontal and the vertical component. An explicit formula, convenient for code applications, has been derived to calculate the critical value of structural response to the two principal horizontal components acting along any incident angle with respect to the structural axes, and the vertical component of ground motion. The critical response is defined as the largest value of response for all possible incident angles. The ratio r_cr/r_srss between the critical value of response and the SRSS response—corresponding to the principal components of ground acceleration applied along the structure axes—is shown to depend on three dimensionless parameters: the spectrum intensity ratio γ between the two principal components of horizontal ground motion characterized by design spectra A(T_n) and γA(T_n); the correlation coefficient α of responses r_x and r_y due to design spectrum A(T_n) applied in the x‐ and y‐directions, respectively; and β = r_y/r_x. It is demonstrated that the ratio r_cr/r_srss is bounded by 1 and . Thus the largest value of the ratio is , 1.26, 1.13 and 1.08 for γ = 0, 0.5, 0.75 and 0.85, respectively. This implies that the critical response never exceeds times the result of the SRSS analysis, and this ratio is about 1.13 for typical values of γ, say 0.75. The correlation coefficient α depends on the structural properties but is always bounded between −1 and 1. For a fixed value of γ, the ratio r_cr/r_srss is largest if β = 1 and α = ±1. The parametric variations presented for one‐storey buildings indicate that this condition can be satisfied by axial forces in columns of symmetric‐plan buildings or can be approximated by lateral displacements in resisting elements of unsymmetrical‐plan buildings. Copyright © 2000 John Wiley & Sons, Ltd.     

反应谱特征参数的提取及其变化规律研究

以误差最小原则，用自动搜索的方式对强地震反应谱提取特征参数，并分析了这些参数与震级和距离的关系，结果表明，在不同场地条件下，反应谱的特征周期和谱平台高度随震级的增大而增大；同时，随着距离的增大，特征周期增大，谱平台高度降低，下降段衰减系数平均值为1.5左右。     

Theory of the electromagnetic transient response of the ionosphere for plane wave excitation

Summary The reflection and transmission of a transient plane wave by an ionosphere with a linear electron density profile and constant collision frequency are calculated. The exact frequency domain solution is inverted numerically, and the resultant reflected and transmitted waveforms are found to satisfy causality. A linearly varying, nondispersive dielectric half-space is also considered, but the nonphysical nature of the model causes the reflected waveform to be noncausal. Using convolution the waveforms for a step modulated sinusoid excitation are also obtained from the impulse response of the ionosphere. The results provide insight into the physical mechanism involved in the ionospheric propagation of HF electromagnetic pulsed signals.     

行波激励下大跨度连续刚构桥的地震反应分析

地晨输入问题一直是工程结构抗震研究所关注的焦点。大跨度桥梁结构各地面支承距离较大、延伸较长，进行地震反应分析时应考虑地震波有限波速传播所引起的行波效应。本文基于行波激励下大跨度桥梁地震反应分析的方法，对某一大跨度的四跨预应力混凝土连续刚构桥进行了行波激励下地震反应的数值模拟，并与一致地震激励下的计算结果进行了比较，对该四跨预应力混凝土连续刚构桥的工程建设具有直接的指导意义。     

Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation

The Rayleigh damping model, which is pervasive in nonlinear response history analysis (RHA) of buildings, is shown to develop ‘spurious’ damping forces and lead to inaccurate response results. We prove that a viscous damping matrix constructed by superposition of modal damping matrices—irrespective of the number of modes included or values assigned to modal damping ratios—completely eliminates the ‘spurious’ damping forces. This is the damping model recommended for nonlinear RHA. Replacing the stiffness‐proportional part of Rayleigh damping by the tangent stiffness matrix is shown to improve response results. However, this model is not recommended because it lacks a physical basis and has conceptual implications that are troubling: hysteresis in damping force–velocity relationship and negative damping at large displacements. Furthermore, the model conflicts with the constant‐damping model that has been the basis for fundamental concepts and accumulated experience about the inelastic response of structures. With a distributed plasticity model, the structural response is not sensitive to the damping model; even the Rayleigh damping model leads to acceptable results. This perspective on damping provides yet another reason to employ the superior distributed plasticity models in nonlinear RHA. OpenSees software has been extended to include a damping matrix defined as the superposition of modal damping matrices. Although this model leads to a full populated damping matrix, the additional computational demands are demonstrated to be minimal. Copyright © 2015 John Wiley & Sons, Ltd.     

Geophysical excitation of the Earth orientation parameters EOP and its contribution to GGOS

We discuss how the geophysical fluids affect the Earth orientation parameters (EOP) and in particular polar motion and nutation. We show that the Earth orientation modeling is a perfect example of the integrated approach recommended by GGOS. GGOS considers the Earth system as a whole, including the solid Earth as well as the fluid components; geodesy observes and models the dynamics inside this system through the static and time-varying gravity field, the station displacements, and the Earth orientation parameters and the associated length-of-day variation, nutation and polar motion. Global-scale transfer in the Earth system and its geodetic consequences is proposed to be the central theme of GGOS. We show that the Earth orientation parameters perfectly fit this theme.     

Geophysical excitation of the Earth orientation parameters EOP and its contribution to GGOS

We discuss how the geophysical fluids affect the Earth orientation parameters (EOP) and in particular polar motion and nutation. We show that the Earth orientation modeling is a perfect example of the integrated approach recommended by GGOS. GGOS considers the Earth system as a whole, including the solid Earth as well as the fluid components; geodesy observes and models the dynamics inside this system through the static and time-varying gravity field, the station displacements, and the Earth orientation parameters and the associated length-of-day variation, nutation and polar motion. Global-scale transfer in the Earth system and its geodetic consequences is proposed to be the central theme of GGOS. We show that the Earth orientation parameters perfectly fit this theme.     

Time-frequency analysis of seismic excitation and estimates of attenuation parameters for the Friuli (Italy) local earthquakes

Stochastic modelling is applied to the analysis of local earthquake recordings, which are usually extremely rich in random incident-wave trains that are chaotically superimposed because of scattering effects in the Earth's crust. The presence in the seismic signal of effects connected with the scale of inhomogeneity in the lithosphere cannot be deterministically described in detail. The application of a stochastic second-order autoregressive model to accelerometric records for the higher magnitude (M_L ? 6) Friuli earthquakes and to short-period seismometric records for the aftershocks of the strong earthquake of 6 May 1976 has allowed inferences to be drawn about the spectral properties of seismic signals and the propagation mechanisms of seismic waves. These inferences are based on an extremely small number of parameters of a mathematical model suitable for simultaneously describing the random sequence of scattered wave trains in the time and frequency domains. Useful physical information has been obtained about the dynamic characteristic correlation times and the predominant frequency of the seismic signals; moreover, the strength, σ²_e(t), of the innovation of the stochastic process fitting the real digital data set has been estimated. From the envelopes of σ²_e(t), the quantity heuristically used in the stochastic approach to describe seismic excitation, the·mean free-path between successive scatterings (l), or the equivalent diffusivity coefficient (d) and turbidity (g), and their dependence on seismic wave frequency have been investigated. For Friuli, using seismometric data at an epicentral distance of ～ 20 km and earthquakes with a magnitude just under 2, mean free-path estimates obtained by means of autoregressive parameters vary from ～ 5 km for the strong interaction model to ～ 30 km for the single scattering model. Furthermore, by means of accelerometric records for the strongest earthquakes in Friuli during May and September 1976, the dependence for the maximum of the seismic excitation on the epicentral distance R was estimated as (σ²_e)_max ～ R^?ν (with ν 1.94 ± 0.13), which is in good agreement with results obtained for the same region using standard methods by means of acceleration peaks versus R. Lastly, stochastic modelling provides a method of estimating change versus time for the predominant frequency and characteristic correlation time of narrow band digital recordings. These two parameters were computed by means of autoregressive parameters in different physical situations and were found to be functions of the earthquake source, the instrumentation frequency response, and the Earth's filtering effects.     

地震动作用下刚体扭转效应的振动台模拟试验

2008年汶川地震中江油市太白公园曲径桥上的石雕发生转动破坏现象,本文对这一转动现象进行了振动台模拟试验。模拟试验结果表明:① 在振动台三向加载1.5倍的汶川地震江油台记录的平动加速度后,模型的转动情况与实际观测的石雕转动情况比较一致;② 石雕的转动与石雕的非对称性、地震动输入角度和地震动的竖向作用有关;③ 加载竖向地震动作用后,石雕模型会发生摇摆现象,说明竖向地震动是造成模型扭转现象的重要原因,这也说明在分析相似震害现象时竖向地震动作用不可忽视。      

Neural network analysis of overturning response under near-fault type excitation

Under strong seismic excitation, a rigid block will uplift from its support and undergo rocking oscillations which may lead to （complete） overturning. Numerical and analytical solutions to this highly nonlinear vibration problem are first highlighted in the paper and then utilized to demonstrate how sensitive the overturning behavior is not only to the intensity and frequency content of the base motion, but also to thc presence of strong pulses, to their detailed sequence, and even to their asymnletry. Five idealised pulses capable of representing ＂rupture-directivity＂ and ＂fling＂ affected ground motions near the fault, are utilized to this end ： the one-cycle sinus, the one-cycle cosinus, the Ricker wavelet, the truncated （T）-Ricker wavelet, and the rectangular pulse ＂Overturning-Acceleration Amplification＂ and ＂Rotation＂ spectra are introduced and presented. Artificial neural network modeling is then developed as an alternative numerical solution. The neural network analysis leads to closed-form expressions for predicting the overturning failure or survival of a rigid block, as a function of its geometric properties and the characteristics of the excitation time history. The capability of the developed neural network modeling is validated through comparisons with the numerical solution. The derived analytical expressions could also serve as a tool for assessing the destructiveness of near-fault ground motions, for structures sensitive to rocking with foundation uplift.     

Periodic response of a sliding oscillator system to harmonic excitation

This paper deals with the periodic response of an oscillating system which is supported on a frictional interface. The base excitation is assumed harmonic and the frictional force is assumed to be of the Coulomb type. Though each segment of the motion of such a system is described by linear equations, its complete response is highly non-linear and varied. The most fundamental periodic solutions are derived analytically and numerically. The results indicate that such a system has several subharmonic resonant frequencies and that while the friction reduces the peak response of the system when it is excited at its ‘fixed-base’ natural frequency, ω_n, the sliding can induce considerably higher levels of response, when compared with those of a non-sliding, fixed-base system, for frequencies less than ω_n. The results obtained herein may find application in the area of vibration isolation.