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 various combinations of response and excitation parameters

In recent papers the author has shown that when determining optimum parameters for an absorber which minimizes the vibration response of a complex system, the latter may be treated as an equivalent single degree-of-freedom system if its natural frequencies are well separated. Emphasis was on minimizing the displacement response when the excitation was a harmonic force. In the present paper simple expressions for optimum absorber parameters are derived for undamped one degree-of-freedom main systems for harmonic and white noise random excitations with force and frame acceleration as input and minimization of various response parameters. These expressions can be used to obtain optimum parameters for absorbers attached to complex systems provided that optimization is with respect to an absolute, rather than a relative, quantity. The requirement that the natural frequencies should be well separated is investigated numerically for the different cases. The effect of damping in the main system on optimum absorber parameters is investigated also.     

Optimum damping in linear isolation systems

Optimum isolation damping for minimum acceleration response of base-isolated structures subjected to stationary random excitation is investigated. Three linear models are considered to account for the energy dissipation mechanism of the isolation system: a Kelvin element, a linear hysteretic element and a standard solid linear element, commonly used viscoelastic models for isolation systems comprising natural rubber bearings and viscous dampers. The criterion selected for optimality is the minimization of the mean-square floor acceleration response. The effects of the frequency content of the excitation and superstructure properties on the optimum damping and on the mean-square acceleration response are addressed. The study basically shows that the attainable reduction in the floor acceleration largely depends on the energy dissipation mechanism assumed for the isolation system as well as on the frequency content of the ground acceleration process. Special care should be taken in accurately modelling the mechanical behaviour of the energy dissipation devices.     

A re-evaluation of equivalent linear models for simple yielding systems

Commonly used equivalent linear models for simple yielding systems subjected to harmonic and earthquake excitations are re-evaluated. It is shown that with respect to damping, these models contain the same basic information. Reported differences in the literature are simply due to scaling: since the product of the equivalent stiffness and equivalent damping is a constant, smaller damping values would be obtained by the use of the small amplitude equivalent stiffnesses. It is argued that for harmonic excitation, the secant stiffness is an appropriate representation of equivalent stiffness, leading to large equivalent damping values that increase with ductility. For earthquake excitation the Iwan proposal is shown to be the preferred model leading to larger damping values than previously reported. A comparison of the models for harmonic and earthquake excitations shows that, in general, and at comparable ductilities, damping values due to harmonic excitation are about five times those due to earthquake excitation, and the period changes due to harmonic excitation are about twice those due to earthquake excitation.     

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 segmentation of simple objects in high-resolution remote sensing imagery in coastal areas

The optimum segmentation of ground objects in a landscape is essential for interpretation of high-resolution remotely sensed imagery and detection of objects; and it is also a technical foundation to efficiently use spatial information in remote sensing imagery. Landscapes are complex system composed of a large number of heterogeneous components. There are many explicit homogeneous image objects that have similar spectral character and yet differ from surrounding objects in high-resolution remote sensing imagery. Thereby, a new concept of Distinctive Feature of fractal is put forward and used in deriving Distinctive Feature curve of fractal evolution in multiscale segmentation. Through distinguishing the extremum condition of Distinctive Feature curve and the inclusion relationship of fractals in multiscale representation the Scalar Order is built. This can help to determinate the optimum scale in image segmentation for simple-objects, and the potential meaningful image-object fitting the intrinsic scale of the dominant landscape object can be obtained. Based on the application in high-resolution remote sensing imagery in coastal areas, a satisfactory result was acquired.     

Birefringence parameters: Indicators of anisotropic symmetry systems

The difference in travel times between split shear waves (travel-time splitting) in anisotropic media depends on nine combinations of the density normalized elastic parameters (the birefringence parameters). These combinations are all zero in isotropic media, where there is no shear-wave splitting. The number of nonzero birefringence parameters increases with decreasing symmetry elements in the medium: from one in cubic media to nine in triclinic media.The birefringence parameters may be recovered from travel-time splitting observations. Their azimuthal behavior may then be interpreted in terms of crack orientation (strike and dip directions).     

Optimum multiple tuned mass dampers for structures under the ground acceleration based on the uniform distribution of system parameters

The five MTMD models, with natural frequencies being uniformly distributed around their mean frequency, have been recently presented by the first author. They are shown to have the near‐zero optimum average damping ratio (more precisely, for a given mass ratio there is an upper limit on the total number, beyond which the near‐zero optimum average damping ratio occurs). In this paper, the eight new MTMD models (i.e. the UM‐MTMD1～UM‐MTMD3, US‐MTMD1～US‐MTMD3, UD‐MTMD1 and UD‐MTMD2), with the system parameters (mass, stiffness and damping coefficient) being, respectively, uniformly distributed around their average values, have been, for the first time here, proposed to seek for the MTMD models without the near‐zero optimum average damping ratio. The structure is represented by the mode‐generalized system corresponding to the specific vibration mode that needs to be controlled. Through minimization of the minimum values of the maximum dynamic magnification factors (DMF) of the structure with the eight MTMD models (i.e. through the implementation of Min.Min.Max.DMF), the optimum parameters and values of Min.Min.Max.DMF for these eight MTMD models are investigated to evaluate and compare their control performance. The optimum parameters include the optimum mass spacing, stiffness spacing, damping coefficient spacing, frequency spacing, average damping ratio and tuning frequency ratio. The six MTMD models without the near‐zero optimum average damping ratio (i.e. the UM‐MTMD1～UM‐MTMD3, US‐MTMD1, US‐MTMD2 and UD‐MTMD2) are found through extensive numerical analyses. Likewise, the optimum UM‐MTMD3 offers the higher effectiveness and robustness and requires the smaller damping with respect to the rest of the MTMD models in reducing the responses of structures subjected to earthquakes. Additionally, it is interesting to note, by comparing the optimum UM‐MTMD3 with the optimum MTMD‐1 recently investigated by the first author, that the effectiveness and robustness for the optimum UM‐MTMD3 is almost identical to that for the optimum MTMD‐1 (without inclusion of the optimum MTMD‐1 with the near‐zero optimum average damping ratio). Recognizing these performance benefits, it is preferable to employ the optimum UM‐MTMD3 or the optimum MTMD‐1 without the near‐zero optimum average damping ratio, when installing the MTMD for the suppression of undesirable oscillations of structures under earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

A procedure on ground motion selection and scaling for nonlinear response of simple structural systems

This study presents a ground-motion selection and scaling methodology that preserves the basic seismological features of the scaled records with reduced scatter in the nonlinear structural response. The methodology modifies each strong-motion recording with known fundamental seismological parameters using the estimations of ground-motion prediction equations for a given target hazard level. It provides robust estimations on target building response through scaled ground motions and calculates the dispersion about this target. This alternative procedure is not only useful for record scaling and selection but, upon its further refinement, can also be advantageous for the probabilistic methods that assess the engineering demand parameters for a given target hazard level. Case studies that compare the performance of the proposed procedure with some other record selection and scaling methods suggest its usefulness for building performance assessment and loss models. Copyright © 2012 John Wiley & Sons, Ltd.     

A simple approach to estimating freshwater discharge in branched estuarine systems

In tidal estuaries, quantifying freshwater discharge is still a difficult problem that has not yet been overcome due to the inherent difficulty in measuring and analysing the tidal discharge, especially during periods of low river flow. Because observations are often made in the stations further upstream, where the ratio of river to tidal discharge is large, it remains difficult to determine the discharge rate in the saline region. Freshwater discharge estimation is even more difficult in a branched estuary system having multiple diversion channels that connect with each other at a junction. To date, several methods have been developed for estimating freshwater discharge in estuaries. The most widely used are analytical and conceptual models that employ salinity as the principal trace and numerical simulations. However, these methods are very time consuming and costly as they require large sets of observations before the computations can take place. This paper presents a simple approach to investigating the discharge distribution over branched channels by considering the energy loss due to friction. We develop an analytical model that can obtain the discharge rate quantitatively at a junction where the main flow bifurcates into two branches. The model uses the bed roughness, tidal water level, and cross‐sectional profile under tidally averaged conditions as input data. Two selected estuarine systems in the Hiroshima delta in Japan and the Mekong delta in Vietnam have been investigated. Computations of the newly developed model show good agreement with earlier published results computed by sophisticated analytical and numerical models.     

Effects of torsion factors on simple non-linear systems using fully-bidirectional analyses

An ensemble of earthquake records is used to carry out non-linear analyses of simple torsionally unbalanced systems considering both resisting elements and earthquake components along two perpendicular directions. These fully bidirectional analyses are focused to study the effect of the following factors: (i) seismic-force reduction factor; (ii) factors α and δ used to compute the design eccentricity; (iii) initial lateral period; and (iv) initial stiffness eccentricity. Results indicate that the amplification factor α can be specified as a function of the force reduction factor, the lateral uncoupled period, and the stiffness eccentricity. It is concluded that the coefficient δ depends on the lateral period, the stiffness eccentricity, and the geometrical eccentricity. It was observed that negative shears caused by torsion should be neglected in the design of the stiff element, particularly in the case of systems with large stiffness eccentricity. Results suggest that additional studies should be performed to verify the assumed (partial) equivalence between unidirectional (resisting elements and earthquake components along one direction only) and fully bidirectional analyses to study building torsion problems. Copyright © 1999 John Wiley & Sons, Ltd.     

Correlation study between ground motion intensity measure parameters and deformation demands for bilinear SDOF systems

The correlation between ground motion intensity measures （IM） and single-degree-of-freedom （SDOF） deformation demands is described in this study. Peak ground acceleration （APG）, peak ground velocity （VPG）, peak ground displacement （DPG）, spectral acceleration at the first-mode period of vibration [As（T1）] and ratio of VPG to APG are used as IM parameters, and the correlation is characterized by correlation coefficients p. The numerical results obtained by nonlinear dynamic analyses have shown good correlation between As（T1） or VPG and deformation demands. Furthermore, the effect of As（T1） and VPG as IM on the dispersion of the mean value of deformation demands is also investigated for SDOF systems with three different periods T=0.3 s, 1.0 s, 3.0 s respectively.     

Optimal weight absorber designs for vibrating structures exposed to random excitations

Optimal mass ratios that minimize the response of a laminated beam with an attached absorber are tabulated for various values of beam damping. The beam is treated as an equivalent one degree of freedom (1DOF) main system vibrating in the fundamental mode. The beam is subjected to Gaussian white noise force and Gaussian white noise base frame acceleration. Optimal absorber frequency ratios and absorber damping ratios have been tabulated by others; the results for the classical 1DOF main system with attached absorber suggest that the optimized non-dimensional response decreases monotonically as the mass ratio increases. However, to generalize this monotonic relation may lead to inappropriate conclusions. If we define a constraint such that an increase in absorber mass leads to a proportional decrease in available beam construction material, i.e. effectively the combined mass of the beam and absorber is minimized, then variations in the mass ratio will affect the beam's parameters such as mass, stiffness and damping. Since some of these parameters are used for non-dimensionalising the response, inspection of non-dimensional responses may in some cases lead to inappropriate conclusions. This paper shows the optimal mass ratios for minimizing the response of a structure exposed to earthquake or fluid flow type random excitations.     

Optimum strong-motion array geometry for source inversion

Optimum strong-motion array geometry for source inversion is quantitatively determined for each of three types of earthquake faults: strike—slip, dip-slip and offshore subduction thrust. The estimation is done by using the source inversion method^1,2 previously developed and based on Wolberg's prediction analysis.³ Only the far-field S waves are taken into account in source inversion; we test only the ability to estimate seismic moments of subfault elements. A comparison of the optimum array geometries obtained in this study with the ones proposed on the basis of an empirical judgment at the 1978 International Workshop on Strong-Motion Earthquake Instrument Arrays⁴ shows that the Workshop geometries are not the best ones as far as source studies are concerned. The most preferable array involves two different kinds of stations regardless of the target fault type: stations close to the fault and aligned parallel to its strike, and stations surrounding the fault area with good azimuthal coverage. The former stations resolve the later stage of the rupturing process while the latter stations resolve the earlier stage.     

Optimum nets

Summary Within a given configuration of points of a geodetic net measurements may be carried out according to different designs. The selected design generates a certain value of the determinant of the covariance matrix of the estimate of the net parameters being determined. Of two designs which both require the same number of measurements, that which generates a smaller value of the determinant of the covariance matrix is considered the better. The paper describes the procedure which determines the best design by method of iteration, or determines the design which differs from the best negligibly.     

Sampling strategies based on sets of behavioural parameters. Application to a simple pesticide fate model

Sampling strategies are necessary to minimise the cost of data acquisition. We consider the case when several samples must be analysed at the same time, knowing rainfall data, optionally discharge data. We assume also that a rainfall-runoff and pesticide transfer model is available. Three methods are presented based on behavioural sets calculated on prior events, which provide optimal sampling times with respect to different statistical criteria, for a fixed number of samples. A methodology to compare these strategies, adapted to a context of data scarcity is proposed for proper validation. We consider that the combination of a model and a strategy is efficient if it does better than a strategy without a model based on equal volumes. Even with a simple and relatively poor model, it can be concluded that the different strategies are efficient and show similar efficiency in spite of their different levels of conceptual and algorithmic complexity.     

Optimum seismic zoning for multiple types of structures

We consider zoning for the design criterion that minimizes the expected present value of the total cost, including the initial cost as well as losses due to damage and failure. The problem consists of the following: given the number of zones, their boundaries and design coefficients must be such that they minimize the expected present value of all structures built in the region. We will refer to solutions in one or more dimensions, depending on the number of the types of structures built in the region to be zoned. Two methods are proposed to solve the problems. The first method is based on the different combinations performed in order to attain optimum zoning. The second method uses an analogy to the evolution of biological systems. The work ends by applying the methods developed to a region of known seismicity. Copyright © 2003 John Wiley & Sons, Ltd.     

An extrusion energy absorber suitable for the protection of structures during an earthquake

A structure moving under the influence of an earthquake is normally required to absorb its own energy of motion. However, in many cases it is possible to attach to the structure energy absorbing devices which absorb most of its energy of motion. One such device is an energy absorber which works by extruding lead back and forth through an orifice. On being extruded the deformed lead recrystallizes immediately, thereby recovering its original mechanical properties before the next extrusion or stroke. Accordingly, the amount of energy absorbed is not limited by work hardening or fatigue of the lead, but rather by the heat capacity of the device, the melting point of lead being the upper limit to the operating temperature. Furthermore, the device is able to absorb energy during a large number of earthquakes. A number of 20 kN × 2 cm stroke to 200 kN × 26 cm stroke extrusion energy absorbers have been tested at rates of 10^?6 to 3.6 × 10^?6 cm/min. They behaved as ‘plastic solids’ or ‘coulomb dampers’ with nearly rectangular hysteresis loops and little rate dependence.     

Dynamic behavior and applicability of lead alloy absorber

Introduction As the result of economic development, metropolitans spring out in China. In metropolitans,the cities contact with each other through life line systems, the density of population is larger thanother areas, and social treasure in the unit area is much higher than other cities (GAO, 2003). Atthe same time, the risk of potential earthquake disaster in metropolitans increases greatly. One ofcharacters of metropolitan earthquake damage is that each city in the metropolitan will …     

Optimum pilot sweep

The successful application of high-resolution seismic methods requires evaluating each element in the seismic system and ensuring that each part of the system contributes optimally to the success of the method. Unfortunately, unlike data processing, seismic signal generation is not carefully optimized. The purpose of our study was to optimize the source signal in order to better coordinate field operations with subsequent data processing to achieve their common objective. We developed an iterative method for a rational frequency distribution of the energy of a seismic source. The method allows the optimum amplitude spectrum of a source signal to be calculated, thus providing the best data quality at the end of the processing. We assume that the source signal is affected by a total transfer function, by the reflectivity function of a target interval, and by ambient noise, whose characteristics, if not known, can be estimated or measured in practice. The transfer function includes data processing other than the correlation stage and the final trace-optimizing filter. The variance of a reflectivity estimate is considered to be a measure of the data quality and improvement of the characteristic corresponds to a decrease in the variance. For this reason, a constrained Wiener deconvolution filter is used as the final trace-optimizing filter. It not only minimizes the variance of a reflectivity estimate but also ensures a specific signal-to-noise ratio. The method is made feasible by following the Vibroseis technique, primarily because of the versatility of the technique in controlling the signal spectrum. With the optimum amplitude spectrum obtained, the corresponding optimum pilot sweep can be readily calculated. Examples using synthetic data are presented to illustrate the method.