Input Energy Spectra Research Articles

A Study on Elastic Input Energy Spectra Based on the Compound Intensity Indicator

Determination of a SDOFS elastic input energy is the primary problem to solve for energy-based design approach. The effect of ground motion and damping ratio were analyzed on the input energy spectra. is selected as the compound ground motion intensity indicator to represent the damage potential of strong ground motion. Through inputting of 188 seismic records according to the site classification of Chinese seismic code, three-segment elastic energy spectra are proposed based on normalization methods. The calculation formula of the peak and the value of long-period section of the input energy spectra are presented for four categories of site conditions by statistical analysis. Moreover, calculation procedure of the total energy input is given in the paper.

Probabilistic seismic hazard assessment in Greece – Part 2: Acceleration response spectra and elastic input energy spectra

Abstract. This second part of the study, deals with the evaluation of the earthquake hazard in Greece in terms of the response spectral acceleration and the elastic input energy equivalent velocity. Four sets of predictive equations were selected, two for each type of spectra. Probabilistic hazard maps were created by determining the seismic hazard at grid points covering the region of interest. The maps are presented for the dominant periods of 0.2 s and 1.0 s for each spectrum. Uniform hazard response spectra (UHRS) for six cities located in the regions of highest estimated hazard are also presented. The comparison with elastic design spectra proposed by the latest national building code, has shown that the UHRS values exceed the design values at almost all periods.

Evaluation of seismic energy demand and its application on design of buckling-restrained braced frames

In this study seismic analyses of steel structures were carried out to examine the effect of ground motion characteristics and structural properties on energy demands using 100 earthquake ground motions recorded in different soil conditions, and the results were compared with those of previous works. Analysis results show that ductility ratios and the site conditions have significant influence on input energy. The ratio of hysteretic to input energy is considerably influenced by the ductility ratio and the strong motion duration. It is also observed that as the predominant periods of the input energy spectra are significantly larger than those of acceleration response spectra used in the strength design, the strength demand on a structure designed based on energy should be checked especially in short period structures. For that reason framed structures with buckling-restrained-braces (BRBs) were designed in such a way that all the input energy was dissipated by the hysteretic energy of the BRBs, and the results were compared with those designed by conventional strength-based design procedure.

Power delivered to mechanical systems by random vibrations

This paper develops deformational response power descriptions of multiple degree-of-freedom systems due to stationary random vibration excitation. Two new concepts are developed. The deformational response power density (DRPD) can be computed when a structure's natural frequencies and modal masses are available. The DRPD shows the spectral content of the deformational power delivered to a specific structure by the stationary, random excitation. This function can be found through a weighted windowing of the power spectrum of the input acceleration excitation. Deformational response input power spectra (DRIPS), similar to the input energy spectrum and shock response spectrum, give the power delivered to single-degree-of-freedom systems as a function of natural frequency. It is shown that the DRIPS is simply a smoothed version of the power spectrum of the input acceleration excitation. The DRIPS gives rise to a useful power-based data smoothing operation.

Power Delivered to Mechanical Systems by Random Vibrations

This paper develops deformational response power descriptions of multiple degree-of-freedom systems due to stationary random vibration excitation. Two new concepts are developed. The deformational response power density (DRPD) can be computed when a structure's natural frequencies and modal masses are available. The DRPD shows the spectral content of the deformational power delivered to a specific structure by the stationary, random excitation. This function can be found through a weighted windowing of the power spectrum of the input acceleration excitation. Deformational response input power spectra (DRIPS), similar to the input energy spectrum and shock response spectrum, give the power delivered to single-degree-of-freedom systems as a function of natural frequency. It is shown that the DRIPS is simply a smoothed version of the power spectrum of the input acceleration excitation. The DRIPS gives rise to a useful power-based data smoothing operation.

The Next Generation of Seismic Isolation Going Beyond Seismic Design Dominated by Earthquakes

Seismic isolation can provide superior building safety and dynamic response during strong earthquakes, however, performance is only assured below the design earthquake intensity level. This paper opens with a study of observed strong, near-source ground motions and long-period earthquake waves proposed by researchers. Through the examination of a widerange of earthquake response and input energy spectra, up to a period of 100 seconds, the most suitable range of damping values and isolation periods are found. The optimal period range is further confirmed by evaluating earthquake-wave amplification features during propagation from bedrock to the ground surface. Three types of next-generation seismic isolation systems are proposed along with new parameters to evaluate the dynamic response of seismically isolated structures. By comparing the dynamic response performance of four isolation systems, including a "conventional" 4-second period system, the superior seismic performance of the three next-generation isolation systems is confirmed. The paper shows the direction for a new generation of seismically isolated structures, with periods exceeding 10 seconds, and which minimize the elastic strain energy stored in the structure. Seismically isolated structures possessing these properties will survive strong earthquake input regardless of the uncertainty inherent in earthquake ground motions.

Testing the acceleration spectra given by China and USA seismic codes based on energy supply in near-fault region

For near-fault ground motion, there should be a remarkable impulsive energy supply. Therefore, it is essential to check the validity of actual seismic design codes with energy balance concept. Based on the relationship between the spectrum velocity and the input energy equivalent velocity with 5% damping ratio, the input energy spectra compatible with main China and USA seismic codes were derived, and the accuracy and applicability were verified by using near-fault records. The recommended energy input design spectrum (EIDS) applicable to the distance of 0∼15 km from fault was introduced to check the validity of modern seismic codes. Comparison tests show that the GB50011-2001 Code of China can just match the energy effect of near-fault ground motion to a certain extent only under seldom occurred earthquake with fortification intensity of 9 degree for site soil of III and IV, indicating that the impact of near-fault effect has not been embodied in the current code acceleration spectrum. In order to make the design spectrum be applicable to near-fault region, it is necessary to adjust the spectrum platform parameters. On the contrary, for distinct fault distance and site soil, the UBC97 Code of USA can match well with the energy supply of near-fault ground motion except for the site soil of hard rock (SA). Accordingly, correctness of the formula derivation in this paper is certified.

Design elastic input energy spectra based on Iranian earthquakes

The goal of this paper is to propose input energy spectra applicable to seismic design of structures based on Iranian earthquakes. In terms of input energy, these spectra represent the load effects of a strong earthquake that a structure may encounter during its lifetime. For this purpose, from among 1800 existing earthquake records in Iran, 110 records were selected. By using these records and through dynamic response analyses, the design input energy spectra for four ground types, defined by the Iranian earthquake code of practice, have been derived.

Applications of the wavelet transform in the generation and analysis of spectrum-compatible records

A wavelet-based procedure to generate artificial accelerograms compatible with a prescribed seismic design spectrum is described. A procedure to perform a baseline correction of the compatible accelerograms is also described. To examine how the frequency content of the modified records evolves with time, they are analyzed in the time and frequency using the wavelet transform. The changes in the strong motion duration and input energy spectrum are also investigated. An alternative way to match the design spectrum, termed the two-band matching procedure, is proposed with the objective of preserving the non-stationary characteristics of the original record in the modified accelerogram.

Earthquake‐resistant structural design through energy demand and capacity

AbstractAn energy‐based earthquake‐resistant structural design method is proposed. The proposed method uses specific input energy spectra, modal or time‐history analyses, and energy distribution among structural members. For a given member strength and stiffness, a relationship between the energy attributable to damage absorbed by a member and its cumulative ductility demand can be determined. Member strength, stiffness and energy capacity are design parameters which are simultaneously used in the design. The method can avoid soft‐storey design. The damage is measured based on a cumulative basis considering earthquake magnitude, frequency, and duration. Tests have been carried out to determine energy absorbing capacities of various structural components. More efforts are needed to make the energy‐based earthquake‐resistant structural design practical, but ssimple formulations for this method are possible. Copyright © 2007 John Wiley & Sons, Ltd.

Studies of systematic uncertainties in the estimation of the monocular aperture of the HiRes experiment

We have studied several sources of systematic uncertainty in calculating the aperture of the High Resolution Fly’s Eye experiment (HiRes) in monocular mode, primarily as they affect the HiRes-II site. The energy dependent aperture is determined with detailed Monte Carlo simulations of the air showers and the detector response. We have studied the effects of changes to the input energy spectrum and composition used in the simulation. A realistic shape of the input spectrum is used in our analysis in order to avoid biases in the aperture estimate due to the limited detector resolution. We have examined the effect of exchanging our input spectrum with a simple E −3 power law in the “ankle” region. Uncertainties in the input composition are shown to be significant for energies below ∼10 18 eV for data from the HiRes-II detector. Another source of uncertainties is the choice of the hadronic interaction model in the air shower generator. We compare the aperture estimate for two different models: QGSJet01 and SIBYLL 2.1. We also describe the implications of employing an atmospheric database with hourly measurements of the aerosol component, instead of using an average as has been used in our previously published measurements of the monocular spectra.

Study on comparison between absolute and relative input energy spectra and effects of ductility factor

Based on 266 strong ground motion records, an attenuation relationship was developed for both absolute and relative input energy spectra. The comparison of the two kinds of input energy spectra constructed from the attenuation relationship was made in this paper. The results show that there is little difference between the absolute input energy spectra and relative input energy spectra at the periods of 0.5–1.0 s for elastic systems and at the period of 0.5 s for inelastic systems. The absolute input energy spectra are much larger than relative input energy spectra in very short period range but some less than relative input energy spectra in long period range. It is also found that the ductility factor has a significant effect on both absolute and relative input energy spectra. The absolute input energy spectra increase with the increasing of ductility factor in the period range of less than 0.3 s but decrease in the period range of larger than 0.3 s. The absolute input energy spectra for different ductility factor are almost equivalent at the period about 0.3 s, but for relative input energy spectra, the period is about 0.5 s. The effect of ductility on the relative input energy spectra in the short period range is much larger than that on the absolute input energy spectra, especially on the softer site class.

Dual scattering foil design for poly-energetic electron beams**Presented at the Current Topics in Monte Carlo Treatment Planning, Advanced Workshop, McGill University, Montréal, Québec, Canada, 3–5 May 2004.

The laser wakefield acceleration (LWFA) mechanism can accelerate electrons to energies within the 6–20 MeV range desired for therapy application. However, the energy spectrum of LWFA-generated electrons is broad, on the order of tens of MeV. Using existing laser technology, the therapeutic beam might require a significant energy spread to achieve clinically acceptable dose rates. The purpose of this work was to test the assumption that a scattering foil system designed for a mono-energetic beam would be suitable for a poly-energetic beam with a significant energy spread. Dual scattering foil systems were designed for mono-energetic beams using an existing analytical formalism based on Gaussian multiple-Coulomb scattering theory. The design criterion was to create a flat beam that would be suitable for fields up to 25 × 25 cm2 at 100 cm from the primary scattering foil. Radial planar fluence profiles for poly-energetic beams with energy spreads ranging from 0.5 MeV to 6.5 MeV were calculated using two methods: (a) analytically by summing beam profiles for a range of mono-energetic beams through the scattering foil system, and (b) by Monte Carlo using the EGS/BEAM code. The analytic calculations facilitated fine adjustments to the foil design, and the Monte Carlo calculations enabled us to verify the results of the analytic calculation and to determine the phase-space characteristics of the broadened beam. Results showed that the flatness of the scattered beam is fairly insensitive to the width of the input energy spectrum. Also, results showed that dose calculated by the analytical and Monte Carlo methods agreed very well in the central portion of the beam. Outside the useable field area, the differences between the analytical and Monte Carlo results were small but significant, possibly due to the small angle approximation. However, these did not affect the conclusion that a scattering foil system designed for a mono-energetic beam will be suitable for a poly-energetic beam with the same central energy. Further studies of the dosimetric properties of LWFA-generated electron beams will be done using Monte Carlo methods.

地震動の新しいパワースペクトル密度関数モデルの提案とそれに基づく地震入力エネルギーの評価

The Kanai-Tajimi model, the most widely used power spectral density model for ground accelerations, has inability to control its spectral level at very low frequencies and consequently sometimes induces overestimations of structural responses for longer-period structures. To overcome this deficiency, we propose a new power spectral density model corresponding to the "pseudo-acceleration" spectral density of an adapted single-degree-of-freedom system under a white noise excitation. The validity of the proposed model is demonstrated through the estimation of the earthquake input energy on the basis of the random response analysis. The analytical explicit expression of the earthquake input energy spectra derived for linear single-degree-of-freedom structures is proved to be also applicable to nonlinear structures with sufficient accuracy.

Incorporating low-cycle fatigue model into duration-dependent inelastic design spectra

Seismic performance of structures is related to the damage inflicted on the structure by the earthquake, which means that formulation of performance-based design is inherently coupled with damage assessment of the structure. Although the potential for cumulative damage during a long-duration earthquake is generally recognized, most design codes do not explicitly take into account the damage potential of such events. In this paper, the classical low-cycle fatigue model commonly used for seismic damage assessment is cast in a framework suitable for incorporating cumulative damage into seismic design. The model, in conjunction with a seismic input energy spectrum, may be used to establish an energy-based seismic design. In order to ensure satisfactory performance in a structure, the cyclic plastic strain energy capacity of the structure is designed to be larger than or equal to the portion of seismic input energy contributing to cumulative damage. The resulting design spectrum, which depends on the duration of the ground motion, indicates that the lateral strength of the structure must be increased in order to compensate for the increased damage due to an increased number of inelastic cycles that occur in a long-duration ground motion. Examples of duration-dependent inelastic design spectra are developed using parameters currently available for the low-cycle fatigue model. The resulting spectra are also compared with spectra developed using a different cumulative damage model. Copyright © 2004 John Wiley & Sons, Ltd.

Exact computation of input‐energy spectra from Fourier amplitude spectra

AbstractA theoretically exact relation is presented between the Fourier amplitude spectrum and the elastic input‐energy spectrum. This energy spectrum is computed from the Fourier acceleration amplitude spectrum and the real part of the relative velocity transfer function of the single‐degree‐of‐freedom elastic oscillator. Some accelerometric records collected worldwide are used to prove the solution. It is shown that the relation presented in this work opens the door for a better understanding of the relationship between the input‐energy spectrum and other seismological variables, such as magnitude and focal distance. Copyright © 2003 John Wiley & Sons, Ltd.

ESPECTROS DE ENERGÍA DE MOVIMIENTOS FUERTES REGISTRADOS EN MÉXICO

Se hace un análisis de la energía obtenida a partir de acelerogramas de algunos sismos fuertes obtenidos en la zona epicentral y en el valle de México. Primero se comparan los espectros de energía de entrada de algunos registros cercanos al epicentro con los espectros de respuesta de aceleración y de velocidad y se correlacionan cualitativamente con el daño. Se analiza la ecuación de energía, las definiciones de energía absoluta y relativa y la variación de éstas en el tiempo. Para sitios instrumentados en zona de lago del valle de México se comentan brevemente las características de atenuación y la variación de energía con la magnitud y dirección del movimiento. Además, se comenta la variación de los espectros de energía de entrada y de histéresis con la resistencia y con la demanda de ductilidad. Por último, se presentan los espectros elásticos de energía de entrada y de energía histerética normalizada para el sismo del 25 de abril de 1989 y los correspondientes mapas con curvas de igual energía para cuatro diferentes periodos estructurales. También se presentan curvas de igual energía y periodo estructural de dos segundos para cuatro sismos que tuvieron una intensidad importante en el valle de México.

An energy-based methodology for the assessment of seismic demand

A methodology for the assessment of the seismic energy demands imposed on structures is proposed. The research was carried out through two consecutive phases. Inelastic design input energy spectra for systems with a prescribed displacement ductility ratio were first developed. The study of the inelastic behavior of energy factors and the evaluation of the response modification in comparison with the elastic case were performed by introducing two new parameters, namely: (1) the Response Modification Factor of the earthquake input energy ( R E), representing the ratio of the elastic to inelastic input energy spectral values and (2) the ratio α of the area enclosed by the inelastic input energy spectrum in the range of periods between 0.05 and 4.0 s to the corresponding elastic value. The proposed design inelastic energy spectra, resulting from the study of a large set of strong motion records, were obtained as a function of ductility, soil type, source-to-site distance and magnitude. Subsequently, with reference to single degree of freedom systems, the spectra of the hysteretic to input energy ratio were evaluated, for different soil types and target ductility ratios. These spectra, defined to evaluate the hysteretic energy demand of structures, were described by a piecewise linear idealization that allows to distinguish three distinct regions as a function of the vibration period. In this manner, once the inelastic design input energy spectra were determined, the definition of the energy dissipated by means of inelastic deformations followed directly from the knowledge of hysteretic to input energy ratio. The design spectra of both input energy and hysteretic to input energy ratio were defined considering an elasto-plastic behavior. Nevertheless, other constitutive models were taken into account for comparison purposes.

Evaluation of seismic energy demand

AbstractIn this paper, a method is proposed in order to obtain a simplified representation of hysteretic and input energy spectra. The method is based on the evaluation of the equivalent number of cycles correlated to the earthquake characteristics by the proposed seismic index ID. This procedure allows us to obtain peak values of the hysteretic and input energy that depend on the demanded ductility, on the seismic index ID and on the peak pseudo‐velocity. The assessment of the input energy represents a first step towards the definition of a damage potential index capable of taking into account the effect of the duration of the ground motions. Copyright © 2001 John Wiley & Sons, Ltd.

A PROCEDURE FOR ESTIMATING INPUT ENERGY SPECTRA FOR SEISMIC DESIGN

In this paper, the damage potential of an earthquake ground motion is evaluated in terms of the total power of the acceleration of the ground motion. By assuming an appropriate spectral shape for the input energy spectrum, and using the well-known Parseval theorem for evaluating the total power of a random signal, the peak amplification factor for the equivalent input energy velocity spectrum can be determined. It is shown that the peak amplification factor for the input energy spectrum depends on the peak-ground-acceleration to peak-ground-velocity ratio and duration of the strong motion phase of the ground motion. Values for the equivalent input energy velocity amplification factor vary from about 2 to 10 for most of the recorded ground motions used in this study. Although a considerable scatter of data is observed in this study, the peak amplification factor predicted by the Fourier amplitude spectrum of the ground acceleration provides a fairly good estimate of the mean value of the peak input energy compared to that determined from inelastic dynamic time history analyses, particularly for systems with high damping and low lateral strength. The peak amplification factor derived in this paper provides a more consistent approach for estimation of seismic demand when compared to an earlier empirical expression used for the formulation of duration-dependent inelastic seismic design spectra, even though only a slight difference in the required lateral strength results from the use of the new formula.