Selection of random vibration theory procedures for the NGA-East project and ground-motion modeling

2021 ◽  
Vol 37 (1_suppl) ◽  
pp. 1420-1439
Author(s):  
Albert R Kottke ◽  
Norman A Abrahamson ◽  
David M Boore ◽  
Yousef Bozorgnia ◽  
Christine A Goulet ◽  
...  
Keyword(s):  
Ground Motion ◽  
Time Domain ◽  
Random Vibration ◽  
Amplitude Spectrum ◽  
Motion Modeling ◽  
Peak Response ◽  
Vibration Theory ◽  
Random Vibration Theory ◽  
The Time Domain ◽  
The Impact

Traditional ground-motion models (GMMs) are used to compute pseudo-spectral acceleration (PSA) from future earthquakes and are generally developed by regression of PSA using a physics-based functional form. PSA is a relatively simple metric that correlates well with the response of several engineering systems and is a metric commonly used in engineering evaluations; however, characteristics of the PSA calculation make application of scaling factors dependent on the frequency content of the input motion, complicating the development and adaptability of GMMs. By comparison, Fourier amplitude spectrum (FAS) represents ground-motion amplitudes that are completely independent from the amplitudes at other frequencies, making them an attractive alternative for GMM development. Random vibration theory (RVT) predicts the peak response of motion in the time domain based on the FAS and a duration, and thus can be used to relate FAS to PSA. Using RVT to compute the expected peak response in the time domain for given FAS therefore presents a significant advantage that is gaining traction in the GMM field. This article provides recommended RVT procedures relevant to GMM development, which were developed for the Next Generation Attenuation (NGA)-East project. In addition, an orientation-independent FAS metric—called the effective amplitude spectrum (EAS)—is developed for use in conjunction with RVT to preserve the mean power of the corresponding two horizontal components considered in traditional PSA-based modeling (i.e., RotD50). The EAS uses a standardized smoothing approach to provide a practical representation of the FAS for ground-motion modeling, while minimizing the impact on the four RVT properties ( zeroth moment, [Formula: see text]; bandwidth parameter, [Formula: see text]; frequency of zero crossings, [Formula: see text]; and frequency of extrema, [Formula: see text]). Although the recommendations were originally developed for NGA-East, they and the methodology they are based on can be adapted to become portable to other GMM and engineering problems requiring the computation of PSA from FAS.

A note on the use of random vibration theory to predict peak amplitudes of transient signals

1984 ◽  
Vol 74 (5) ◽  
pp. 2035-2039
Author(s):  
David M. Boore ◽  
William B. Joyner
Keyword(s):  
Short Duration ◽  
Random Vibration ◽  
Ground Motions ◽  
Standard Theory ◽  
Transient Signals ◽  
Peak Response ◽  
Long Period ◽  
Vibration Theory ◽  
Radiated Energy ◽  
Random Vibration Theory

Abstract Random vibration theory offers an elegant and efficient way of predicting peak motions from a knowledge of the spectra of radiated energy. One limitation to applications in seismology is the assumption of stationarity used in the derivation of standard random vibration theory. This note provides a scheme that allows the standard theory to be applied to the transient signals common in seismology. This scheme is particularly necessary for predictions of peak response of long-period oscillators driven by short-duration ground motions.

scholarly journals Dynamic Response of an Optomechanical System to a Stationary Random Excitation in the Time Domain

2011 ◽  
Vol 18 (5) ◽  
pp. 747-758 ◽  
Author(s):  
Jeremy A. Palmer ◽  
Thomas L. Paez
Keyword(s):  
Time Domain ◽  
Random Vibration ◽  
Response Probability ◽  
Random Excitation ◽  
Cumulative Distribution ◽  
Housing System ◽  
Type I ◽  
Optomechanical System ◽  
Peak Response ◽  
The Time Domain

Modern electro-optical instruments are typically designed with assemblies of optomechanical members that support optics such that alignment is maintained in service environments that include random vibration loads. This paper presents a nonlinear numerical analysis that calculates statistics for the peak lateral response of optics in an optomechanical sub-assembly subject to random excitation of the housing. The work is unique in that the prior art does not address peak response probability distribution for stationary random vibration in the time domain for a common lens-retainer-housing system with Coulomb damping. Analytical results are validated by using displacement response data from random vibration testing of representative prototype sub-assemblies. A comparison of predictions to experimental results yields reasonable agreement. The Type I Asymptotic form provides the cumulative distribution function for peak response probabilities. Probabilities are calculated for actual lens centration tolerances. The probability that peak response will not exceed the centration tolerance is greater than 80% for prototype configurations where the tolerance is high (on the order of 30 micrometers). Conversely, the probability is low for those where the tolerance is less than 20 micrometers. The analysis suggests a design paradigm based on the influence of lateral stiffness on the magnitude of the response.

scholarly journals A Non-ergodic Spectral Acceleration Ground Motion Model for California Developed with Random Vibration Theory

2021 ◽  
Author(s):  
Grigorios Lavrentiadis ◽  
Norman A. Abrahamson
Keyword(s):  
Standard Deviation ◽  
Ground Motion ◽  
Random Vibration ◽  
Epistemic Uncertainty ◽  
Response Spectrum ◽  
Motion Model ◽  
Small Magnitude ◽  
Vibration Theory ◽  
Ground Motion Model ◽  
Random Vibration Theory

Abstract A new approach for creating a non-ergodic PSA ground-motion model (GMM) is presented which account for the magnitude dependence of the non-ergodic effects. In this approach, the average PSA scaling is controlled by an ergodic PSA GMM, and the non-ergodic effects are captured with non-ergodic PSA factors, which are the adjustment that needs to be applied to an ergodic PSA GMM to incorporate the non-ergodic effects. The non-ergodic PSA factors are based on EAS non-ergodic effects and are converted to PSA through Random Vibration Theory (RVT). The advantage of this approach is that it better captures the non-ergodic source, path, and site effects through the small magnitude earthquakes. Due to the linear properties of Fourier Transform, the EAS non-ergodic effects of the small events can be applied directly to the large magnitude events. This is not the case for PSA, as response spectrum is controlled by a range of frequencies, making PSA non-ergodic effects depended on the spectral shape which is magnitude dependent. Two PSA non-ergodic GMMs are derived using the ASK14 (Abrahamson et al., 2014) and CY14 (Chiou and Youngs, 2014) GMMs as backbone models, respectively. The non-ergodic EAS effects are estimated with the LAK21 (Lavrentiadis et al., In press) GMM. The RVT calculations are performed with the V75 (Vanmarcke, 1975) peak factor model, the Da0.05−0.85 estimate of AS96 (Abrahamson and Silva, 1996) for the ground-motion duration, and BT15 (Boore and Thompson, 2015) oscillator-duration model. The California subset of the NGAWest2 database (Ancheta et al., 2014) is used for both models. The total aleatory standard deviation of the two non-ergodic PSA GMMs is approximately 30 to 35% smaller than the total aleatory standard deviation of the corresponding ergodic PSA GMMs. This reduction has a significant impact on hazard calculations at large return periods. In remote areas, far from stations and past events, the reduction of aleatory variability is accompanied by an increase of epistemic uncertainty.

Numerical Simulation of Subway Train Vertical Random Vibration Load in Time Domain

2012 ◽  
Vol 433-440 ◽  
pp. 68-73
Author(s):  
Ya Zhou Qin ◽  
Jian Cong Xu ◽  
Ding Wang
Keyword(s):  
Time Domain ◽  
Random Vibration ◽  
Amplitude Spectrum ◽  
Vertical Acceleration ◽  
Response Measurement ◽  
Time Curve ◽  
Transform Method ◽  
Vibration Load ◽  
Subway Train ◽  
The Time Domain

It is of importance to identify the subway train random vibration load correctly. On the basis of the in-situ dynamic response measurement, the deterministic data for vertical acceleration of rail were obtained. The problem of identifying the random vibration load of subway train was solved in Matlab, according to the simplified vibration model of vehicle system, and in Newmark-β method. Then the time curve and the amplitude spectrum curve of the vertical random vibration train load were obtained. Compared with Fast Fourier Transform method, Newmark-β method is more simple and practical to simulate the train vertical random vibration load directly in the time domain.

scholarly journals Calibration of ultrasonic hardware for enhanced total focusing method imaging

2020 ◽  
Vol 62 (7) ◽  
pp. 408-415
Author(s):  
M Ingram ◽  
A Gachagan ◽  
A Nordon ◽  
A J Mulholland ◽  
M Hegarty
Keyword(s):  
Time Domain ◽  
Pressure Profile ◽  
Side Lobe ◽  
Destructive Testing ◽  
Experimental Variation ◽  
Focal Position ◽  
Measured Time ◽  
The Time Domain ◽  
Ray Path ◽  
The Impact

Experimental variation from ultrasonic hardware is one source of uncertainty in measured ultrasonic data. This uncertainty leads to a reduction in the accuracy of images generated from these data. In this paper, a quick, easy-to-use and robust methodology is proposed to reduce this uncertainty in images generated using the total focusing method (TFM). Using a 128-element linear phased array, multiple full matrix capture (FMC) datasets of a planar reflection are used to characterise the experimental variation associated with each element index in the aperture. Following this, a methodology to decouple the time-domain error associated with transmission and reception at each element index is presented. These time-domain errors are then introduced into a simulated array model used to generate the two-way pressure profile from the array. The side-lobe-to-main-lobe energy ratio (SMER) and beam offset are used to quantify the impact of these measured time-domain errors on the pressure profile. This analysis shows that the SMER is raised by more than 6 dB and the beam is offset by more than 1 mm from its programmed focal position. This calibration methodology is then demonstrated using a steel non-destructive testing (NDT) sample with three side-drilled holes (SDHs). The time delay errors from transmission and reception are introduced into the time-of-flight (TOF) calculation for each ray path in the TFM. This results in an enhancement in the accuracy of defect localisation in the TFM image.

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