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.

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.

scholarly journals Modification of Random Vibration Theory for the Near-fault Region

2021 ◽  
Author(s):  
Van-Bang Phung ◽  
Norm Abrahamson
Keyword(s):  
Earthquake Engineering ◽  
Empirical Model ◽  
Random Vibration ◽  
Ground Motions ◽  
Data Set ◽  
Conditional Model ◽  
Near Fault ◽  
Vibration Theory ◽  
Input Parameters ◽  
Random Vibration Theory

Abstract Standard random vibration theory (RVT) methods for estimating the horizontal spectral acceleration (PSA) amplitudes given the Fourier spectral amplitude (FAS) and ground-motion duration underestimate the PSA values for near-fault ground motions from large magnitudes. An empirical model that is unbiased for near-fault ground motions is developed using the statistical moments of the FAS and the duration as model input parameters, similar to standard RVT, but with a modification to also include magnitude and distance as input parameters. The data set used for the regression includes strong-motion recordings from active crustal regions in the NGA-West2 Pacific Earthquake Engineering Research (PEER) database from California earthquakes (M3.0-7.25) and global earthquakes (M5.0 – 7.9). The zeroth, first, and second spectral moments of the FAS of the 5%-damped oscillator response are used in the empirical model. The scaling with the moments of the FAS replaces the peak factor terms used in RVT. A parametric model for the 5-80% duration that depends on magnitude and distance is also developed to simplify the application of the model. Compared to the standard RVT approach, the conditional model significantly improves the estimation of near-fault PSA values estimated from the FAS. The conditional model is appropriate for use in converting non-ergodic FAS GMMs to non-ergodic PSA GMMs.

Analysis on Wind-Induced Vibration Dynamic Responses of Transmission Tower-Line System

2013 ◽  
Vol 327 ◽  
pp. 284-289
Author(s):  
Xiao Guang Hu ◽  
Jing Bo Yang ◽  
Feng Li Yang
Keyword(s):  
Random Vibration ◽  
Coupling Effect ◽  
Dynamic Responses ◽  
Building Structures ◽  
Transmission Tower ◽  
Line System ◽  
Vibration Theory ◽  
Random Vibration Theory ◽  
Wind Induced Vibration ◽  
Line Coupling

Tower-line system of overhead transmission line are sensitive to wind. Therefore, dynamic effect of wind load should be taken into consideration, for instance, wind-induced vibration coefficient. There might be some errors in the calculation of the coefficient in accordance with ‘Load code for the design of building structures’, for its ignoring the irregular figure, scattered masses and coupling effect of tower-line system. Tower-line system is set up in virtual environment, with tower-line coupling considered, and research wind-induced vibration dynamic responses under Davenport wind speed spectrum. Random vibration theory was applied to calculate the coefficient. Whole tower was divided by hight, and calculated segment’s the wind-induced vibration coefficient seprately. Compare the coefficient from Load Code and random vibration theory, the latter with tower-line coupling effect and tower figure considered, is close to the actual.

scholarly journals A source study of the October, 2007 earthquake sequence of Morelia, Mexico

2012 ◽  
Vol 51 (1) ◽  
Author(s):  
Shri Krishna Singh ◽  
Arturo Iglesias ◽  
Luis Quintanar ◽  
Victor Hugo Garduño ◽  
Mario Ordaz
Keyword(s):  
Green Function ◽  
Random Vibration ◽  
Earthquake Sequence ◽  
Vibration Theory ◽  
Empirical Green Function ◽  
De Se ◽  
Random Vibration Theory ◽  
Source Study

En este artículo se analiza una secuencia de siete sismos (2.5<Mw<3.0) ocurridos en la Ciudad de Morelia, México. Esta serie de temblores ocurrieron en un intervalo de 33 horas en el mes de octubre de 2007. Fueron registrados por dos estaciones locales ubicadas en esa Ciudad. Morelia se encuentra en la la parte central de la Faja Volcánica Trans-Mexicana (CTMVB, por sus siglas en inglés). Las formas de onda y los espectros de estos sismos son sorprendentemente similares, sugiriendo que sus localizaciones y mecanismos focales son casi idénticos. La inversión de forma de onda, restringida a partir de fallas descritas anteriormente en el área (rumbo ~E-O, buzando al norte), arroja un mecanismo focal definido por , y , lo cual es consistente con los mecanismos focales reportados previamente en la región. Dado que, para estos pequeños eventos, la señal se confunde con el ruido para frecuencias f<0.2Hz, se estimó el momento sísmico a partir del espectro de las ondas S en una banda de frecuencias definida en el intervalo 0.2≤f≤1Hz. Sin embargo, en esta banda de frecuencias, existe una amplificación significativa de las ondas símicas debida a una capa de baja velocidad provocada por rocas volcánicas superficiales presentes en cualquier sitio localizado en el CTMVB. En la estimación del y en la interpretación de los espectros observados, se aproximó esta amplificación usando el cociente espectral H/Z. Asumiendo un modelo de fuente , los espectros observados pueden ser explicados con ternas (Δσ, t*, ) (5MPa, 0.02s, 20Hz) y (20 MPa, 0.03 s, 20 Hz), donde Δσ es la caída de esfuerzos asumiendo el modelo de Brune y t* y .son los parámetros de atenuación. Con el fin de simular el movimiento fuerte del terreno, para un sismo postulado de , se usaron estas combinaciones de parámetros junto con las técnicas de Empirical Green Function (EGF) y Random Vibration Theory (RVT). Las aceleraciones horizontales PGA y velocidades PGV en los sitios de referencia están en el rango de 23 a 46 cm/ y de 1.5 a 3.52 cm/s para una caída de esfuerzos de Δσ=5Mpa. Los valores pronosticados para una caída de esfuerzos Δσ=20Mpa son casi el doble (44-89 cm/ and 2.5-6.1 cm/s). Las estimaciones obtenidas, especialmente para Δσ=5MPa, son considerablemente más pequeñas que las reportadas a partir de datos globales. Esta comparación sugiere que existe una alta atenuación en la región volcánica o una inadecuada estimación del efecto de t* y .

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