Statistical Properties of Random Vibration in the Time Domain

2014 ◽  
pp. 259-293 ◽  
Author(s):  
Christian Lalanne
Keyword(s):  
Time Domain ◽  
Random Vibration ◽  
Statistical Properties ◽  
The Time Domain

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 Random Solution to Ice-Induced Vibrations of Conical Structures

2015 ◽  
Author(s):  
Xiang Liu ◽  
Yingying Chen ◽  
Hai Gu ◽  
Jer-Fang Wu
Keyword(s):  
Time Domain ◽  
Random Vibration ◽  
Limit State ◽  
Flexible Structures ◽  
Design Parameters ◽  
Bohai Bay ◽  
Random Solution ◽  
The Time Domain ◽  
Ice Force ◽  
Conical Structures

Offshore installations designed to withstand extreme ice actions, such as the multi-leg structures in Cook Inlet, the gravity based Molikpaq during its mobilization in the Beaufort Sea, lighthouses and channel markers in the Baltic Sea, jackets and mooring poles in Bohai Bay and multi-leg structures offshore Sakhalin, have experienced ice-induced vibrations (IIVs). Full-scale data from Bohai Bay also demonstrate that a conical waterline geometry of the structure does reduce the magnitude of the ice forces, but it still experiences IIVs that can be treated as a stochastic process. ISO 19906 recommends that the dynamic ice actions and the corresponding IIVs shall be considered in the design as the fatigue limit state (FLS). ISO 19906 provides the guidance for the time-domain random dynamic ice action on conical structures. The dynamic structural response to such ice action can take the form of a random vibration. As an alternative to the time-domain approach, random vibration analysis can also be done in the frequency domain by the spectral approach. In addition to the time-domain random dynamic ice action on conical structures provided in ISO 19906, a type of ice-force spectrum on conical structures has been developed. In this paper, a simplified single-degree-of-freedom system (SDOF system) and the ice-force spectrum are used to derive an analytical random solution to assess the IIVs of conical structures. As ISO 19906 points out that particular attention shall be given to dynamic actions on narrow structures and flexible structures, the developed random solution can be useful for designers to make a fast estimate of IIVs (i.e., displacement, velocity and acceleration) and to efficiently screen out the key design parameters of a conical ice-resistant structure.

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.

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.

Apodisation in the time domain

1992 ◽  
Vol 2 (4) ◽  
pp. 615-620
Author(s):  
G. W. Series
Keyword(s):  
Time Domain ◽  
The Time Domain

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

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