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.

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.

Time-Domain Modeling of the Random Vibrations of Tubes Subjected to Turbulence-Conveying Flows

2011 ◽  
Author(s):  
Jose Antunes ◽  
Xavier Delaune ◽  
Philippe Piteau
Keyword(s):  
Turbulent Flows ◽  
Time Domain ◽  
Practical Interest ◽  
Random Excitation ◽  
Practical Significance ◽  
Domain Modeling ◽  
Two Dimensional ◽  
Axial Velocity Component ◽  
Random Forces ◽  
The Time Domain

The vibrations of multi-supported tubes subjected to flow excitation have been the subject of active research for many years, in particular connected with the critical design of heat exchangers and fuel bundles of nuclear power facilities. Because tubes are often loosely supported, their nonlinear dynamics are conveniently addressed through time-domain numerical simulations, for the predictive analysis with respect to wear and fatigue. Turbulence is one of the main excitation mechanisms which drive tube vibrations. We recently revisited the problem of random excitation generation in the time domain, for transverse flows. A new simplified an efficient technique was developed, which properly emulates the spectral and spatial features of the turbulence force field. Results were successfully compared with those from another generation method based on the classical work by Shinozuka and co-workers. In the present paper, we extend our previous work by modeling the time-domain random excitation from flows which display a significant axial velocity component, leading to the convection of turbulence fluctuations. This problem has been addressed by many authors in the past, mainly focusing on linear analysis in the frequency domain, for flow-excited plates, pipes and tubes. Here, for the purpose of nonlinear analysis, we focus on two techniques for generating time-domain turbulence excitations which properly account for the effects of the axial transport term in convective flows. We start by extending our original random force generation method, in order to emulate axial turbulent flows. For the purpose of physical discussion and computational efficiency evaluation, we also implemented an updated version of Shinozuka’s excitation generation technique. We discuss the use of random forces applied at fixed locations, but also investigate the use of axially convected travelling forces. The practical significance of the cross-spectral convection term is evaluated for pure axial and mixed flows. Finally, because time-domain dynamical simulations of practical interest are usually two-dimensional, we discuss the correlation of the orthogonal random forces generated along the motion directions, when simulating two-dimensional turbulence fields.

A New Method for Optimizing Friction Damping in Randomly Excited Systems

1989 ◽  
Author(s):  
T. M. Cameron ◽  
J. H. Griffin
Keyword(s):  
Time Domain ◽  
Turbine Blades ◽  
Single Mode ◽  
Random Excitation ◽  
Degree Of Freedom ◽  
System Response ◽  
Friction Damping ◽  
Single Mode Approximation ◽  
The One ◽  
The Time Domain

A method is developed that can be used to calculate the stationary response of randomly excited nonlinear systems. The method iterates to obtain the fast Fourier transform of the system response, returning to the time domain at each iteration to take advantage of the ease in evaluating nonlinearities there. The updated estimates of the nonlinear terms are transformed back into the frequency domain in order to continue iterating on the frequency spectrum of the staionary response. This approach is used to calculate the response of a one degree of freedom system with friction damping that is subjected to random excitation. The one degree of freedom system provides a single mode approximation of systems (e.g. turbine blades) with friction damping. This study investigates various strategies that can be used to optimize the friction load so as to minimize the response of the system.

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
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