Coupled Slow and Fast Dynamics of Flow Excited Elastic Cable Systems

2003 ◽  
Vol 125 (2) ◽  
pp. 155-161 ◽  
Author(s):  
W.-J. Kim ◽  
N. C. Perkins
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Equilibrium Configuration ◽  
Fluid Model ◽  
Dynamic Responses ◽  
Slow Drift ◽  
Large Amplitude Motions ◽  
Cable Systems ◽  
Lock In ◽  
Fast Dynamic

Analytical studies of vortex-induced vibration (VIV) of cables during lock-in have considered small amplitude and relatively fast dynamic responses about an equilibrium configuration. However, this equilibrium may change as a result of the significantly increased mean drag created during lock-in. In response to increased drag, the cable may slowly drift downstream causing appreciable changes in cable geometry and tension. The resonance conditions for lock-in may be preserved during this slow drift or they may be disrupted. A nonlinear cable/fluid model is discussed that captures both fast (small amplitude) motions due to VIV and slow (large amplitude) motions due to drift.

Coupled Slow and Fast Dynamics of Flow Excited Elastic Cable Systems

2001 ◽  
Author(s):  
WanJun Kim ◽  
N. C. Perkins
Keyword(s):  
Small Amplitude ◽  
Equilibrium Configuration ◽  
Fluid Model ◽  
Dynamic Responses ◽  
Slow Drift ◽  
Large Amplitude Motions ◽  
Cable Systems ◽  
Lock In ◽  
Fast Dynamic ◽  
Different Time Scales

Abstract Analytical studies of vortex-induced vibration (VTV) of cables during lock-in have considered small amplitude and relatively fast dynamic responses about an equilibrium configuration. However, this equilibrium may change as a result of the significantly increased mean drag created during lock-in. In response to increased drag, the cable may slowly drift downstream causing appreciable changes in cable geometry and tension. The resonance conditions for lock-in may be preserved during this slow drift or they may be disrupted. A nonlinear cable/fluid model is discussed mat captures both fast (small amplitude) motions due to VIV and slow (large amplitude) motions due to drift. These two different time scales of motion are clearly observed in numerical simulations. The significant interplay of the slow drifting motion and the fast VTV is highlighted.

Exploring the Dynamic Characteristics of Degree-4 Vertex Origami Metamaterials

2017 ◽  
Author(s):  
Yutong Xia ◽  
Hongbin Fang ◽  
K. W. Wang
Keyword(s):  
Dynamic Characteristics ◽  
Large Amplitude ◽  
Small Amplitude ◽  
The Other ◽  
Dynamic Responses ◽  
Piecewise Constant Function ◽  
Intrinsic Geometry ◽  
Mechanical Metamaterials ◽  
Folding Dynamics ◽  
Stiffness Profile

Origami-inspired mechanical metamaterials could exhibit extraordinary properties that originate almost exclusively from the intrinsic geometry of the constituent folds. While most of current state of the art efforts have focused on the origami’s static and quasi-static scenarios, this research explores the dynamic characteristics of degree-4 vertex (4-vertex) origami folding. Here we characterize the mechanics and dynamics of two 4-vertex origami structures, one is a stacked Miura-ori (SMO) structure with structural bistability, and the other is a stacked single-collinear origami (SSCO) structure with locking-induced stiffness jump; they are the constituent units of the corresponding origami metamaterials. In this research, we theoretically model and numerically analyze their dynamic responses under harmonic base excitations. For the SMO structure, we use a third-order polynomial to approximate the bistable stiffness profile, and numerical simulations reveal rich phenomena including small-amplitude intrawell, large-amplitude interwell, and chaotic oscillations. Spectrum analyses reveal that the quadratic and cubic nonlinearities dominate the intrawell oscillations and interwell oscillations, respectively. For the SSCO structure, we use a piecewise constant function to describe the stiffness jump, which gives rise to a frequency-amplitude response with hardening nonlinearity characteristics. Mainly two types of oscillations are observed, one with small amplitude that coincides with the linear scenario because locking is not triggered, and the other with large amplitude and significant nonlinear characteristics. The method of averaging is adopted to analytically predict the piecewise stiffness dynamics. Overall, this research bridges the gap between the origami quasi-static mechanics and origami folding dynamics, and paves the way for further dynamic applications of origami-based structures and metamaterials.

On the Force Coefficients of a Flooded, Open Ends Short Length Squeeze Film Damper: From Theory to Practice (and Back)

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Luis San Andrés ◽  
Sean Den ◽  
Sung-Hwa Jeung
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Forced Response ◽  
Short Length ◽  
Theory And Practice ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Force Coefficients ◽  
Deep Groove ◽  
Large Amplitude Motions

Gas turbine aircraft engine manufacturers push for simple squeeze film damper (SFD) designs, short in length, yet able to provide enough damping to ameliorate rotor vibrations. SFDs employ orifices to feed lubricant directly into the film land or into a deep groove. The holes, acting as pressure sources (or sinks), both disrupt the film land continuity and reduce the generation of squeeze film dynamic pressure. Overly simple predictive formulations disregard the feedholes and deliver damping (C) and inertia (M) force coefficients not in agreement with experimental findings. Presently, to bridge the gap between simple theory and practice, the paper presents measurements of the dynamic forced response of an idealized SFD that disposes of the feedholes altogether. The short-length SFD, whose diameter D = 127 mm, has one end submerged (flooded) within a lubricant bath and the other end exposed to ambient. ISO VG 2 lubricant flows by gravity through the film land of length L = 25.4 mm and clearance c = 0.122 mm. From dynamic load tests over excitation frequency range 10–250 Hz, experimental damping coefficients (CXX, CYY) from the flooded damper agree well with predictions from the classical open ends model with a full film for small amplitude whirl motions (r/c ≪ 1), centered and off-centered. Air ingestion inevitably occurs for large amplitude motions (r/c > 0.4), thus exacerbating the difference between predictions and tests results. For reference, identical tests were conducted with a practical SFD supplied with lubricant (Pin = 0.4 bar) via three orifice feedholes, 120 deg apart at the film land midplane. A comparison of test results shows as expected that, for small amplitude (r/c ∼ 0.05) orbits, the flooded damper generates on average 30% more damping than the practical configuration as the latter's feedholes distort the generation of pressure. For large amplitude motions (r/c > 0.4), however, the flooded damper provides slightly lesser damping and inertia coefficients than the SFD with feedholes whose pressurized lubricant delivery alleviates air ingestion in the film land. The often invoked open ends SFD classical model is not accurate for the practical engineered design of an apparently simple mechanical element.

On the Force Coefficients of a Flooded, Open Ends Short Length Squeeze Film Damper: From Theory to Practice (and Back)

2017 ◽  
Author(s):  
Luis San Andrés ◽  
Sean Den ◽  
Sung-Hwa Jeung
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Forced Response ◽  
Short Length ◽  
Theory And Practice ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Force Coefficients ◽  
Deep Groove ◽  
Large Amplitude Motions

Gas turbine aircraft engine manufacturers push for simple squeeze film damper (SFD) designs, short in length, yet able to provide enough damping to ameliorate rotor vibrations. SFDs employ orifices to feed lubricant directly into the film land or into a deep groove. The holes, acting as pressure sources (or sinks), both disrupt the film land continuity and reduce the generation of squeeze film dynamic pressure. Overly simple predictive formulations disregard the feedholes and deliver damping (C) and inertia (M) force coefficients not in agreement with experimental findings. Presently, to bridge the gap between simple theory and practice, the paper presents measurements of the dynamic forced response of an idealized SFD that disposes of the feedholes altogether. The short-length SFD, whose diameter D = 125 mm, has one end submerged (flooded) within a lubricant bath and the other end exposed to ambient. ISO VG 2 lubricant flows by gravity through the film land of length L = 25.4 mm and clearance c = 0.122 mm. From dynamic load tests over excitation frequency range 10–250 Hz, experimental damping coefficients (CXX, CYY) from the flooded damper agree well with predictions from the classical open ends model with a full film for small amplitude whirl motions (r/c << 1), centered and off-centered. Air ingestion inevitably occurs for large amplitude motions (r/c > 0.4) thus exacerbating the difference between predictions and tests results. For reference, identical tests were conducted with a practical SFD supplied with lubricant (Pin = 0.4 bar) via three orifice feedholes, 120° apart at the film land mid plane. A comparison of test results shows as expected, that for small amplitude (r/c ∼ 0.05) orbits, the flooded damper generates on average 30% more damping than the practical configuration as the latter’s feedholes distort the generation of pressure. For large amplitude motions (r/c > 0.4), however, the flooded damper provides slightly lesser damping and inertia coefficients than the SFD with feedholes whose pressurized lubricant delivery alleviates air ingestion in the film land. The often invoked open ends SFD classical model is not accurate for the practical engineered design of an apparently simple mechanical element.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

scholarly journals Understanding (coupled) large amplitude motions: the interplay of microwave spectroscopy, spectral modeling, and quantum chemistry

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ha Vinh Lam Nguyen ◽  
Isabelle Kleiner
Keyword(s):  
Fourier Transform ◽  
Quantum Chemistry ◽  
Large Amplitude ◽  
Environmental Chemistry ◽  
Broad Band ◽  
Microwave Spectroscopy ◽  
Rotational Spectrum ◽  
Spectral Modeling ◽  
Rotational Spectra ◽  
Large Amplitude Motions

AbstractA large variety of molecules contain large amplitude motions (LAMs), inter alia internal rotation and inversion tunneling, resulting in tunneling splittings in their rotational spectrum. We will present the modern strategy to study LAMs using a combination of molecular jet Fourier transform microwave spectroscopy, spectral modeling, and quantum chemical calculations to characterize such systems by the analysis of their rotational spectra. This interplay is particularly successful in decoding complex spectra revealing LAMs and providing reference data for fundamental physics, astrochemistry, atmospheric/environmental chemistry and analytics, or fundamental researches in physical chemistry. Addressing experimental key aspects, a brief presentation on the two most popular types of state-of-the-art Fourier transform microwave spectrometer technology, i.e., pulsed supersonic jet expansion–based spectrometers employing narrow-band pulse or broad-band chirp excitation, will be given first. Secondly, the use of quantum chemistry as a supporting tool for rotational spectroscopy will be discussed with emphasis on conformational analysis. Several computer codes for fitting rotational spectra exhibiting fine structure arising from LAMs are discussed with their advantages and drawbacks. Furthermore, a number of examples will provide an overview on the wealth of information that can be drawn from the rotational spectra, leading to new insights into the molecular structure and dynamics. The focus will be on the interpretation of potential barriers and how LAMs can act as sensors within molecules to help us understand the molecular behavior in the laboratory and nature.

Solitary Filaments of Coupled Electromagnetic Wave and Finite Amplitude Ion Fluctuations

1976 ◽  
Vol 31 (12) ◽  
pp. 1517-1519 ◽  
Author(s):  
P. K. Shukla ◽  
M. Y. Yu ◽  
S. G. Tagare
Keyword(s):  
Electromagnetic Wave ◽  
Electromagnetic Radiation ◽  
Plasma Density ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Finite Amplitude ◽  
Nonlinear Coupling ◽  
Incoming Radiation

Abstract We show analytically that the nonlinear coupling of a large amplitude electromagnetic wave with finite amplitude ion fluctuations leads to filamentation. The latter consists of striations of the electromagnetic radiation trapped in depressions of the plasma density. The filamentation is found to be either standing or moving normal to the direction of the incoming radiation. Criteria for the existence of localized filaments are obtained. Small amplitude results are discussed.

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