Identification of mode couplings in nonlinear vibrations of the steelpan

The authors are grateful to Bertrand David (Telecom-ParisTech) for computing the code allowing the STFT filtering procedure used in Section 5.1. The filter has been designed in the framework of the PAFI project (Plateforme d’Aide la facture Instrumentale, www.pafi.fr) which is also thanked.The vibrations and sounds produced by two notes of a double second steelpan are investigated, the main objective being to quantify the nonlinear energy exchanges occurring between vibration modes that are responsible of the peculiar sound of the instrument. A modal analysis first reveals the particular tuning of the modes and the systematic occurence of degenerate modes, from the second one, this feature being a consequence of the tuning and the mode localization. Forced vibrations experiments are then performed to follow precisely the energy exchange between harmonics of the vibration and thus quantify properly the mode couplings. In particular, it is found that energy exchanges are numerous, resulting in complicated frequency response curves even for very small levels of vibration amplitude. Simple models displaying 1:2:2 and 1:2:4 internal resonance are then fitted to the measurements, allowing to identify the values of the nonlinear quadratic coupling coefficients resulting from the geometric nonlinearity. The identified 1:2:4 model is finally used to recover the time domain variations of an impacted note in normal playing condition, resulting in an excellent agreement for the temporal behaviour of the first four harmonics

Multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures with geometric nonlinearities

A general low-order fluid-structure interaction model capable of evaluating the multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures is presented. Cross-flow motions due to unsteady lift forces of inclined sagged cables and tensioned beams in uniform currents are investigated. In contrast to a linear equation governing the transverse motion of straight beams or cables typically considered in the literature, coupled horizontal/vertical (axial/transverse) displacements and geometric nonlinearities of curved cable (straight beam) are accounted for. A distributed nonlinear wake oscillator is considered in the approximation of space-time varying hydrodynamics. This semi-empirical fluid force model in general depends on the mass-damping parameter and has further been modified to capture both the effects of varying initial curvatures of the inclined cylinder and the Reynolds number. Numerical simulations are performed in the case of varying flow velocities and parametric results highlight several meaningful aspects of vortex-induced vibrations of long flexible cylinders. These comprise multi-mode lock-in, sharing, switching and interaction features in the space and time domains, the estimated maximum modal and total amplitudes, the resonant nonlinear modes of flexible cylinders and their space-time modifications, and the influence of fluid/structure parameters. A shortcoming of single-mode or linear structural model is underlined. Some quantitative and qualitative comparisons of numerical/experimental results are discussed to demonstrate the validity and required improvement of the proposed modelling and analysis predictions

Infragravity energy in the surf zone

Field measurements of onshore and longshore velocities in the surf zone have been obtained on Martinique Beach, Nova Scotia, for the purpose of investigating the dynamics of the infragravity band (0.003- 0.03 Hz) of the spectra. A total of35 data runs were obtained during a 1-week period. Of particular interest the response of the infragravity energy to the changing incident waves, which increased considerably in size during the latter half of the week due to an approaching hurricane. It is shown theoretically, using equilibrium arguments that the infragravity amplitude should vary approximately linearly with incident wave amplitude. This is supported from the field data if significant wave height is used as a measure of incident amplitude. The incident band of spectra observed by instruments in the surf zone is limited by breaking. Thus the infragravity band appears to dominate these spectra during storms. The analysis is carried out in terms of a spectral transformation, the spectrum which would be observed at an offshore instrument if the shoreline amplitude spectrum were white with unit spectral energy density. For onshore velocity the formation predicts the observed spectral structure in the infragravity band, showing that the structure did not represent any true frequency selection. The match of theory and data also implies that the onshore motions are free waves, forced near resonance. The longshore spectra are red and show no structure which would be associated with free waves. This is consistent with the theoretical prediction that many edge wave nodes, including high modes, would be forced given the broad directional spread of the storm waves. It is noted that further field experiments would be simpler on the Pacific coast where the typical, narrow-band, incident swell should force only a few, low, edge wave modes, a more accommodating situation to observe and analyze.Copyrighted by American Geophysical Union

Two-degree-of-freedom VIV of circular cylinder with variable natural frequency ratio : experimental and numerical investigations

Slender offshore structures possess multiple natural frequencies in different directions which can lead to different resonance conditions when undergoing vortex-induced vibration (VIV). This paper presents an experimental and numerical investigation of a two-degree-of-freedom VIV of a flexibly mounted circular cylinder with variable in-line-to-cross-flow natural frequency ratio. A mechanical spring-cylinder system, achieving a low equivalent mass ratio in both in-line and cross-flow directions, is tested in a water towing tank and subject to a uniform steady flow in a sub-critical Reynolds number range of about 2×103–5×104. A generalized numerical prediction model is based on the calibrated Duffing-van der Pol (structure-wake) oscillators which can capture the structural geometrical coupling and fluid-structure interaction effects through system cubic and quadratic nonlinearities. Experimental results for six measurement datasets are compared with numerical results in terms of response amplitudes, lock-in ranges, oscillation frequencies, time-varying trajectories and phase differences of cross-flow/in-line motions. Some good qualitative agreements are found which encourage the use of the implemented numerical model subject to calibration and the sensitivity analysis of empirical coefficients. Moreover, comparisons of the newly-obtained and published experimental results are carried out and discussed, highlighting a good correspondence in both amplitude and frequency responses. Various patterns of figure-of-eight orbital motions associated with dual two-to-one resonances are observed experimentally as well as numerically: the forms of trajectories are noticed to depend on the system mass ratio, damping ratio, reduced velocity parameter and natural frequency ratio of the two-dimensional oscillating cylinder

The middeck 0-gravity dynamics experiment

The Middeck 0-Gravity Dynamics Experiment (MODE), flown onboard the Shuttle STS-48 Mission, consists of three major elements: the Experiment Support Module, a dynamics test bed providing computer experiment control, analog signal conditioning, power conditioning, an operator interface consisting of a keypad and display, experiment electrical and thermal control, and archival data storage: the Fluid Test Article assembly, used to investigate the dynamics of fluid-structure interaction in 0-gravity; and the Structural Test Article for investigating the open-loop dynamics of structures in 0-gravity. Deployable, erectable, and rotary modules were assembled to form three one- and two-dimensional structures, in which variations in bracing wire and rotary joint preload could be introduced. Change in linear modal parameters as well as the change in nonlinear nature of the response is examined. Trends in modal parameters are presented as a function of force amplitude, joint preload, and ambient gravity. An experimental study of the lateral slosh behavior of contained fluids is also presented. A comparison of the measured earth and space results identifies and highlights the effects of gravity on the linear and nonlinear slosh behavior of these fluids

First total extraction of global decadal Alfven vibration of the Sun (resonance and antiresonance) exposes solar-type stars as revolving-field multipart magnetoalternators instead of elusive dynamos

The Sun reveals itself in the 385.8-2.439-nHz band of polar ({\phi}Sun>|70{\deg}|) fast (>700 km s^-1) solar wind's decade-scale dynamics as a globally completely vibrating, revolving-field magnetoalternator rather than a proverbial engine. Thus North-South separation of 1994-2008 Ulysses <10 nT wind polar samplings spanning ~1.6 10^7-2.5 10^9-erg base energies reveals Gauss-Vanicek spectral signatures of an entirely >99%-significant Sun-borne global sharp Alfven resonance (AR), Pi=PS/i, imprinted into the winds to the order n=100+ and co-triggered by the PS=~11-yr Schwabe global mode northside, its ~10-yr degeneration equatorially, and ~9-yr degeneration southside. The Sun is a typical ~3-dB-attenuated ring-system of differentially rotating and contrarily (out-of-phase-) vibrating conveyor belts and layers, with a continuous spectrum and resolution (<81.3 nHz (S), <55.6 nHz (N)) in lowermost frequencies (<2 {\mu}Hz in most modes). AR is accompanied by an also sharp >99%-significant symmetrical antiresonance P(-) whose both N/S tailing harmonics P(-17) are the well-known PR=~154-day (PS/3/3/3 to +-0.1%) Rieger period dominating planetary dynamics and space weather. Unlike a resonating motor restrained from separating its casing, the freely resonating Sun exhausts the wind in an axial shake-off beyond L1 at highly coherent discrete wave modes generated in the Sun. The result was verified against remote data and the experiment, thus instantly replacing dynamo with magnetoalternator and advancing Standard Stellar Models of billions of trillions of solar-type stars. Shannon's theory-based Gauss-Vanicek spectral analysis revolutionizes astrophysics and space sciences by rigorously simulating fleet formations from a single spacecraft and physics by directly computing nonlinear global dynamics (rendering spherical approximation obsolete).Comment: 30 pages, 7 figures, 3 tables; abstract and highlights updated, results clarified, conclusions expanded, references expanded and updated, typos correcte