Determination of the natural oscillating frequencies of shells of complex shape with free edges
Resonant frequencies of circular cylindrical, elliptical, turbine shaped, and conical shells
Salnikov, G. M.↗
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On the Spectrum of Natural Oscillations of Two-Dimensional Laminar Flows
In the investigation of stability of a two-dimensional laminar flow with respect to small disturbances, a disturbance of the stream function moving downstream (in the direction of the x-axis) by the "partial wave formula" is described.
Grohne, D.↗
Forced Oscillation Grid Vulnerability Analysis and Mitigation Using Inverter-Based Resources: Texas Grid Case Study
Forced oscillation events have become a challenging problem with the increasing penetration of renewable and other inverter-based resources (IBRs), especially when the forced oscillation frequency coincides with the dominant natural oscillation frequency. A severe forced oscillation event can deteriorate power system dynamic stability, damage equipment, and limit power transfer capability. This paper proposes a two-dimension scanning forced oscillation grid vulnerability analysis method to identify areas/zones in the system that are critical to forced oscillation. These critical areas/zones can be further considered as effective actuator locations for the deployment of forced oscillation damping controllers. Additionally, active power modulation control through IBRs is also proposed to reduce the forced oscillation impact on the entire grid. The proposed methods are demonstrated through a case study on a synthetic Texas power system model. The simulation results demonstrate that the critical areas/zones of forced oscillation are related to the areas that highly participate in the natural oscillations and the proposed oscillation damping controller through IBRs can effectively reduce the forced oscillation impact in the entire system.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Skylab fluid mechanics demostration - A study of water droplet oscillations in space
In the Skylab experiment a drop of water was caused to oscillate at its natural oscillation frequency. The drop was observed until its oscillation began to decay due to its internal damping. A determination of the change in amplitude with time made it possible to verify the applicability of a theoretical model. The fundamental concept of the model is that fluid surfaces tend to an equilibrium shape produced by the balance of the forces of fluid pressure and surface tension. The theoretical model is based on the assumption that the wave amplitude is small compared with the wavelength.
Vaughan, O. H.↗
Pulsation phenomena observed in long-duration vlf whistler-mode signals.
Whistler-mode signals from station NAA (14.7 and 17.8 kHz), Cutler, Maine, show periodic fluctuations (?pulsations') in amplitude and bandwidth. The data were recorded at Eights station, Antarctica, during unmodulated (?key-down') transmissions from NAA lasting up to 2 min. In three of four instances, the pulsations consist of a series of moderate enhancements of the amplitude and bandwidth of the signal, each pulsation lasting about 50 msec. The fourth instance, however, was unusual in that the key-down signal exhibited remarkably regular and intense amplitude variations. In all four occurrences, the period of the pulsation was in the range from 0.3 to 0.6 sec. In three occurrences, this period was roughly the same as the one-hop whistler-mode delay along the field-line path; however, no demonstrable mechanism to explain this association could be found. An explanation of pulsations in terms of multipath fading effects could not be supported by the data. More likely explanations include intrinsic oscillation in the emission generation mechanism, natural oscillation in the energetic-particle population, or modulation of the VLF growth rate by Pc 1 micropulsations in the region of wave growth.
Bell, T. F.↗
Geophysical searches for three-neutrino oscillations
The possibilities of using cosmic ray induced neutrinos to detect oscillations in deep underground experiments were considered. The matter effects are nonnegligible in the two neutrino case, they reduce a mixing angle of 45 deg to 7.5 deg for 1 GeV neutrinos of squared mass difference 10/4 eV59 going through the Earth making the oscillation totally unobservable. They produce a natural oscillation length of about 6000 km in the case of massless neutrinos. Adding a third neutrino flavor considerably modifies the oscillation pattern and suggests that scales down to 5 x 10/5 eV could be observed even when we take into account matter effects and the electron contribution to the incoming flux. The effect of matter on the probability curves for different cases are shown by varying the masses and the mixing matrix. The ratio upward upsilon + upsilon/downward upsilon + upsilon as a function of the zenith angle at Cleveland, neglecting angular smearing and energy threshold effects is predicted.
Cudell, J. R.↗
Apparatus and method for gas turbine active combustion control system
An Active Combustion Control System and method provides for monitoring combustor pressure and modulating fuel to a gas turbine combustor to prevent combustion dynamics and/or flame extinguishments. The system includes an actuator, wherein the actuator periodically injects pulsed fuel into the combustor. The apparatus also includes a sensor connected to the combustion chamber down stream from an inlet, where the sensor generates a signal detecting the pressure oscillations in the combustor. The apparatus controls the actuator in response to the sensor. The apparatus prompts the actuator to periodically inject pulsed fuel into the combustor at a predetermined sympathetic frequency and magnitude, thereby controlling the amplitude of the pressure oscillations in the combustor by modulating the natural oscillations.
Umeh, Chukwueloka↗
Approximation of the Frequency-Amplitude Curve Using the Homotopy Analysis Method
The Frequency-Amplitude (F-A) curve on power system oscillation under a large disturbance characterizes how a natural oscillation mode transitions to nonlinear oscillations with growing amplitudes and decaying frequencies. The existing formulation of the F-A curve is derived by solving elliptical integrals on oscillation of a single-machine-infinite-bus equivalent about the targeted oscillation mode. The formula is in a form of infinite series and needs to sum a large number of terms for satisfactory accuracy. This paper introduces an explicit, approximate expression obtained from the Homotopy Analysis Method on the F-A curve. The proposed F-A curve expression is derived from an SMIB system and verified on the IEEE 3-machine 9-bus system to show how the oscillation frequency of a dominant mode varies with oscillation amplitude under large disturbances.
frequency-amplitude (F-A) curve↗
Nonlinear effects on the natural modes of oscillation of a finite length inviscid fluid column, supplement 2
The aspects of nonlinear behavior of a finite length liquid column is investigated with an emphasis on bridge dynamics. The primary objectives are to determine the nonlinear corrections to the interface shape of a naturally oscillating finite length liquid column and to determine the nonlinear corrections to the oscillation frequencies for various modes of oscillation. Application of the Lindstedt-Poincare expansion in conjunction with the domain perturbation techniques results in an hierarchical system of equations.
Lyell, M. J.↗
Nature's Autonomous Oscillators
Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.
Mayr, H. G.↗
Modeling Wavelength Dependent Mid-infrared (5.5–25 μm) Optical Constants of Silicate Glasses: A Genetic Algorithm Approach
Wavelength-dependent mid-infrared (400–1,800 cm -1 ; 5.56–25 μm) optical constants (real and imaginary indices of refraction; n and k) are determined using reflectance spectra at a spectral sampling of 4 cm -1 for several silicate glasses of varying SiO 2 wt% which include (a) basaltic volcanic glass from Kilauea, Hawaii, (b) synthetic andesite, (c) two synthetic dacites, (d) obsidian volcanic glass from Mount Lassen, California, (e) synthetic rhyodacite, and (f) rhyolitic volcanic glass from Mexico. Because glasses are optically isotropic, no specific orientation was required for spectral measurements, and polished glass samples were measured at random orientations using micro-FTIR spectrometer. Lorentz-Lorenz dispersion theory and Fresnel reflectance model for high symmetry materials were used to model the optical constants by optimizing oscillator parameters in modeled spectra to match laboratory spectra. A genetic algorithm (GA) approach automatically finds the natural oscillators and their parameters for each spectrum, and then uses these parameters in a non-linear least squares optimization routine. The study compared spectral parameters such as Christiansen feature, reststrahlen bands (RBs), and the peaks centered around 860–1,100 (peak 1) and 400–480 cm -1 (peak 2) of n and k to their respective SiO 2 wt% of the glasses. CF, RBs, peak 1 of n and k, and peak 2 of n shift to higher wavenumbers with increased SiO 2 wt%, whereas peak 2 of k shifts to lower wavenumbers with increased SiO 2 wt%. Derived optical constants of these glasses will improve quantitative abundance mapping of volcanic materials on the surfaces of silicate targets in the Solar System.
58 GEOSCIENCES↗
The source of 5 minute period photospheric umbral oscillations
We observed the oscillations in the umbrae of two sunspots, using the MCCD imaging spectrograph at the Mees Solar Observatory on Haleakala, Maui. We perform four spatial analyses of the umbral velocity and find that (1) there is more power traveling toward the center of the umbrae than leaving the center of the umbrae (this provides a direct measure of the absorption of p-modes by the sunspot umbrae); (2) the umbral oscillations display power in the same spatial and temporal frequency band as the quiet-sun oscillations; (3) Fourier-Bessel analysis of one umbra shows no obvious resonant frequencies which might represent natural oscillation modes; and (4) the centers of the umbrae have less rms velocity at high spatial wavenumber than the edges of the umbrae. We conclude: (1) the photospheric umbral oscillations are driven by a source external to the sunspot, the global p-mode oscillations; (2) there are no resonant frequencies in the oscillations; and (3) the absorption of acoustic waves occurs inside the umbrae.
Penn, M. J.↗
Influence of configuration effects on multiple burst simulation testing
During the initial phase of a lightning strike attachment on an aircraft, fast current pulses (rise time approximately 100 ns, I(sub max) approximately few kA) were measured, which can create equipment upsets or disturbances. This threat, made of repetitive pulses and usually called 'multiple bursts', can be reproduced at the equipment interfaces assuming that the transfer function of the structure was determined. The normalized waveform H (10 kA - 100 ns rise time) is the reference for one of these pulses. The importance of the coaxial return path termination for the injection of the wave H is emphasized. According to the constitutive materials of the test bed, and the adaptation of the line, the natural oscillations of the structure and the internal coupling mechanisms can be modified. As a conclusion, various test configurations in relation with the nature of the test bed and the characteristics of the generator are detailed, for a more accurate ground simulation of the attachment phase.
Emanuely, J. L.↗
Mathematical Modeling of an Oscillating Droplet
Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.
Berry, S.↗
Surface Oscillations of An Electromagnetically Levitated Droplet
Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is usually performed by electromagnetic levitation. The natural oscillation frequency a f the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity values to experimentally-obtained results.
Berry, S.↗
Interaction of an oscillating vortex with a turbulent boundary layer
An oscillating vortex embedded within a turbulent boundary layer was generated experimentally by forcing a periodic lateral translation of a half-delta wing vortex generator. The objective of the experiment was to investigate the possibility that a natural oscillation, or meander, might be responsible for flattened vortex cores observed in previous work, which could also have contaminated previous turbulence measurements. The effect of this forced oscillation was characterized by comparison of measurements of the mean velocities and Reynolds stresses at two streamwise stations, for cases with and without forcing. The Reynolds stresses were affected significantly by the forced oscillation, mainly through contributions from the individual production terms, provided that the vortex was not too diffuse.
Westphal, R. V.↗
Examining AGN UV/Optical Variability beyond the Simple Damped Random Walk
We present damped harmonic oscillator (DHO) light-curve modeling for a sample of 12,714 spectroscopically confirmed quasars in the Sloan Digital Sky Survey Stripe 82 region. DHO is a second-order continuous-time autoregressive moving-average process, which can be fully described using four independent parameters: a natural oscillation frequency (ω 0 ), a damping ratio (ξ), a characteristic perturbation timescale (τ perturb ), and an amplitude for the perturbing white noise (σ ϵ ). The asymptotic variability amplitude of a DHO process is quantified by σ DHO —a function of ω 0 , ξ, τ perturb , and σ ϵ . We find that both τ perturb and σ ϵ follow different dependencies with rest-frame wavelength (λ RF ) on either side of 2500 Å, whereas σ DHO follows a single power-law relation with λ RF . After correcting for wavelength dependence, σ DHO exhibits anticorrelations with both the Eddington ratio and the black hole mass, while τ perturb —with a typical value of days in the rest frame—shows an anticorrelation with the bolometric luminosity. Modeling active galactic nuclei (AGN) variability as a DHO offers more insight into the workings of accretion disks close to the supermassive black holes at the center of AGN. The newly discovered short-term variability (characterized by τ perturb and σ ϵ ) and its correlation with bolometric luminosity pave the way for new algorithms that will derive fundamental properties (e.g., Eddington ratio) of AGN using photometric data alone.
79 ASTRONOMY AND ASTROPHYSICS↗
Identification of dynamic characteristics of flexible rotors as dynamic inverse problem
The problem of dynamic and balancing of flexible rotors were considered, which were set and solved as the problem of the identification of flexible rotor systems, which is the same as the inverse problem of the oscillation theory dealing with the task of the identifying the outside influences and system parameters on the basis of the known laws of motion. This approach to the problem allows the disclosure the picture of disbalances throughout the rotor-under-test (which traditional methods of flexible rotor balancing, based on natural oscillations, could not provide), and identify dynamic characteristics of the system, which correspond to a selected mathematical model. Eventually, various methods of balancing were developed depending on the special features of the machines as to their design, technology, and operation specifications. Also, theoretical and practical methods are given for the flexible rotor balancing at far from critical rotation frequencies, which does not necessarily require the knowledge forms of oscillation, dissipation, and elasticity and inertia characteristics, and to use testing masses.
Roisman, W. P.↗