Effects Of Frequency Ratio Research Articles

Effect of frequency ratio and phase difference on the dynamic behavior of a cavitation bubble induced by dual-frequency ultrasound

The best cavitation can be obtained only with an appropriate frequency ratio and phase difference. To optimize dual-frequency ultrasonic cavitation and to analyze the influence of the frequency ratio and phase difference, a dynamic model of dual-frequency ultrasonic cavitation that considers energy and material exchange inside and outside the bubble was established. The results show that the negative-pressure amplitude of dual-frequency ultrasound is higher than that of single-frequency ultrasound for the same energy input. For a harmonic, the phase difference that results in a maximum of the negative-pressure amplitude of dual-frequency ultrasound is periodic for different frequency ratios. The phase difference that results in expansion–contraction oscillations of the bubble changes periodically as 1.5π → π → 0.5π → 0 → 1.5π for different frequency ratios. The maximum bubble radius and the maxima of the pressure, energy, and number of water vapor molecules inside the bubble all reduce spirally and the intensity of cavitation decreases with an increase of the frequency ratio. Compared with a harmonic, the maxima of the cavitation parameters are less affected by the phase difference for an ultraharmonic. Therefore, similar cavitation can be easier to obtain by employing an ultraharmonic, which is helpful in achieving stable cavitation.

2-DOF vortex-induced vibration of two tandem square cylinders with varying natural frequency ratios

In this paper, the two-degree-of-freedom (2-DOF) flow-induced vibrations of two square cylinders in tandem are studied numerically. Both cylinders have a mass ratio of 2 and are placed at a distance of 5D in the inline direction. A characteristics-based split (CBS) finite element algorithm is employed to solve the incompressible flow equations. The Reynolds number (Re) is kept constant at 100, whereas reduced velocity (Ur ) ranges from 3-13. Computations are made for three natural frequency ratios i.e. fr = fnx/fny = 1, 1.5 and 2. Results of the upstream cylinder are similar to that of an isolated square cylinder by other researches; however, the downstream cylinder shows different characteristics due to the effect of wake from the upstream cylinder. All the results for frequency ratios 1 and 1.5 overlapped to each other, indicating that the effect of frequency ratio is inconsiderable, however as fr increases to 2, the effect is observed in both the cylinders. It is to be noted that the effect is sensitive only in the lock-in region. For all fr, fully developed wake patterns at Ur corresponding to the peak vibration amplitudes are of C(2S) type while that for the other higher Ur , are of 2S type. Cylinder motion trajectories are also discussed; except Ur = 7 of fr= 2 at which phase between lift and the lateral displacement is 90°, all the trajectories are appeared to be figure “8” type.

Two degree of freedom flow-induced vibration of cylindrical structures in marine environments: frequency ratio effects

The flow-induced vibration of a cylindrical structure is a very common problem in marine environments such as undersea pipelines, offshore risers, and cables. In this study, the vortex-induced vibration (VIV) of an elastically mounted cylinder at a low Reynolds number is simulated by a transient coupled fluid–structure interaction numerical model. Considering VIV with low damping ratio, the response, hydrodynamic forces, and vortex shedding modes of the cylinder is systematically analyzed and summed up the universal rule under different frequency ratios. On the basis of the analysis, we find that the frequency ratio α is a very important parameter. It decides the locked-in, beat, and phase-switch phenomena of the cylinder, meanwhile, it also influence the vortex mode of the cylinder. The trajectory of the two degrees of freedom (2 DOF) case at different natural frequency ratios is discussed, with most trajectories having a “figure of 8” shape and a few having a “crescent” shape. A fast Fourier transformation technique is used to obtain the frequency characteristics of the vibration of the cylindrical structure. Using the 2 DOF cylinder model in place of the 1 DOF model presents several advantages in simulating the nonlinear characteristics of cylindrical structures, including the capacity to model the crosswise vibration generated by in-line vibration.

昆虫翼の受動的ピッチング運動に対する周波数比の影響

昆虫翼の受動的ピッチング運動に対する周波数比の影響

Simulation of a low-reynolds number flow around a cylinder following a figure-8-path

Abstract This numerical study investigates a circular cylinder placed in a uniform stream and moving along a slender figure-8-path, using a 2D computational method based on the finite difference method. The effects of in-line amplitude of oscillation and of frequency ratio are investigated. Computations for varying amplitude values were carried out at Re = 150, 200 and 250 for a clockwise orbit (in the upper loop). Time-mean and rms values of force coefficients yielded smooth curves and tended to increase with amplitude. The effect of frequency ratio was investigated at Re = 200, 250 and 300 in the lock-in domain for both clockwise (CW) and anticlockwise (ACW) orientation. Results differ substantially depending on the direction of orientation. Mechanical energy transfer was always positive in ACW direction, which may lead to vortex-induced vibration, and always negative for CW orientation. The time-mean of drag was much lower for CW over the whole frequency ratio domain investigated. For the CW orbit vortex switches were found at specific frequency ratios at Re = 250 and 300. Limit cycle curves for the CW orbit before and after a jump were symmetric, mirror images, and quite complex, while vorticity contours were close to symmetry. These results indicate the possibility of symmetry-breaking bifurcation.

Effects of frequency ratio on bridge aerodynamics determined by free-decay sectional model tests

A series of wind tunnel free-decay sectional model dynamic tests were conducted to examine the effects of torsional-to-vertical natural frequency ratio of 2DOF bridge dynamic systems on the aerodynamic and dynamic properties of bridge decks. The natural frequency ratios tested were around 2.2:1 and 1.2:1 respectively, with the fundamental vertical natural frequency of the system held constant for all the tests. Three 2.9 m long twin-deck bridge sectional models, with a zero, 16% (intermediate gap) and 35% (large gap) gap-to-width ratio, respectively, were tested to determine whether the effects of frequency ratio are dependent on bridge deck cross-section shapes. The results of wind tunnel tests suggest that for the model with a zero gap-width, a model to approximate a thin flat plate, the flutter derivatives, and consequently the aerodynamic forces, are relatively independent of the torsional-to-vertical frequency ratio for a relatively large range of reduced wind velocities, while for the models with an intermediate gap-width (around 16%) and a large gap-width (around 35%), some of the flutter derivatives, and therefore the aerodynamic forces, are evidently dependent on the frequency ratio for most of the tested reduced velocities. A comparison of the modal damping ratios also suggests that the torsional damping ratio is much more sensitive to the frequency ratio, especially for the two models with nonzero gap (16% and 35% gap-width). The test results clearly show that the effects of the frequency ratio on the flutter derivatives and the aerodynamic forces were dependent on the aerodynamic cross-section shape of the bridge deck.

Fermi resonance and its effect on the mean transition time and rate

Fermi resonance and its effect on the mean transition time and rate are studied. The necessary frequency ratio 1:2 for Fermi resonance to occur is explained by applying the deterministic averaging method to the two-dimensional conservative Pippard system, and a more frequent fluctuation of energy process due to Fermi resonance is shown by using the samples obtained from digital simulation of the stochastic Pippard system. In the case of weak coupling, the mean transition time of the reacting oscillator energy is evaluated for both nonresonance and Fermi resonance by using the standard (Stratonovich) stochastic averaging method. The theoretical results for the mean transition time in the case of Fermi resonance and nonresonance is then extended to the stochastic system with bistable potential, and the effects of frequency ratio and coupling coefficient on the mean reaction rate are analyzed. In the case of strong coupling, it is pointed out that the exciting oscillator and reacting oscillator move together like one oscillator and no Fermi resonance can occur. In this case, the mean transition rate of the system total energy is studied by using the stochastic averaging method for quasi-non-integrable Hamiltonian systems. All the theoretical results are confirmed through comparison with those from digital simulation, and the effect of Fermi resonance on the transition time and rate is discussed.

Effect of frequency ratio on infants' and adults' discrimination of simultaneous intervals.

Effect of frequency ratio on infants' and adults' discrimination of simultaneous intervals.

Effect of Frequency Ratio and Environmental Information on Spacial Coupling: A Study of Attention

Two experiments were conducted to investigate the interference between two drawing tasks. Fifteen participants drew lines (horizontal or vertical) and circles simultaneously on two digitizer boards to measure the interference (called spatial coupling) of line drawing on circle drawing. In Experiment 1, the drawing of circles and lines was timed by two beeps of different pitches in simple rhythms and polyrhythms. Results showed that spatial coupling was affected by the frequency ratio as indicated in the Farey Series. In Experiment 2, a dot in circular or linear motion was displayed while the dual task was carried out. Participants followed the timing shown in the display. The spatial coupling from line drawing to circle drawing was reduced when a dot in circular motion was displayed, and it was increased when the dot was moving in a straight line. The results we discuss are within the locus of interference and the limits of attention.