Observations on a spatial-resonance phenomenon

The phenomenon was observed during experiments in which a beaker containing water was vibrated in one of its bell modes (the inextensional flexural vibrations of the wall). For certain combinations of driving force and frequency, a standing water wave of large amplitude was generated whose peripheral wavenumber might be either zero (i.e. the wave was radially symmetric) or twice that of the bell mode. This relationship between the wavenumbers of the bell mode and water wave, and the fact that the driving frequency was many times that of the water wave, indicated that this was an instance of a general mechanism that has been studied theoretically by Mahony & Smith (1972). For a model situation, allowing for dissipative effects and nonlinear coupling between nearly resonant oscillations at greatly differing frequencies, they derived a relation-ship between the driving force and frequency representing conditions of neutrals tability (i.e. such that the rate of energy transfer from the high frequency to the low frequency oscillations is zero). The aim of the experimental observations reported here was to check this relationship and other predictions of their theory.

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Hysteresis and nonlinear detuning in a spatial-resonance phenomenon

Journal of Fluid Mechanics ◽

10.1017/s0022112073000777 ◽

1973 ◽

Vol 61 (2) ◽

pp. 401-413

Author(s):

Ian Huntley ◽

Ronald Smith

Keyword(s):

Free Surface ◽

Experimental Work ◽

Alternative Model ◽

Pressure Field ◽

Low Frequency ◽

Theoretical Description ◽

Resonance Phenomenon ◽

Theoretical Problem ◽

Frequency Wave ◽

Spatial Resonance

The experimental work of Franklin, Price & Williams (1973) shows that for moderately large driving amplitudes there are features of spatial resonance that are not predicted by the model representation of Mahony & Smith (1972). We here derive an alternative model, which remains valid for moderately large driving amplitudes, and we are able to obtain a theoretical description of both hysteresis and nonlinear detuning of the low frequency wave response. An experiment in which surface waves were generated by a sinusoidal pressure field at the free surface (and which corresponds almost exactly to the theoretical problem) was conducted in order to test these predictions.

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Cardiopulmonary resonance at 0.1 Hz demonstrated by averaged Lomb-Scargle periodogram

Open Physics ◽

10.2478/s11534-009-0101-1 ◽

2010 ◽

Vol 8 (3) ◽

Cited By ~ 5

Author(s):

Jarosław Piskorski ◽

Przemysław Guzik ◽

Tomasz Krauze ◽

Sebastian Żurek

Keyword(s):

Low Frequency ◽

Resonance Curve ◽

Resonance Phenomenon ◽

Oscillatory Activity ◽

Total Power ◽

Pressure Waveform ◽

Low Frequency Oscillations ◽

Forced Breathing ◽

Cardiopulmonary System ◽

Dominant Peak

AbstractWe demonstrate the resonant-like behaviour of the cardiopulmonary system in healthy people occurring at the natural low frequency oscillations of 0.1 Hz, which are often visible in the continuous pressure waveform. These oscillations represent the spontaneous oscillatory activity of the vasomotor centre and are sometimes called the Mayer waves. These 10-second rhythms probably couple with forced breathing at the same frequency and cause the observed cardiopulmonary resonance phenomenon. We develop a new method to study this phenomenon, namely the averaged Lomb-Scargle periodogram method, which is shown to be very effective in enhancing common frequencies in a group of different time series and suppressing those which vary between datasets. Using this method we show that in cardiopulmonary resonance the cardiopulmonary system behaves in a very similar way to a simple mechanical or electrical oscillator, i.e. becomes highly regular and its averaged spectrum exhibits a clear dominant peak and harmonics. If the forcing frequency is higher than 0.1 Hz, the total power and the share of power in the dominant peak and harmonics are lower and the prominence of the dominant peak and its harmonics greatly diminishes. It is shown that the power contributions from different forcing frequencies follow the resonance curve.

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Investigation of the process of peeling walnuts between two parallel plates

Vibrations in engineering and technology ◽

10.37128/2306-8744-2019-3-14 ◽

2019 ◽

pp. 110-117

Author(s):

Yurii Polievoda

Keyword(s):

Driving Force ◽

Low Frequency ◽

Parallel Plates ◽

Technological Parameters ◽

Low Frequency Oscillations ◽

Crushing Force ◽

Perpendicular Crack ◽

Vertical Positioning ◽

Brittle Destruction

The article provides a detailed overview of the process of splitting the kernel of a walnut. Examples of many ways to split the shell are given, all of their disadvantages and advantages are listed. The mechanical method of peeling nuts using low-frequency oscillations has been theoretically investigated and substantiated. The kinematics of the process of crushing nuts between two parallel plates has been extensively analyzed. Graphical correlations were obtained between the size of the nut shell and the dynamics of the driving force of the nut moisture. It is revealed that the process of destruction of the shell of a walnut consists of four stages, corresponding to the laws of brittle destruction. Presents: - dependence of the maximum force of crushing of a shell of a nut at 5% humidity; - the dependence of the maximum crushing force of nuts at different shell thickness for the case of horizontal positioning of the nut between two plates with perpendicular force on the surface of the joint halves of the nut; - the dependence of the maximum crushing force according to the humidity of the nuts at different shell thicknesses for the case of vertical positioning of the nut between two parallel plates with a vertical driving force; - the dependence of the maximum crushing force with the moisture of the nuts at different shell thicknesses for the case of horizontal positioning of the nut between two parallel plates with a force action along the slit. The energy of splitting (crushing) of nuts at their location in different positions between two parallel plates is also determined. Where it has been proved that the energy consumed in the process of crushing increases with the thickness of the shell of a walnut. At the same time, it is proved that energy consumption depends on the location of the nut in the process of crushing. Graph analyzes were performed to show that maximum crushing energy is recorded in the case of a horizontal arrangement of a nut with a perpendicular crack action. In this study, a large amount of information was obtained regarding the splitting of the walnut, depending on the structural and mechanical characteristics of the products, which in the process of processing are important for the determination of certain rational technological parameters.

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