Function Of Frequency Ratio Research Articles

Design of the Helmholtz resonators assembly for optimizing the broadband sound absorption of acoustic metasurface

The acoustic metasurface (AMS) can give a broadband sound absorption by a planar periodic array assembling small Helmholtz resonators tuned at different resonant frequencies, which work as unit cells which have equivalent small area to a fraction of the wavelength. The author has suggested that the broadband flat sound absorption is obtained by the AMS assembling the small Helmholtz resonators of more quantities at the lower resonant frequencies in the target frequency range. Their resonant frequencies are ordinary tuned by parameters of an airtight cavity with a multiple folded long neck reaching to the opening on the sound incident surface, which have a longer neck for a lower resonant frequency in this study. The formulation for the sound absorption coefficient of the AMS referring to the prior study shows the flat and nearly perfect sound absorption in one octave band with its center frequency of 125 Hz, 250 Hz and 500 Hz. Numerical case studies suggests that the area ratio of unit cells for the flat sound absorption of the AMS is formulated as a power function of frequency ratio to the center frequency and that its formulation will be identical for any center frequency.

On the Natural Keulegan–Carpenter Number for Subsea Industrial Modulus Installation

Abstract The behavior of subsea equipment has been widely studied by companies to minimize risks during subsea installation, which brings huge costs to the operation. The prediction of equipment motions typically is accomplished by utilizing either commercial software or recommended practices from Classification Societies to comply with the minimum requirements for launching operations. This article analyzes subsea installation in time and frequency domains using experimental, numerical, and analytical approaches. Experiments have been carried out at Instituto de Pesquisas Tecnológicas (IPT) to investigate the dependency of drag and added mass coefficients on Keulegan–Carpenter (KC) number and at Laboratory of Waves and Currents (LOC-COPPE/UFRJ) to study equipment and cable responses on the installation. A numerical model is made in orcaflex® for determining the transmissibility of displacement and force in function of frequency ratio, and the time series of manifold responses. Linearized models from DNV (DNV-GL, 2017, “Recommended Practice (DNVGL-RP-N103) – Modelling and Analysis of Marine Operations.”) and the so-called natural KC (proposed in the present article) are taken in the investigation and compared to previous methodologies. The natural KC approach arises as an innovative way of investigating subsea equipment as the literature only provides parametric analysis considering an arbitrary KC value (i.e., Pestana et al., 2021, “Subsea Manifold Installation: Operational Windows Estimation Based on Hydrodynamic Model Testing,” Ocean. Eng., 219, p. 108364). The analyses notice a good agreement among experiments, orcaflex® model, and natural KC model, whereas the curves found by the DNV method usually overpredict the response of subsea equipment, especially around resonance region.

Electrical matching of low power piezoelectric ultrasonic transducers for microelectronic bonding

The electrical matching of low power piezoelectric ultrasonic transducers for microelectronic bonding is studied in this paper. The admittance characteristics of the transducers are described through admittance circle diagrams and the electrical matching analysis for the transducers is presented. The frequency ratio function has been introduced and analyzed. The result shows that the frequency ratio function increases with the static capacitance, dynamic capacitance and dynamic resistance, and decreases with the dynamic inductance. When the static capacitance, dynamic capacitance, dynamic resistance and dynamic inductance are small, there are little differences between the resonance frequency and the series resonance frequency, and it is not necessary to operate electrical matching when the frequency ratio function is less than 0.001. A typical low power piezoelectric transducer used in microelectronic bonding has been adopted to verify the results of electrical matching analysis. The analysis and experimental results show that the transducer can work well at its vibration frequency without electrical matching.

A Generalized Dual-Band Wilkinson Power Divider With Parallel $L, C,$ and $R$ Components

A generalized model of a two-way dual-band Wilkinson power divider (WPD) with a parallel LC circuit at midpoints of two-segment transformers is proposed and compared with that of a conventional two-way dual-band WPD with a parallel LC circuit at the ends of two-segment transformers. The sum of power reflected at an output port and power transmitted to an isolation port from another isolation port in the proposed divider is smaller than that in the conventional divider. Therefore, wide bandwidths for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">22</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> , and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">32</sub> can be expected for proposed dividers. In the case of equal power division, frequency characteristics of return loss at output ports and isolation of the proposed divider are wider than those of the convention one. The resonant frequencies of LC circuits in the proposed divider and a conventional divider are equal; however, the inductance <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> used in the proposed divider is always smaller than that in the conventional divider. Design charts and calculated bandwidths as a function of frequency ratio from 1 to 7 are presented. In experiments, two symmetrical and two asymmetrical circuits were fabricated. The experimental results showed good agreement with theoretical results.

Generalized Two-Way Two-Section Dual-Band Wilkinson Power Divider With Two Absorption Resistors and Its Miniaturization

A generalized two-way two-section dual-band Wilkinson power divider with two absorption resistors and its size-reduced model are presented. Design equations for dual-band and arbitrary power division are derived from modified even- and odd-mode analysis. The frequency ratio of the lower and upper band frequencies must be lower than three. The channel bandwidth is presented as a function of frequency ratio with mathematical expressions. A coupled line section is introduced to reduce circuit size based on the assumptions of linear phase characteristics and equal phase velocities of the even and odd modes. Two two-way dual-band power dividers, one three-way planar dual-band power divider, and one size-reduced dual-band power divider were fabricated. Experimental results were in good agreement with predicted values.

Elastic moduli of dry and water-saturated carbonates — Effect of depositional texture, porosity, and permeability

Elastic moduli of water-saturated sedimentary rocks are in some cases different from moduli derived using Gassmann fluid substitution on data for rocks in the dry state. To address this discrepancy, we use a data set representing 115 carbonate samples from different depositional settings and a wide range of porosity and permeability. Depositional texture is reflected in the effect of water on elastic moduli and in the porosity-permeability relationship. Depositional texture is taken into account when porosity and permeability are combined in the effective specific surface of pores, which is related for a given pore fluid to the reference frequency as defined by Biot. For a given frequency of elastic waves, we obtain Biot’s frequency ratio between measured ultrasonic wave frequency and Biot reference frequency. For mostsamples with a frequency ratio above 10, elastic moduli in the water-saturated case are higher than predicted from elastic moduli in the dry case by Gassmann fluid substitution. This stiffening effect of water in some cases may be described by Biot’s high-frequency model, although in heterogeneous samples, a squirt mechanism is more probable. For data representing frequency ratios of 0.01 to 1, Gassmann fluid substitution works well. For samples with frequency ratios below 0.001, elastic moduli in the water-saturated case are lower than would be expected according to Gassmann’s equations or to Biot’s theory. This water-softening effect becomes stronger with decreasing frequency ratio. Water softening or stiffening of elastic moduli may be addressed by effective-medium modeling. In this study, we used the isoframe model to quantify water softening as a function of frequency ratio.

Three-dimensional imaging of single isolated cell nuclei using optical projection tomography

A method is presented for imaging single isolated cell nuclei in 3D, employing computed tomographic image reconstruction. The system uses a scanning objective lens to create an extended depth-of-field (DOF) image similar to a projection or shadowgram. A microfabricated inverted v-groove allows a microcapillary tube to be rotated with sub-micron precision, and refractive index matching within 0.02 both inside and outside the tube keeps optical distortion low. Cells or bare cell nuclei are injected into the tube and imaged in 250 angular increments from 0 to 180 degrees to collect 250 extended DOF images. After these images are further aligned, the filtered backprojection algorithm is applied to compute the 3D image. To estimate the cutoff spatial frequency in the projection image, a spatial frequency ratio function is calculated by comparing the extended depth-of-field image of a typical cell nucleus to the fixed focus image. To assess loss of resolution from fixed focus image to extended DOF image to 3D reconstructed image, the 10-90% rise distance is measured for a dyed microsphere. The resolution is found to be 0.9 microm for both extended DOF images and 3D reconstructed images. Surface and translucent volume renderings and cross-sectional slices of the 3D images are shown of a stained nucleus from fibroblast and cancer cell cultures with added color histogram mapping to highlight 3D chromatin structure.

Interpretation of standard distortion product otoacoustic emission measurements in light of the complete parametric response.

Emission characteristics (at 2f1-f2) are measured in Mongolian gerbil as a function of the independent variation of all four stimulus parameters, the frequencies (f1 and f2) and the intensities (L1 and L2) of the two stimulus tones. The main five-dimensional display chosen is a logarithmic grid of frequencies, where for each frequency pair there is a contour map of the emission amplitude as a function of the two stimulus levels. The feature which leads to the greatest complexity in the proper interpretation of emission responses is the widespread presence of "notches" in these contour maps. Notches are lines of relative minima in the emission amplitude, and are found at either: (1) constant L1, but only in regions where L1 > L2; or (2) at constant L2, only where L2 > or = L1. Notches are not found at any other orientations, and are associated with emission phase shifts of about 180 degrees as the notch line is traversed. These notch characteristics are explained by phase cancellation in a simple cochlear amplifier model in which there is a change, as a function of the stimulus level alone, of relevant characteristics of the cochlear response to a single tone. Only one mechanism of emission generation is required to explain the observed patterns, i.e., there is no need to invoke different "active" and "passive" mechanisms. Unless properly accounted for, the presence of notches adversely affects all of the standard emission measurements, i.e., all methods which cover a restricted parameter set such as DPgrams, input-output or "growth" functions, and frequency ratio functions. Conversely, because the notch location appears approximately invariant in the cochlea, notches potentially make it possible to use certain emission growth functions to estimate forward and reverse middle-ear transfer functions.