Mode Frequencies Research Articles

Structural and electronic properties of AgNPs adsorbed by glucose molecules determined using DFT theory

In order to build and design stable molecular structures of α‐D‐glucose molecules after adding to a cluster of silver atoms, an optimization process was precisely carried out for α‐D glucose/Ag3 molecule at low energy. The correlation between glucose molecule and silver atoms is evaluated by investigating configurational and electronic features of the named molecules by adopting the Density functional theory DFT using the hybrid B3LYP functional and 6–311+G∗ as a basis set for C, O, and H atoms, while LANL2DZ set for silver (Ag) atoms. Frequencies of vibrational modes are essential analyses that have been instrumental in understanding the IR spectra of studied molecules. These analyses enable the detection of the active groups along the spectrum chart including C–O–C, C=O, C–O, O–H, C–C and C–H peaks confirming the previous experimental findings. Another important finding is the energy gap (Eg) obtained by the difference between the higher occupied molecular orbital (HOMO) and lower unoccupied molecular orbital (LUMO). Remarkably, Eg was found to increase from 3.440 to 4.358 eV in a configuration consisting of two glucose molecules with one Ag atom (2α‐D glucose/Ag-C12H24O12Ag) to another with one glucose molecule with three Ag atoms (α‐D glucose/Ag3-C6H12O6Ag3) configuration. Additionally, the potential of the molecular electrostatic isosurface (MEP) in 3D diagram for two configurations is clarified by the colour-coded bar with the distributions of charge density distributions to examine the nucleophilicity and electrophilicity behaviour.

Compressible ocean waves generated by sudden seabed rise near a step-type topography

A typical tsunami generation occurs through submarine earthquakes leading to large volume displacement. The corresponding mathematical problem involves modeling surface water waves generated by an arbitrary temporal motion of the ocean floor. The propagation of tsunami wave and the subsequent scattering from a sudden drop in bathymetry away from the ground motion is studied following linearized water wave theory and a weakly compressible ocean, including static oceanic background compression. The Fourier transformation and eigenfunction expansion techniques are employed to find the surface displacement and pressure profiles by leveraging appropriate matching conditions between regions of different depths. A novel energy balance relationship is derived by considering both the pure-gravity and acoustic-gravity modes. The model is validated in the limit that the depth difference approaches zero, showing a vanishing reflection contribution from the depth change. An efficient numerical code is developed that accurately captures the contribution of the cutoff frequencies of acoustic-gravity modes. Apart from the time-domain propagation of tsunami waves away from the origin, standing wave formations are observed within the shallow region, supported by significantly large pressure fluctuations in time. These standing waves or, equivalently, the pressure fluctuations sustain longer for larger ocean depth. The increase in tsunami speed in the deeper region is readily visible in the time-domain simulations. A three-dimensional axisymmetric solution is also developed, and results show a more gradual sloping tsunami wavefront compared to the equivalent two-dimensional solution for shallower depths. Animation movies corresponding to the two- and three-dimensional surface profiles are provided for better visualization.

High efficiency AOT-controlled boost converter with pseudo-constant switching frequency

An on-time generator for boost converters is proposed to achieve an adaptive on-time (AOT) control with pseudo-constant frequency in continuous conduction mode (CCM). Since the first-order parasitic effect of the components and devices is considered in the design of the on-time generator, the switching frequency (fsw) variation of the boost converter in CCM can be better suppressed with the load current (ILOAD), input voltage (VIN) and output voltage (VOUT) changes, which can effectively solve the EMI noise problem. In addition, the idea of capacitor pre-charging is applied to simplifying circuit complexity. Meanwhile, an on-demand modulation strategy is applied to improve the conversion efficiency. Simulation results show that the boost converter based on the proposed on-time generator can realize the fsw variation of 0.4 % in case of 200 mA ILOAD change. Moreover, the VIN may range from 0.8 to 1.5 V, the VOUT is set to 1.8 V, and the peak efficiency of the simulation is 96.9 %.

Scalar Quasi-Normal Modes of a loop quantum black hole

We compute the Quasi-Normal Mode (QNM) frequencies for scalar perturbations for modified Schwarzschild black holes in Loop Quantum Gravity. We study the singularity-free polymerized metric characterized by two parameters encoding loop quantum effects: the minimal area gap a 0 and the polymeric deformation parameter P. We perform numerical computations using Leaver's continued fraction method and compare our results to other semi-analytical methods and existing literature. We study the effects on the QNM spectrum of variation of both deformation parameters and systematically compare to the standard Schwarzschild case. In particular we find that the scalar fundamental mode is modified from the third decimal for values of P in accordance with the most recent astrophysical constraints. We also show that qualitative differences arise for highly damped modes: on the one hand, a new crossing of the imaginary axis occurs for high values of a 0 and, on the other hand, increasing P produces a positive shift of the real part and an increase of the spacing in imaginary part between modes.

Opracowanie konstrukcji świdra wiertniczego do zwiercania skał o różnych właściwościach mechanicznych

This paper presents a description of a bit design with a combined cutter layout, aimed at increasing the efficiency of breaking rocks with different mechanical properties. The results from industrial testing of the manufactured bits are analyzed, revealing the need to improve their hydraulic flushing system. Computer modeling was conducted using the Flow Simulation CAD/CAM package of the Solid Works system, where various models of the design options for the bit, the borehole bottom, and a segment of the drill string were created. For each variant, numerical calculations of the fluid motion were carried out using the finite element method. Based on the simulation results, optimal angles of inclination for the jet nozzles relative to the bit axis and their distance from this axis were determined. Key factors influencing the stability of the bit cutters, which destroy the rock by cutting with axial vibrations, were identified, and analytical dependencies for their predictive stability were derived. The wear rate of the bit cutters was determined by instantaneous values of such physical parameters as: the degree of wear, rock cutting speed, temperature, axial loading force on the cutter, and the friction coefficient at the contact between the cutter and rock. Temperature is especially impactful, reaching levels exceeding 1000°C in the cutting zone; it is often regarded as the primary factor influencing bit cutter stability. To maximize the efficiency of rock-breaking in the process of drilling wells, it is necessary to set the following vibration parameters: frequency, amplitude, and vibration mode, which can be determined from the results of mathematical modeling.

Structural and dynamical properties of two dimensional disordered metal chalcogenides AB (A [formula omitted] Zn, Cd; B [formula omitted] S, Se): A classical molecular dynamic study

In recent years, the synthesis of two-dimensional (2D) materials, particularly the crystalline and disordered phases of 2D transition metal chalcogenides (TMCs), has gained considerable attention due to their wider electronic band gaps. This distinctive feature is pivotal in shaping their potential applications in solar cells, sensors, field-effect transistors (FETs), and photocatalysis for water decomposition. In the present study, we report molecular dynamics simulation of 2d disordered configuration of ZnX and CdX (X: S, Se) compounds using the Stillinger–Weber potential. We have explored their structural features by calculating their radial distribution functions and ring statistics. These systems are thermodynamically stable. The disordered network with numerous voids in these compounds play a pivotal role in lowering their melting temperature compared to their 2D crystalline counterparts, which falls within the range of 600 K to 700 K. The phonon density of states for all these systems shows a higher number of lower frequency (acoustic) modes than optical modes, which is understandably due to the presence of open regions and 2-fold sites in such systems.

Separate prediction of underwater noise from drain pipes base on Vibration-acoustic coupling method

Abstract Since drain pipes on ships radiate underwater noise when in use, the components and radiation characteristics of flow noise and flow-induced noise from drain pipes on ships are explored, and the relationship between peak spectral values and wet mode frequencies is analyzed. The numerical calculation models of the flow field and structure for drain pipes are created respectively to obtain pulsating pressures in the flow field and structural mode values. Then, the flow noise and flow-induced noise are separately measured in an acoustic model developed for drain pipes upon the mapping of wall fluid meshes, structural meshes and acoustic meshes. A vibration-acoustic coupling model with the radiated sound field nephogram is presented based on the wall pulsating pressure and structural mode values. The numerical calculation indicated a significantly louder flow noise from drain pipes than the negligible flow-induced noise. The resulting wet mode of drain pipes solved by the Boundary Element Method (BEM) reflects the similarity between the peak spectral value and the wet mode frequency of flow-induced noise, marking that the fluid pulsating pressure excites noise.

Analyzing the inspiratory airflow unsteadiness in the respiratory tract using dynamic mode decomposition method

To enhance the understanding of airflow characteristics in the human respiratory tract, the inspiratory airflow field was simulated under both tidal and quasi-steady inspiratory flow rates at the mouth inlet using the large eddy simulation method. Special attention was paid on analyzing the inspiratory airflow unsteadiness using the dynamics mode decomposition (DMD) method based on the vorticity field and comparing it with the proper orthogonal decomposition (POD) method. The following novel findings were obtained. (1) Power spectral density indicates that the inspiratory airflow is highly turbulent in the pharynx–larynx region. The vorticity field in the upper airway is more affected by inspiratory patterns compared to turbulence fluctuations. (2) The DMD results indicate that the shear flow in the pharynx–larynx region is mainly caused by flow under low-frequency modes, while the disturbances of the jet flow are caused by flow under multiple frequency modes. Steady-state inspiratory pattern demonstrates the decay characteristics different from the tidal inspiratory pattern. (3) Compared to the POD method, which may contain multiple frequency components, the DMD decomposition yields modes with a single frequency, enabling a more accurate capture of the frequency and decay characteristics of the respiratory flow under each mode. In conclusion, this study demonstrates that the DMD method is more suitable for studying the respiratory airflow unsteadiness and further confirms the necessity of adopting clinically measured inspiratory data to investigate airflow unsteadiness.

Influential mechanism of operational parameters on internal resonance of drill strings by numerical simulations

Abstract Drill string vibration is highly conductive to drill string fatigue and component failure. In this study, a finite element model of a drill string with bottom hole assembly (BHA) is constructed to investigate the effect of different operational parameters, such as different string length, density, pressure, and velocity of drilling fluid on drill string natural frequencies, and thus internal resonance by considering fluid-structure interaction (FSI) in ANSYS. Numerical simulations demonstrate that the natural frequencies decrease as the length of the drill string increases, which is especially true for the axial mode. The condition of 1:1 internal resonance between the axial and torsional modes only occurs when the length of drill string is sufficiently high. Nevertheless, this resonance fades away in the presence of fluid. The increment of fluid density slightly increases the natural frequency in lateral mode, whereas decreases that in axial mode. On the other hand, this effect of density is negligible in the torsional mode. The natural frequencies for axial, torsional and lateral modes decrease as the fluid velocity increases, and the impact of fluid pressure on natural frequency is almost not observable. The numerical results for the case without drill fluid are in qualitative agreement with analytical solutions. when considing the effect of drill length on natural frequency.

Thermomechanical and Viscoelastic Characterization of Continuous GF/PETG Tape for Extreme Environment Applications

The thermomechanical and viscoelastic properties of a glass fiber polyethylene terephthalate glycol (GF/PETG) continuous unidirectional (UD) tape were investigated using differential scanning calorimetry (DSC), thermomechanical analysis (TMA), and dynamic mechanical analysis (DMA). This study identified five operational conditions based on the Army Regulation 70-38 Standard. The DSC results revealed a glass transition temperature of 78.0 ± 0.3 °C, guiding the selection of temperatures for TMA and DMA tests. TMA provided the coefficient of thermal expansion in three principal directions, consistent with known values for PETG and GF materials. DMA tests, including strain sweep, temperature ramp, frequency sweep, creep, and stress relaxation, defined the material’s linear viscoelastic region and temperature-dependent properties. The frequency sweep indicated an increased modulus with rising frequency, identifying several natural frequency modes. Creep and stress relaxation tests showed time-dependent behavior, with strain increasing under higher loads and stress decreasing over time for all tested input values. Viscoelastic models fitted to the data yielded R2 values of 0.99, demonstrating good agreement. The study successfully measured thermomechanical and viscoelastic properties across various conditions, providing insights into how temperature influences the material’s mechanical response under extreme conditions.

Generation of short microwave pulse trains based on a hybrid mode-locked optoelectronic oscillator.

A novel approach, to the best of our knowledge, for generating short microwave pulse trains based on a hybrid mode-locked optoelectronic oscillator (HML-OEO) is proposed and demonstrated. In the proposed scheme, a saturable absorber (SA) device is inserted into the active mode-locked OEO (AML-OEO) to compress the pulse width of the microwave pulse trains. Numerical simulations and experimental results show that the HML-OEO generates a short microwave pulse train with a repetition rate of 98.994 kHz through fundamental frequency mode locking, and its pulse width is compressed by about 50% compared to the AML-OEO. Additionally, in the experiment, microwave pulse trains with different repetition rates are generated by second-, third-, fourth-, and fifth-order harmonic mode locking, respectively. Compared to the AML-OEO, the HML-OEO achieves pulse compression effects of 49.3%, 49.8%, 49.4%, and 49.9%, respectively. Notably, compared to the AML-OEO, the proposed scheme also exhibits outstanding performance in frequency stability.

TIC 441725813: A new bright hybrid hot B subdwarf pulsator with differential core versus envelope rotation

Context. The Transiting Exoplanet Survey Satellite (TESS) performs high-precision photometry over almost the whole sky primarily in search of exoplanet transits. It also provides exquisite data to study stellar variability, in particular for pulsating hot B subdwarf (sdB) stars. Aims. We present a detailed analysis of a new hybrid (p- and g-mode) sdB pulsator, TIC 441725813 (TYC 4427-1021-1), discovered and monitored by TESS for 670 days. Methods. The TESS light curves available for this star were analysed using prewhitening techniques to extract mode frequencies accurately. The pulsation spectrum was then interpreted through methods that include asymptotic period spacing relationships and the identification of rotational multiplets. We also exploited a high signal-to-noise ratio (S/N), low-resolution spectrum of TIC 441725813 using grids of non-local thermodynamic equilibrium (NLTE) model atmospheres to derive its atmospheric parameters. Results. The light curve analysis reveals that frequencies are mostly found in the g-mode region, but several p-modes are also detected, indicating that TIC 441725813 is a hybrid sdB pulsator. We identify 25 frequencies that can be associated with ℓ = 1 g-modes, 15 frequencies corresponding to ℓ = 2 g-modes, and six frequencies characteristic of p-modes. Interestingly, several frequency multiplets interpreted as rotational splittings of deep-probing g-modes indicate a slow rotation period of at least 85.3 ± 3.6 day, while splittings of mostly envelope-probing p-modes suggest a significantly shorter rotation period of 17.9 ± 0.7 day, which implies the core (mainly the helium mantle with possibly the deeper partially mixed helium-burning core that it surrounds) rotates at least 4.7 times slower than the envelope. The radial velocity curves indicate that TIC 441725813 is in a close binary system with a low-luminosity companion, possibly a white dwarf. While elusive in the available TESS photometry, a low-frequency signal that would correspond to a period of ∼6.7 h is found, albeit at a low S/N. Furthermore, we estimate the inclination angle to be ∼60° by two independent means. Conclusions. TIC 441725813 is a particularly interesting sdB star whose envelope rotates faster than the core. We hypothesise that this might be caused by the effects of a tidal interaction with a companion, although in the present case, the presence of such a companion will have to be further investigated. This analysis paves the way towards a more detailed seismic probing of TIC 441725813 using optimisation techniques, which will be presented in a second paper.

Passive control of thermoacoustic instability in a high-efficiency domestic gas stove with fine-tuning burner

Thermoacoustic oscillation is a significant challenge in the development of advanced thermal power and propulsion systems. The present work focuses on the whistling phenomenon in the practical burners of a developing high-efficiency domestic gas stove. The acoustic analysis is conducted by a Helmholtz acoustic solver, identifying the 1/2 wave longitudinal mode in the outer ring or center nozzle and its upstream pipe and estimating the modal eigenfrequencies fa=599Hz and fb=647Hz which are close to the main frequency of the whistling measured in experiments. The sequential flame images captured by a high-speed camera are processed by a dynamic mode decomposition method to illustrate flame structure oscillations at the peak frequency mode. The results verify that thermoacoustic oscillations are the generation mechanism of the whistling and display the periodic fluctuation characteristics of the flame and the spatial distribution of heat release. Moreover, both structural fine-tuning designs help to achieve better suppression for thermoacoustic oscillations and avoid the whistling phenomenon. These structural fine-tuning strategies have been researched for several decades but rarely reported to be applied to industrial burners in previous work. Motivated by this, it will provide a new insight into the investigation of burner structures on thermoacoustic behaviors and the application of these passive control strategies.

Compact dwarfs made of light-quark nuggets

Utilizing an equiparticle model with both linear confinement and leading-order perturbative interactions, we obtain systematically the properties of strangelets and nonstrange quark matter (udQM) nuggets at various baryon (A) and charge (Z) numbers, where the detailed single-quark-energy levels are fixed by solving Dirac equations in mean-field approximation. We then examine the structures of compact dwarfs made of light strangelets or udQM nuggets forming body-centered cubic lattices in a uniform electron background. Despite that the strangelets and udQM nuggets generally become more stable at larger A, the compact dwarfs are still stable since the fusion reactions between those objects do not take place in the presence of a Coulomb barrier, which is similar to the cases of light nuclei in normal white dwarfs. If udQM dwarfs or strangelet dwarfs are covered with normal matter, their masses and radii become larger but do not exceed those of ordinary white dwarfs. Finally, we investigate the radial oscillation frequencies of udQM dwarfs and strangelet dwarfs and find that their frequencies are typically higher than traditional white dwarfs. The stability of compact dwarfs are then analyzed by examining radial oscillation frequencies of the fundamental mode, where compact dwarfs covered by normal matter are still stable. Published by the American Physical Society 2024

Dynamic characteristics of bridges with short pylons and outwardly inclined cable planes

This study developed a cable-stayed bridge characterised by short pylons and outwardly inclined cable planes. The dynamic characteristics of this bridge were investigated using the Lanczos eigenvalue and finite element methods. The first ten mode shapes and frequencies were analysed to this end. The influences of key parameters, such as the inclination angle of the pylons and the height and stiffness of the cable–pylon anchorage, on the dynamic characteristics of the bridge were examined. The results showed that the transverse bending modes of the main girder occurred first, while modes related to pylons appeared later. The torsional vibrational modes appeared in the 10th order, indicating the bridge had suitable wind resistance. Further, the outwardly inclined cable planes enhanced the lateral seismic resistance of the bridge. Increasing the rigidities of the cable–pylon anchorage and main girder can improve the dynamic characteristics of the bridge. This is accomplished by reducing the height of the cable–pylon anchorage and adding auxiliary piers.

The effect of hydrogen enrichment on the conical premixed methane–air flame response and thermoacoustic modes coupling

This paper investigates the thermoacoustic dynamic responses of hydrogen-enriched laminar premixed conical methane–air flames under dual-mode coupling. Utilizing the level set method and the G-equation model, one meticulously derives the flame describing function (FDF) in relation to variations in hydrogen enrichment levels (ηH). This precisely derived FDF is then integrated into the low-order network model of the Rijke tube to analyze the thermoacoustic unstable modes of the system. Finally, dual-frequencies incoming flow velocity perturbations are reintroduced as inputs to obtain the flame response under thermoacoustic modes coupling. Results show that while keeping the unstretched steady flame aspect ratio constant, an increase in ηH not only raises the FDF’s cut-off frequency but also enhances the FDF gain within the nonlinear frequency region, leading to more unstable modes, especially high frequency modes within the Rijke tube system. Furthermore, the flame response is further altered under the excitation of dual unstable modes. When both modes are within the linear frequency region of the FDF, the flame response is co-controlled by the two modes, predominantly by the mode with a larger velocity perturbation amplitude, with weaker modes coupling leading to the additional frequency perturbation having a suppressive effect on the flame response at the original frequency. Conversely, when one or two modes are within the nonlinear frequency region of the FDF, the flame response is dominated by the lower-frequency mode, with higher nonlinear modes coupling allowing the additional frequency perturbation to both promote and suppress the response at the original frequency and also couple to produce a significant difference frequency response. Novelty and significance The novelty of this paper lies in the determination of the flame describing function (FDF) with varying hydrogen enrichment levels and the stability of thermoacoustic systems, and more significantly, conducting an in-depth and comprehensive investigation into the nonlinear dynamic responses of hydrogen-enriched flames to different types of dual-mode coupling perturbations. The dual-mode perturbations result in either attenuation or amplification of the flame response, depending on whether the corresponding frequencies lie within the linear or nonlinear frequency regions of the FDF, which innovatively incorporates the influence of the FDF phase and examines the responses at the difference frequencies generated by the coupling. This lays a foundation for further exploration into the mechanisms of modes coupling in hydrogen-enriched and other thermoacoustic systems.

Characteristic frequencies of transverse electric modes in a double negative slab waveguide with Kerr-type nonlinearity

The evolution equation for guided transverse electrical modes in a slab waveguide having a double negative core is derived for the electrical field. Special solutions of the dispersion equation for the case with double positive symmetric cladding are searched for. Relevant eigenmodes are formulated in terms of characteristic frequencies as a new method, and these frequencies corresponding to the oscillating guided modes are found for different wave numbers and core widths assuming the lossless Drude model can be used for the core medium with a Kerr-type nonlinearity. Results show that normalized characteristic frequencies increase with increasing wave numbers and mode numbers.

Observable strong field effects of extra spacetime dimension in the braneworld black hole

Inspired by the string theory, the braneworld picture introduces extra dimensions beyond the four that may have observable non-trivial effects in short distance (strong field) gravity experiments. A case in point is the Randall–Sundrum braneworld picture that projects the 5d bulk Weyl tensor onto the 3d brane providing a stress tensor in the effective Einstein field equations on the brane. Dadhich, Maartens, Papadopoulos and Rezania (DMPR) derived an exact braneworld black hole solution of the brane vacuum field equations. The solution formally resembles that of Reissner–Nordström but is physically different from it since the ”tidal charge” Υ in the solution is not the electric charge but an imprint from the fifth dimension allowing both signs in the power law modification ±Υ2r2 to the Schwarzschild metric Υ=0. The corresponding black holes are designated as DMPR±. We study here the effect of Υ on strong field lensing observables and compare in the eikonal limit the ring down quasinormal mode (QNM) frequencies of DMPR− with those of DMPR＋ , the two variants of tidal charge modified Schwarzschild black hole (Υ=0). It turns out that the tidal charge can significantly modify the Schwarzschild lensing observables and QNM frequencies. In particular, we find that the Pretorius–Khurana critical exponent γ of circular null orbits in the DMPR− black hole has a lower value than that for the Schwarzschild black hole, which indicates a stronger Lyapunov instability suggesting that the accretion disks of DMPR− black holes would appear brighter. The case of the SgrA* black hole is considered for a possible constraint on Υ from the EHT observation of its shadow size.

Data-driven approach for identifying the factors related to debt collector performance

The company's success and growth heavily rely on its workforce's performance, yet the evaluation of employees has been only partially and inconclusively executed so far. The primary goal of this research is to build an open innovation framework for analyzing the performance of the debt collector. We have developed the Reinforcement Learning based Continual Learning (RLC) approach for evaluating the performance by analyzing the metrics such as visit patterns and collection percentage. We have used the private debt collection dataset to assess the debt collector's performance. We formulated hypotheses derived from insights gained during exploratory data analysis and subsequently validated them through statistical testing. Whether there are noticeable distinctions among debt collectors in terms of visitation frequency, collection rates, and collection modes. This proposed open innovation framework for analyzing the debt collector performance provides significant variation in terms of collection rate. The proposed EDQN-CL achieved a 13.56 % higher classification rate than the existing algorithm for categorizing the debt collector performance.

Fluid–acoustic–structure resonance mechanism of a plane cascade via a low-speed wind tunnel test

Acoustic resonance is an important factor that contributes to aeroengine compressor failure. In this study, a plane cascade of compressor blades was designed to reproduce acoustic resonance via a low-speed wind tunnel test. A high-frequency hot-wire, microphone and strain gauge were used to synchronously measure the fluid, acoustic and structural parameters. We analysed the variation in the amplitude and frequency of the multi-field parameters with increasing mean flow velocity and explored the multi-field interaction mechanism that induces the acoustic resonance of the plane cascade. The plane cascade effectively reproduced the acoustic resonance phenomenon. The first-order acoustic-mode frequency of the plane cascade flow duct, second-order torsional vibration mode frequency of the blade and shedding mode frequency of the tip clearance leakage vortex were equal under acoustic resonance. The fluid, acoustic and structural fields showed a strong interaction effect, achieving the maximum blade vibration amplitude and causing fatigue cracks of torsional vibration at the blade root. The frequency lock-in region of the compressor plane cascade was divided into an ‘acoustic–structure’ interaction region, a ‘fluid–acoustic–structure’ interaction region and a first-order acoustic-mode dominant region with increasing mean flow velocity, which demonstrates an interesting phenomenon in which the fluid–acoustic–structure modes compete: acoustic mode > blade vibration mode > vortex shedding mode. The results demonstrate a unique approach to the study of acoustic resonance that provides insight into the acoustic resonance mechanism in a cascade of compressor blades.