Mode Frequencies Research Articles

Exploring the Scaling Factors for Infrared Modes of PANHs - A Case Study on Cationic 3-Azafluoranthene⋅+ and Protonated 3-Azafluoranthene.

Infrared (IR) emission bands by interstellar polycyclic aromatic hydrocarbons (PAHs) and polycyclic aromatic nitrogen heterocycles (PANHs) are observed towards a large variety of interstellar objects and offer detailed insights into the chemistry and physics of the interstellar medium. The analysis of the emission bands, and thus the interpretation of the molecular characteristics of the carriers, heavily relies on the use of density functional theory (DFT) calculated IR spectra. However, there are significant challenges in accurately predicting the experimental IR band positions, particularly for PANH emission vibrational modes around 6 μm. In this work, we present gas-phase mid-infrared (mid-IR) spectra of cationic 3-azafluoranthene (3AF⋅+) and protonated 3-azafluoranthene (3AFH+) to investigate their experimental IR band positions in relation to DFT calculated bands. The experimental spectra are compared to DFT simulated spectra, where different approaches were followed to correct for anharmonicities. The best agreement is achieved by scaling frequencies of modes with large nitrogen displacements with a different factor. Even though our findings might be limited to a small number of PANH structures, they indicate, that nitrogen atom incorporation needs to be accounted for by carefully adjusting the corresponding scaling factors while computing IR spectra of PANHs on DFT level.

PMUs data based detection of oscillatory events and identification of their associated variable: Estimation of information measures approach

Information theory can be a useful tool for quantifying the perturbations in the associated state variables at the time of disturbance occurrence. The study introduces a framework for the spectral decomposition of multivariate information measures to detect initiation of low frequency oscillations (LFOs), caused due to physical events in the power grid. A frequency-specific quantification of the information is shared between a target variable and two source variables from their time series data. Initially, the approach is applied on different synthetic test signals having different oscillatory frequency modes and decay time constant. Then, approach is extended on PMUs signals. The combination of cross-spectral and information-theoretic approaches is applied for the multi-variable analysis of PMUs signals from the same bus. The interdependence among the frequency, voltage angle and voltage magnitude, corresponding to specific oscillations, manifested due to cause-effect relationships obtained in terms of statistics is estimated. The dynamics in terms of unique (interaction), redundant and synergetic information is determined with the contribution from two of these three signals as source variables to target variable (frequency/voltage angle). This provides a direct coupling to identify driver-response relationships between source variables and target variable to indicate the onset of LFOs, following physical events in power network. The extension of approach among the variables from different buses aids to identify the responsible area of event occurrence.

Effectiveness of dolutegravir in moderate severity COVID-19 patients: A single-center, randomized, double-blind, placebo-controlled trial

Introduction: Drug repurposing as a low-cost, time-saving, and often less risky strategy has been attractive for the treatment of coronavirus disease 2019 (COVID-19) during the pandemic. This trial aimed to evaluate the effectiveness of dolutegravir, an HIV-1 integrase inhibitor, in admitted patients with moderate COVID-19. Methods: This study was a randomized, double-blind, placebo-controlled clinical trial assessing the efficacy of dolutegravir in adults admitted to a hospital in Ghaemshahr, Mazandaran Province, Iran. Patients aged 18-80 years with early symptoms of moderate COVID-19, which was confirmed based on reverse transcription polymerase chain reaction (RT-PCR) and/or chest computed tomography (CT) scan, were considered to be included in this study. Patients were randomly assigned in a 1:1 ratio to receive 50 mg dolutegravir plus the standard treatment regimen or the same value of placebo plus the standard treatment regimen, daily for 7 days. The standard treatment regimen was remdesivir 200 mg on day 1 followed by 100 mg for five days or until discharge. The primary endpoint was recovery 10 days after the beginning of the study. Results: Between August 22 and October 23, 2021, of 120 patients who were enrolled, 93 patients were randomly assigned to receive 50 mg dolutegravir (n = 46) or the placebo regimen (n = 47). No significant difference was observed between the two intervention groups based on the obtained results including frequency of respiratory modes during the first five days of admission, respiratory rate, and O2 saturation during six time periods. Conclusion: The results showed that in adult patients admitted to the hospital with moderate COVID-19, treatment with dolutegravir was not associated with improvement in clinical recovery. Larger randomized trials are required to provide more robust evidence about the effectiveness of dolutegravir.

Compact and miniaturized wideband bandpass filter based on substrate integrated waveguide and microstrip line

In this work, we present a simple design of a compact and miniaturized wideband bandpass filter (BPF) based on substrate integrated waveguide (SIW) and microstrip line. Through the order extension, the filtering effect and the order of the Chebyshev response of the designed BPF can be indirectly controlled by preserving square notches (SNs) on the SIW. By introducing one or two SNs in the SIW structure, the resonance frequencies of different modes can be controlled, thus achieving dual- and tri-mode BPFs with wideband and low insert loss. The working principle of the designed BPFs was illustrated by modal analysis, field distribution, and equivalent circuit theory. Based on this, the dual- and tri-mode BPFs with center frequencies of 6.8 and 7 GHz were designed and demonstrated numerically. Further experimental results indicate that the proposed tri-mode BPF has low insertion loss (0.25 dB), compact size (0.27λg2), and wideband bandwidth (60%). In addition, the tri-mode BPF achieves a broadband out-of-band rejection of 1.5f0 (f0 is the center resonance frequency) below the −10 dB level, making it highly promising for various applications in related fields.

Investigation of structural parameters influencing vibration characteristics of heavy-duty truck diesel tanks.

The working conditions of heavy-duty trucks are very complicated as the diesel shaking and resonance problems, which causes weld tears, separators to fall off, and other failures occur. Through experiments and finite element simulation, the natural frequency and vibration mode of a given 400 L diesel tank were calculated to study the influences of structural parameters such as the fill ratio (0.1-0.9), the number of baffle plates (0, 1, 2), the spacing of the plates (240 mm, 400 mm, 560 mm) and the aperture (38 mm, 78 mm, 118 mm) on the modal parameters with the wet mode method. The results of the hammering mode test and the simulation modal analysis agree well with the maximum error is 4.8%; the natural frequency of the diesel tank will increase with fill ratio decrease; the increase of the baffle plate number (0, 1, 2) can effectively increase the first-order natural frequency of the diesel tank, but the change of the natural frequency is not obvious on the higher order; the higher plates spacing has a smaller natural frequency; increasing the aperture will highly increase the natural frequency, 188 mm has better vibration safety.

Моделирование КВ-радиотрасс на основе волноводного подхода

We present a scheme for modeling HF radio signal characteristics along paths of different lengths, which is based on the waveguide approach — the normal mode method. We use a representation of the recorded signal field in the form of Green function products of the angular operator, excitation coefficients, and reception coefficients of individual normal modes. Algorithms have been developed for calculating distance-frequency, frequency-angular, and amplitude characteristics of signals in large spatial regions through analysis and numerical summation of normal mode series. We have implemented a complex algorithm for simulating propagation conditions of HF radio signals, which includes a medium model, algorithms for calculating signal characteristics, and operational diagnostics of radio channel. We have compared the results of the HF signal propagation characteristic modeling and the experimental oblique sounding data obtained along paths of different lengths and orientation. To analyze experimental ionograms, determine the maximum usable frequencies for propagation modes along radio paths, we employ the method of automatic processing and interpretation of oblique sounding ionograms.

HF radio path modeling by waveguide approach

We present a scheme for modeling HF radio signal characteristics along paths of different lengths, which is based on the waveguide approach — the normal mode method. We use a representation of the recorded signal field in the form of Green function products of the angular operator, excitation coefficients, and reception coefficients of individual normal modes. Algorithms have been developed for calculating distance-frequency, frequency-angular, and amplitude characteristics of signals in large spatial regions through analysis and numerical summation of normal mode series. We have implemented a complex algorithm for simulating propagation conditions of HF radio signals, which includes a medium model, algorithms for calculating signal characteristics, and operational diagnostics of radio channel. We have compared the results of the HF signal propagation characteristic modeling and the experimental oblique sounding data obtained along paths of different lengths and orientation. To analyze experimental ionograms, determine the maximum usable frequencies for propagation modes along radio paths, we employ the method of automatic processing and interpretation of oblique sounding ionograms.

Exact dispersion relation of the quantum Langmuir wave.

The normal modes, i.e., the eigensolutions to the dispersion relation equation, are the most fundamental properties of a plasma. The real part indicates the intrinsic oscillation frequency while the imaginary part the Landau damping rate. In most of the literature, the normal modes of quantum plasmas are obtained by means of small damping approximation, which is invalid for high-k modes. In this paper, we solve the exact dispersion relations via the analytical continuation scheme, and, due to the multi-value nature of the Fermi-Dirac distribution, reformation of the complex Riemann surface is required. It is found that the topological shape of the root locus in quantum plasmas is quite different from classical ones, in which both real and imaginary frequencies of high-k modes increase with k steeper than the typical linear behavior in classical plasmas. As a result, the time-evolving behavior of a high-k initial perturbation becomes ballistic-like in quantum plasmas.

Synergistic effect of physicochemical and geometric techniques for initiating detonation in a small-size pulse detonation engine

This article is devoted to the influence of temperature, obstacle and enrichment of the liquid fuel–air mixture with oxygen, as well as the synergistic effect of the combined action of these techniques on the initiation of detonation in a small-sized pulsed detonation engine with a channel of subcritical dimensions (d = 20 mm and L = 500 mm). Explosive limits for detonation of heptane in the frequency mode (f = 1–50 Hz) have been established in terms of the equivalence ratio (ϕ = 0.7–2.6) and in terms of the oxygen-to-air ratio ([O2/air] > 2 for heptane and [O2/air] > 3 for Jet-A1). It was found that the wave velocity in heptane-oxygen-air and Jet-A1-oxygen-air mixtures varies from 500 m/s to 2500 m/s depending on the technique used to accelerate the DDT. Without the use of special techniques, detonation does not occur, and the wave velocity does not exceed 700 m/s. The use of heat, or obstacle or oxygen enrichment leads to the initiation of detonation at distances of 540–660 mm from the ignition initiator, which is 20–26 calibers of engine diameter. A synergistic effect of the combined use of an obstacle, thermal activation and enrichment of the mixture with oxygen was discovered, which made it possible to reduce the pre-detonation distance by almost 60 % and increase the frequency of the detonation mode by also 60 % (up to 80 Hz) compared to each technique separately.

Structural Optimization Design of Magnetoelectric Thin-Film Antenna for Bandwidth and Radiation Enhancement.

The acoustically actuated nanomechanical magnetoelectric (ME) antennas represent a promising new technology that can significantly reduce antenna size by 1-2 orders of magnitude compared to traditional antennas. However, current ME antennas face challenges such as low antenna gain and narrow operating bandwidth, limiting their engineering applications. In this paper, we enhance the bandwidth and radiation performance of ME antennas through structural optimization, leveraging theoretical analysis and numerical simulations. Our findings indicate that optimizing the inner diameter of the ring-shaped ME antenna can elevate the average stress of the magnetic layer, leading to improved radiation performance and bandwidth compared to circular ME antennas. We establish an optimization model for the radiation performance of the ME antenna and conduct shape optimization simulations using COMSOL Multiphysics. The results of the Multiphysics field optimization align with the stress concentration theory, demonstrating a strong correlation between the radiation performance and bandwidth of the ME antenna with the average stress of the magnetic film. The resonant frequency in the thickness vibration mode is determined to be 170 MHz. Furthermore, shape optimization can enhance the bandwidth by up to 104% compared to circular ME antenna structures of the same size.

Frequency optimisation and performance analysis of photovoltaic-battery water pumping system

Photovoltaic-battery water pumping systems (PVBWPSs) can provide fresh water and irrigation in off-grid areas. Previous research has focused on direct current (DC) voltage versus frequency to control the speed of a pump. However, the use of photovoltaic (PV) modules with batteries to create a high-performance hybrid system with fixed and variable frequencies of supply power remains challenging, particularly in an off-grid water pumping system with limited power and water supplies. Based on a conventional frequency conversion mode and power balance, this work addresses fixed and variable frequencies under changing solar irradiance conditions for a PV system and a PV system combined with a battery (PVB) mode to improve energy utilisation. According to DC power balance and centrifugal pump theories, a mathematical model of the power supply frequency in the PVBWPS is presented, as well as the loss of load probability (LLP) and pumping coefficient (Cp), through which the performance metrics are obtained. The formulated models are validated through the experimental PVBWPS, which includes 2.19 kWp PV modules, a 9.6 kWh battery bank, and a 0.75 kW centrifugal pump. The experimental results show that the root mean square error (RMSE) and maximum relevant error (RE) of the frequency are 0.14 Hz and 0.74 %, respectively. Consequently, the output performances are revealed via software simulation. The calculated results indicate that the maximum pumping volume for fixed-power-frequency operation is 48 Hz, which is 27.56 m3 on a sunny day and 17.63 m3 on a cloudy day. On a rainy day, the maximum pumping volume is 3.27 m3 at 41 Hz. Similarly, the Cp values reach maxima of 2.51 m3/kWh and 2.11 m3/kWh at 48 Hz in both sunny weather and cloudy weather, respectively, while on rainy days, the Cp peaks at 0.77 m3/kWh at 41 Hz. Moreover, every 1 Hz increase in the fixed frequency mode leads to a rise in the LLP, while the minimum change is at 46–48 Hz for cloudy and rainy days. Furthermore, the simulations revealed that for variable frequency control, the volume of water pumped in the PVB mode reached 40.19 m3, 29.36 m3, and 15.11 m3, which are increased by 4.91 %, 21.83 % and 103.09 % compared with the variable frequency PV mode, and 45.83 %, 66.53 % and 362.08 % higher than in PV fixed frequency mode, respectively. Compared with the PV mode, the system weighted efficiency of the variable-frequency PVB mode is increased by 2.06 %, 4.98 %, and 8.36 % under three weather conditions. This work provides critical theoretical guidelines for the design and operation of high-performance PVBWPs.

Calculation and design of GaAs quantum dot devices where the vibrational modes can be frozen out at cryogenic temperatures

We calculate how the frequencies of the vibrational modes in a free-standing GaAs bar are changed as a function of the bar’s geometrical features such as length, thickness and shape. After understanding the effect of the physical characteristics we add finger gates that will be used to define quantum dots on the bar and study the system as a function of the length of the suspended finger gates, and their material properties. Finally, we strengthen the bridges in order that the first vibrational modes occur at a temperature of 100 mK or more, so that all modes can be frozen out when operated in a dilution refrigerator.

Piezoelectric Outputs of Electrospun PVDF Web as Full-Textile Sensor at Different Mechanical Excitation Frequencies.

With the increasing application of electrospun PVDF webs in piezoelectric sensors and energy-harvesting devices, it is crucial to understand their responses under complex mechanical excitations. However, the dependence of the piezoelectric effect on mechanical excitation properties is not fully comprehended. This study aims to investigate the piezoelectric output of randomly oriented electrospun PVDF nanofiber webs fabricated through different electrospinning processes at various mechanical excitation frequencies. The electrospun PVDF web was sandwiched between two textile electrodes, and its piezoelectric output as a full-textile sensor was measured across a frequency range from 0.1 Hz to 10 Hz. The experimental results revealed that the piezoelectric output of the electrospun PVDF web exhibited a nearly linear increase at excitation frequencies below 1.0 Hz and then reached an almost constant value thereafter up to 10 Hz, which is different from the hybrid PVDF or its copolymer web. Furthermore, the dependency of the piezoelectric output on the excitation frequency was found to be influenced by the specific electrospinning process employed, which determined the crystalline structure of electrospun PVDF nanofibers. These findings suggest that determining an appropriate working frequency for randomly oriented electrospun PVDF nanofiber webs is essential before practical implementation, and the piezoelectric response mode in different mechanical activation frequency ranges can be used to detect different human physiological behaviors.

Dynamic Modeling and Experimental Modal Analysis for the Central Rod-Fastened Rotor With Hirth Couplings Based on Fractal Contact Theory

Abstract The central rod-fastened rotor of gas turbine exhibits pronounced noncontinuous characteristics due to the large number of contact interfaces between the compressor and turbine disks. It is necessary to establish an accurate dynamic modeling method for the central rod-fastened rotor that fully considers the contact surface effect. In this work, the contact behavior of the rough surface is characterized by the fractal theory. The normal and tangential contact stiffness models are developed, and the influence of fractal parameters is discussed. Besides, the finite element model for the central rod-fastened rotor is established by developing an improved contact element considering the equivalent stiffness segment of Hirth couplings. Finally, the proposed model is verified by conducting the modal testing and measuring the first four modes of natural frequencies and modal shapes of the central rod-fastened rotor. The results show that the numerical results are in good agreement with the experimental ones, and the fractal contact model can effectively predict the connection stiffness of Hirth couplings, which in turn improves the simulation accuracy for the modal characteristics of the central rod-fastened rotor and provides a dynamic modeling approach with high efficiency and less computational complexity.

Decoupling of peeling and ballooning thresholds for pedestal stability and reduction in ELM frequency via enhanced turbulence with edge electron cyclotron heating in DIII-D

The edge localized mode (ELM) frequency (f ELM) decreased by 63% when electron cyclotron heating (ECH) deposition location is shifted from ρ = 0.4 to ρ = 0.8 in DIII-D discharges where the power ratio between neutral beam injection (NBI) and ECH (P NBI/P ECH) is kept at ∼1. The performance of the pedestal in the ECH heated case is compared with a pure NBI reference discharge while keeping the total input power constant. All these discharges are performed at balanced input torque conditions. Furthermore, in the pure NBI discharge a strong decoupling of the peeling–ballooning (PB) thresholds is observed. The PB decoupling is preserved when the ECH is deposited at ρ = 0.8 and P NBI/P ECH ∼ 1, while the thresholds manifest a closed stability boundary when the ECH is deposited at ρ = 0.4. The inter-ELM pedestal recovery time is considerably larger for the ECH at ρ = 0.8 case. Increased pedestal turbulence is observed in beam emission spectroscopy (BES), Doppler backscattering and magnetic diagnostics for the ECH at the ρ = 0.8 case. Strong growth of a TEM-like mode is observed in BES and the mode growth is correlated with the decrease in f ELM. In view of these observations, the increased pedestal turbulence seems to be the plausible reason behind the delayed pedestal recovery following an ELM event in the ECH at ρ = 0.8 case, and the preservation of PB decoupling through temperature pedestal profile widening. TRANSP interpretative simulations show that the ECH at the ρ = 0.8 case is more susceptible to ITG/TEM turbulence.

"When she goes out, she feels better:" co-designing a Green Activity Program with Hispanic/Latino people living with memory challenges and care partners.

Utilizing a participatory approach, we sought to co-design a 12-week Green Activity Program (GAP) with Hispanic/Latino individuals living with memory challenges and their care partners, local outdoor professionals, and healthcare providers. Participants were recruited via convenience and snowball sampling in the Bronx, New York with Hispanic/Latino persons living with memory challenges and care partners, outdoor activity professionals, and interdisciplinary healthcare providers/dementia experts. Co-design occurred iteratively with 5 focus groups and 4 individual interviews lasting 30-90 min and focused on program and research design. Sessions were recorded and transcribed. Utilizing directed content analysis data was coded using a priori codes program design and research design. 21 participants completed co-design activities: (n = 8 outdoor activity professionals, n = 6 Hispanic/Latino persons living with memory challenges and care partners, and n = 7 interdisciplinary healthcare providers/dementia experts). Participant preferences for program design were captured by subcodes session duration (30-90 min), frequency (4-8 sessions), and delivery modes (in-person and phone). Participants' preferred nature activities included group exercise and outdoor crafts [crocheting], outcomes of social participation, connectedness to nature, decreased loneliness, and stewardship were identified. Preferred language for recruiting and describing the program were "memory challenges," "Hispanic/Latino," and "wellbeing." Referral pathways were identified including community-based organizations and primary care. Co-design was a successful form of engagement for people living with memory challenges that enabled participants to help design key elements of the GAP and research design. Our processes, findings, and recommendations for tailoring co-design to engage Hispanic/Latino people living with memory challenges can inform the development of other programs for this population.

CFD stability improvement using dynamic mode decomposition of solution update vectors

We present a novel method for improving the numerical stability of finite volume simulations by optimizing the mesh through dynamic mode decomposition of solution update vectors. Our approach leverages dynamic mode decomposition to approximate the non-linear solution evolution as a linear mapping, enabling us to represent the dynamic system with fewer degrees of freedom. By conducting eigenanalysis on the reduced system, we gain insights into the growth rate and oscillation frequency of dominant solution modes. We then identify the control volumes and vertices that have a significant influence on each dynamic solution mode. We compute the gradients of the Jacobian diagonal elements with respect to the movement of the selected vertices. Based on these gradients, we adjust the positions of the vertices to improve the diagonal dominance of the corresponding Jacobian rows. We utilize this approach in conjunction with our in-house flow solver as well as with Ansys Fluent to test its effectiveness when applied to different types of CFD software architecture. We show that the presented methodology is fully non-invasive to the host flow solver and does not require any modifications or access to the source code. Our approach offers a substantial computational cost reduction compared to existing methods for numerical stability improvement. Various results demonstrate the strength and efficacy of this state-of-the-art approach for improving numerical stability through mesh optimization.

A study on attenuation patterns of acoustic waves in waveguide structures with flexural boundaries

This research article investigates the attenuation patterns of acoustic waves within waveguide structures featuring flexural boundaries. By employing advanced methods in vibrations and controls, the study aims to enhance our understanding of waveguide behavior and offer valuable insights for optimizing acoustic wave propagation in diverse applications. The entire waveguide structure is tuned through cooperative interactions involving elastic plates, membranes, and rigid boundary surfaces. The lower boundary of the expansion chamber consists of a rigid plate, with elastic membranes covering the upper surfaces of the cavity. The problem is formulated in terms of transmission and reflection coefficients of the modes, enabling the solution of the scattering problem. Matching acoustic pressure and velocity at the waveguide junction yields the scattering coefficients. The results reveal that the scattering coefficients are intricately influenced by both the geometric characteristics of the waveguide and the frequency of the incident waves. Notably, the first higher-order mode of the cut-off frequency of the waveguide structure corresponds to the frequency at which the dissipation coefficient reaches its maximum value. This research provides valuable insights into the scattering behavior of acoustic waves in waveguide configurations, contributing to the design of acoustic devices and systems. Rigorous support and justification for all aspects of the mode-matching method, including pressure and velocity matching, eigen properties, physical edge conditions, convergence criteria, and energy conservation, are provided through thorough algebraic and numerical analyses, confirming the validity of the solution methodology.

Transient internal wave excitation of resonant modes in a density staircase

The density of the ocean generally increases continuously with depth as a consequence of variations in salinity and temperature. In some regions, however, the density profile of the ocean adopts a (double diffusive) staircase structure in which successive layers of uniform density fluid are separated by rapid density jumps. Previous work has theoretically examined the transmission and reflection of periodic internal (gravity) waves incident upon a density staircase. This predicted the existence of transmission spikes (global modes) for certain combinations of frequency and horizontal wave number in which the incident waves transmit perfectly across a density staircase. It was hypothesized that the transmission spikes occur when the incident waves resonate with natural modes of disturbances in the staircase. Here we derive theory to investigate the interactions between incident internal waves and modes. We demonstrate a close correspondence between the frequency for incident waves at a transmission spike and the real part of the frequency of modes at the same horizontal wave number. However, the frequency of the corresponding modes has a negative imaginary part corresponding to exponential decay of the modes in time. We perform numerical simulations to examine the impact of this near-resonant coupling when a vertically localized, quasimonochromatic internal wave packet interacts with a density staircase. In a range of simulations with fixed incident wave frequency and varying horizontal wave number, the measured transmission coefficient does not exhibit transmission spikes, but decreases monotonically with increasing horizontal wave number about the critical wave number separating strong and weak transmission. We show this occurs because the incident wave excites modes that then slowly transmit energy above and below the staircase at a rate consistent with the predicted decay rate of the modes. This rate is slower for staircases with more steps with the decay time increasing as the cube of the number of steps. Published by the American Physical Society 2024

Synchronized shock wave and compliant wall interactions: Experimental characterization and aeroelastic modeling

The static and dynamic interaction of a normal shock wave (upstream Mach number 1.35) with a compliant wall is characterized experimentally by schlieren visualizations and an optical displacement sensor. Depending on the location of the shock wave along the compliant wall, three different regimes of interaction are found: large-amplitude synchronized regime, small-amplitude synchronized regime and unsynchronized regime. The regime of large-amplitude synchronized oscillations is found for shock locations close to the mid-point of the compliant wall along the streamwise direction; at this location, the coupled system locks to the second vibration frequency of the structure. Three regimes of small-amplitude synchronized oscillations are found depending on the shock position. When the shock is located upstream the center of the compliant wall, the shock may oscillate either periodically at the frequency of the first vibration mode or quasi-periodically with highest amplitudes at the three frequencies of the vibration modes. When the shock is located downstream the center of the compliant wall, the shock oscillates periodically at the frequency of the third vibration mode. Finally, close to the trailing edge of the compliant wall, the shock oscillation is not synchronized with the compliant wall which oscillates with a very small amplitude. An empirical model is proposed to investigate the energy exchange between the flow and the compliant wall during the limit cycle oscillations. A negative aerodynamic damping – and, hence, the possibility of a limit cycle – is observed when a sufficiently extended separation is considered in the model for the pressure distribution at the wall.