Wave Characteristics Research Articles

Tight focusing of terahertz vortex beams formed by laser dielectric resonator

Wave characteristics of vortex laser beams during their tight focusing have been theoretically studied. The Rayleigh–Sommerfeld theory was used to describe propagation in free space of laser beams excited by the modes of a waveguide dielectric resonator. It is shown that at the topological charge of the spiral phase plate n = 0, the studied EH11 mode has a maximum of radiation intensity on the axis. Introduction of a topological charge leads to the appearance of a minimum of radiation intensity on the axis as well as to the increase in the size of the focal spot. However, for the TE01 mode with the topological charges n = 0 and n = 2, the intensity distribution retains a ring shape, while at n = 1 the beam profile turns into the Gaussian-like one. The wave front in the focal region of the lens for the components of the EH11 and TE01 modes transforms from spherical to spiral one with increasing the topological charge.

Response Patterns of Acoustic Wave Characteristics to Reservoir Petrophysical Parameters in Different Bedding Directions: A Case Study of Low- and Middle-Rank Coals in Xinjiang, China.

The physical properties of coal reservoirs, important parameters for evaluating the production potential of coalbed methane (CBM) resources, can be assessed nondestructively and in real-time using acoustic wave technology. In this study, we collected 48 low- and middle-rank coal samples oriented in different bedding directions from seven typical coal mines, encompassing the Zhunan, Tuha, and Kuqa-Bay coalfields in Xinjiang, China. We clarified the characteristics of the physical parameters (apparent density, fracture, porosity, and permeability) and acoustic wave of coal variations through acoustic wave, porosity, and permeability experiments, revealing the response law of acoustic wave characteristics to the physical parameters of coal. The results indicated that the acoustic wave velocity and dynamic elastic modulus (E d) of coal samples oriented in the perpendicular bedding direction are larger than those oriented in the parallel bedding direction; however, the dynamic Poisson's ratio (μd) of coal samples oriented in different bedding directions does not significantly differ. The existence of fractures significantly reduces the acoustic wave velocity and E d of the coal. The greater the apparent density of coal, the tighter its structure, resulting in a faster acoustic wave velocity. The larger the porosity of coal, the greater its internal voids, leading to a more pronounced attenuation of acoustic energy and a slower acoustic wave velocity. The more developed and interconnected the bedding fractures of coal bodies oriented in the parallel bedding direction, the higher their permeability, resulting in a smaller decrease in acoustic wave velocity. Conversely, the more developed the bedding fractures of coal bodies oriented in the perpendicular bedding direction, the more pronounced their attenuation of acoustic wave velocity. Finally, the regression equations for E d with the square of P-wave velocity (V P 2) and μd with the square ratio of V P to S-wave velocity (V P 2/V S 2) were established for coal. The study findings can help evaluate and predict the reservoir quality of coal seams, assess CBM, and improve the safety and efficiency of its extraction.

Study on the Effect of Liquefiable Overburden Foundations of Rockfill Dams Based on a Pore Pressure Model

China’s southwestern region boasts abundant hydropower resources. However, the area is prone to frequent strong earthquakes. The areas surrounding dam sites typically have deep overburden, and the liquefaction of saturated sand foundations by earthquakes poses significant safety risks to the construction of high dams in the southwest. The effects of liquefaction and reinforcing measures on the foundations of rockfill dams on liquefiable overburden under seismic action are currently the subject of somewhat unsystematic investigations. The paper utilizes the total stress and effective stress methods, based on the equivalent linear model, to perform numerical simulations on the overburden foundations of rockfill dams. The study explores how factors such as dam height, overburden thickness, liquefiable layer depth, liquefiable layer thickness, ground motion intensity, and seismic wave characteristics affect the liquefaction of the overburden foundations. Additionally, it examines how rockfill dams impact the dynamic response, considering the liquefaction effects in the overburden. The results show that although the total stress method, which ignores the cumulative evolution of pore pressure during liquefaction, can reveal the basic response trend of the dam, its results in predicting the acceleration response are significantly biased compared to those of the effective stress method, which comprehensively considers the cumulative changes in liquefaction pore pressure. Specifically, when the effect of soil liquefaction is considered, the predicted acceleration response is reduced compared to that when liquefaction is not considered, with the reduction ranging from 4% to 30%; with increases in the thickness and burial depth of the liquefiable layer, the effective stress method considering liquefaction significantly reduces the predicted peak acceleration; the effect of liquefiable soil on the attenuation of the speed response is more sensitive to the low-frequency portion of the seismic wave. The study’s findings are a significant source of reference for the planning and building of rockfill dams on liquefiable overburden.

Nonlinear Seismic Response of Tunnel Structures under Traveling Wave Excitation

Tunnels traditionally regarded as resilient to seismic events have recently garnered significant attention from engineers owing to a rise in incidents of seismic damage. In this paper, the reflection characteristics of the elastic plane wave incident on the free surface are analyzed, and the matrix analysis method SWIM (Seismic Wave Input Method) for the calculation of equivalent nodal loads with artificial truncated boundary conditions for seismic wave oblique incidence is established by using coordinate transformation technology, according to the displacement velocity and stress characteristics of a plane wave. The results show that the oblique incidence method is more effective in reflecting the traveling wave effect, and the “rotational effect” induced by oblique incidence must be considered for P wave and SV wave incidence, including the associated stress and deformation. This effect exhibits markedly distinct rotational phenomenon. In particular, the P wave incidence should be focused on the vault and the inverted arch due to the expansion wave. With the increase of the oblique incidence angle, the structural stress and deformation are rotated to a certain extent, and the values are significantly increased. Simultaneously, the shear action of the SV wave may result in “ovaling” of the tunnel structure, thereby facilitating damage to the arch shoulder and the sidewall components. As the oblique incidence angle, the potentially damaging effects of the “rotational effect” to the vault and the inverted arch, but the numerical value does not change significantly. In addition, in comparison to a circular cross-section, the low-frequency amplification of seismic waves in the surrounding rock and the difference of frequency response function in different parts of the lining are more pronounced. In particular, the dominant frequency characteristics are significant at P wave incidence and the seismic wave signal attenuation tends to be obvious with increasing incidence angle. In contrast, SV waves exhibit more uniform characteristics.

Rayleigh Waves in a Thermoelastic Half-Space Coated by a Maxwell–Cattaneo Thermoelastic Layer

This paper investigates the propagation of in-plane surface waves in a coated thermoelastic half-space. First, it investigates a special case where the surface layer is described by the Maxwell–Cattaneo thermoelastic approach, while the half-space is filled by a thermoelastic material described by the classical Fourier law for the heat flux. The contact between the layer and the half-space is assumed to be welded, i.e., the displacements and the temperature, as well as the stresses and the heat flux are continuous through the interface of the layer and the half-space. The boundary and continuity conditions of the problem are formulated and then the exact dispersion relation of the surface waves is established. An illustrative numerical simulation is presented for the case of an aluminum thermoelastic layer coating a thermoelastic copper half-space, highlighting important aspects regarding the propagation of Rayleigh waves in such structures. The exact effective boundary conditions at the interface are also established replacing the entire effect of the layer on the half-space. The general case of the problem is also investigated when both the surface layer and the half-space are described by the Maxwell–Cattaneo thermoelasticity theory. This study helps to further understand the propagation characteristics of elastic waves in layered structures with thermal effects described by the Maxwell–Cattaneo approach.

Identification and Application of Wave Field Characteristics of Channel Waves in Extra-Thick Coal Seams

Channel wave seismic activity often occurs with thin and medium-thick coal seams being the main target layer. To address the problem of channel wave applicability detection in extremely thick coal seams, the propagation and identification characteristics of channel waves remain the focus of research. Therefore, this paper takes the in-seam wave exploration of a 27 m extremely thick coal seam as an example and uses the staggered mesh finite difference method to construct a three-dimensional medium model for numerical simulation. An analysis of the physical parameters of coal and rock, along with the dispersion characteristics of channel waves in extra-thick coal seams, is utilized, through the Zoeppritz equation and the total reflection propagation method, to calculate the imaging. We found the following: (1) The dispersion areas and weak dispersion areas along the detection direction are extremely thick coal seams. (2) There are apparent channel waves in extra-thick coal seams, with a waveform similar to body waves; the length of the wave train is shorter than that of the conventional channel wave, and the arrival time can be estimated accurately. The amplitude of the apparent channel wave is affected by the degree of dispersion, with lower attenuation and higher resolution. The characteristic of total reflection in extremely thick coal seams is that the incident angle is equal to the critical angle, and the dispersion characteristics are weak. (3) The channel waves with weak dispersion characteristics in extra-thick coal seams are mainly Love-type waves.

CFD Analyses of Density Gradients under Conditions of Supersonic Flow at Low Pressures.

This paper deals with CFD analyses of the difference in the nature of the shock waves in supersonic flow under atmospheric pressure and pressure conditions at the boundary of continuum mechanics for electron microscopy. The first part describes the verification of the CFD analyses in combination with the experimental chamber results and the initial analyses using optical methods at low pressures on the boundary of continuum mechanics that were performed. The second part describes the analyses on an underexpanded nozzle performed to analyze the characteristics of normal shock waves in a pressure range from atmospheric pressure to pressures at the boundary of continuum mechanics. The results obtained by CFD modeling are prepared as a basis for the design of the planned experimental sensing of density gradients using optical methods, and for validation, the expected pressure and temperature courses from selected locations suitable for the placement of temperature and pressure sensors are prepared from the CFD analyses.

Characterization of an Advanced Blast Simulator for Investigation of Large Scale Blast Traumatic Brain Injury Studies.

Blast traumatic brain injury (bTBI) is a prominent military health concern. The pervasiveness and long-term impacts of this injury highlight the need for investigation of the physiological outcomes of bTBI. Preclinical models allow for the evaluation of behavioral and neuropathological sequelae associated with bTBI. Studies have implemented rodent models to investigate bTBI due to the relative small size and low cost; however, a large animal model with similar neuroanatomical structure to humans is essential for clinical translation. Small blast simulators are used to induce bTBI in rodents, but a large animal model demands a larger device. This study describes a large advanced blast simulator (ABS4) that is a gas-detonation-driven system consisting of 5 sections totaling 40ft in length with a cross-section of 4 × 4 ft at the test section. It is highly suitable for large animals and human surrogate investigations. This work characterized the ABS4 in preparation of large-scale bTBI testing. An array of tests were conducted with target overpressures in the test section ranging from 10 to 50 psi, and the pressure-time profiles clearly illustrate the essential characteristics of a free-field blast wave, specifically a sharp peak pressure and a defined negative phase. Multiple blast tests conducted at the same target pressure produced very similar pressure profiles, exhibiting the reproducibility of the ABS4 system. With its extensive range of pressures and substantial size, the ABS4 will permit military-relevant translational blast testing.

A higher dimensional model of geophysical fluid with the complete Coriolis force and vortex structure

Here, we present a higher dimensional model from the vorticity equation, which describes the dynamic characteristics of large scale Rossby waves by utilizing the Gardner-Morikawa coordinate transformation and the perturbation method. To reveal the influence of physical parameters on the higher dimensional model, we first give the dispersion relation of the model and the N-soliton solutions by Hirota method. Subsequently, the lump solutions are derived by using the long wave limit method. It demonstrates that the horizontal component of the Coriolis force acts as a forcing force on the nonlinear Rossby waves, and affects the amplitude of the meridional structure. Moreover, under the background of secondary zonal basic flow, for different lump solutions, the flow field will appear dipole blocking or double vortex structure. It is also indicated that the horizontal Coriolis force only causes the vortex to move in the latitudinal direction.

Classical and nonclassical Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to a 3D-modified nonlinear wave equation in liquid involving gas bubbles

The current paper undertakes an in-depth exploration of the dynamics of nonlinear waves governed by a 3D-modified nonlinear wave equation, a significant model in the study of complex wave phenomena. To this end, the study employs both classical and nonclassical Lie symmetries for rigorously deriving invariant solutions of the governing equation. These symmetries enable the formal construction of exact solutions, which are crucial for understanding the complex behavior of the model. Furthermore, the research extends into the realm of bifurcation analysis through the application of planar dynamical system theory. Such an analysis reveals the conditions under which the 3D-modified nonlinear wave equation admits Jacobi elliptic function solutions. The study also delves into the impact of the nonlinear parameter on the physical characteristics of bright and kink solitary waves as well as continuous periodic waves using Maple. Overall, the comprehensive analysis presented not only enhances the understanding of complex nonlinear wave dynamics but also sets the stage for future advancements in vast areas of fluid dynamics and plasma physics.

Effect of combined treatments of hydrolysis and succinylation on the solubility and emulsion stability of rennet casein and micellar casein

Casein is the most abundant protein in milk with good emulsifying properties and bioavailability. However, the tight micellar structure of casein results in poor solubility. In the case of soft solid materials such as processed cheese, imitation cheese, yoghurt and protein-based oil-in-water emulsions, poor solubility directly affects the homogeneity and stability of the texture structure of such products, leading to a poor user experience. In this study, two protein modification techniques, hydrolysis and succinylation, were combined to improve the solubility of casein and the stability of its emulsions. The individual and combined effects of enzymatic hydrolysis and succinylation modification approaches on the stability of rennet casein (RC) and micellar casein (MC) emulsions were further explored. After double-treatment of casein with enzymatic hydrolysis and succinylation, the solubility of RC and MC was up to about 95 %, which was superior to that of single-treatment. Fourier transform infrared spectroscopy showed that the characteristic wave signals of the double-treated samples were located between the two single-treated samples, and that there may be an opposite effect between the two modifications. After 21 days of storage, the emulsions prepared from double-treated caseins still remained stable. The salt ionic stability and freeze-thaw stability were significantly improved, and the physical stability of MC was increased by nearly three times. The results explained the effects of enzymatic hydrolysis and succinylation on the functional properties of casein, provided a reference for the development of food systems based on oil-in-water emulsions, and offered a new idea for the wide application of succinylated casein.

Propagation Characteristics of Electrostatic Surface Plasma Waves at the Spin‐Polarized Quantum Plasma–Vacuum Interface

ABSTRACTThis investigation explores the characteristics of electrostatic surface plasma waves within the framework of a spin‐polarized quantum plasma. Utilizing the spin‐polarized quantum hydrodynamic model and incorporating essential elements like Fermi pressure and Bohm potential, we derive the dispersion relation governing surface plasma waves at a plasma–vacuum interface. Through Fourier decomposition of the hydrodynamic model, we establish the dispersion relation that outlines the behavior of surface plasmons under conditions of small amplitude. Quantum effects, encompassing degenerate pressure, and Bohm potential are considered with specific attention given to the spin polarization effect, treating spin up, and spin down electrons as distinct species. The resulting dispersion relation demonstrates that, regardless of the degree of spin matching, Bohm potential significantly alters the phase speed in the limit of a large wave vector. Increasing spin mismatch in the quantum plasma leads to a decrease in the phase speed of the surface mode for a fixed value of the plasmonic coupling parameter . Our findings bear relevance to graphene‐based plasmonic systems, aligning with some of the observations reported in Gao et al. (2013) and Guo et al. (2019).

A Roadmap for NF-ISAC in 6G: A Comprehensive Overview and Tutorial.

Near-field (NF) integrated sensing and communication (ISAC) has the potential to revolutionize future wireless networks. It enables simultaneous communication and sensing operations on the same radio frequency (RF) resources using a shared hardware platform, maximizing resource utilization. NF-ISAC systems can improve communication and sensing performance compared to traditional far-field (FF) ISAC systems by exploiting the unique propagation characteristics of NF spherical waves with an additional distance dimension. Despite its potential, NF-ISAC research is still in its early stages, and a comprehensive survey of the technology is lacking. This paper systematically explores NF-ISAC technology, providing an in-depth analysis of both NF and FF systems, their applicability in various scenarios, and different channel models. It highlights the advantages and philosophies of ISAC, examining both narrow-band and wide-band NF-ISAC systems. Case studies and simulations offer deeper insights into NF-ISAC design philosophies. Additionally, the paper reviews the existing NF-ISAC literature, methodologies, potentials, and conclusions, and discusses future research areas, challenges, and applications.

Role of seismogeological modeling in the attribute analysis of seismic data using the example of the forecast of the thickness of the Yu3t formation of the southwestern Kazakhatsan oil field

Relevance. The need to introduce the results of two-dimensional seismogeological modeling into seismic data attribute interpretation to identify signs of manifestation of the target object of the forecast in the wave field of seismic recording and assess the influence of interference of the host strata on it. Object. Highly productive terrigenous Upper Jurassic Yu3t formation of the Nizhnekumkol formation of the oil field of southwestern Kazakhstan, formed under conditions of a cone of liquid proluvial fan. Aim. To assess the impact of the interaction of the enclosing strata of the Upper Jurassic Yu3t formation on the seismogeological forecast of its capacities within the considered oil field. Methods. Two-dimensional seismogeological modeling based on the analysis of the frequency response and determination of the shape of the elementary pulse of seismic recording in the interval of the productive formation. Analysis of the thicknesses of geological inhomogeneities overlying the Yu3t formation in order to assess their effect on the wave characteristic of the time interval of research. Results. The performed two-dimensional seismogeological modeling showed that the amplitude characteristic of the negative phase of the wave packet of the target object, characterizing the power of the Yu3t formation, is affected to varying degrees by the overlapping thicknesses of the Yu3a formation and the inter-reservoir seal P1. Based on the modeling results, it was concluded that the basis for predicting the thickness of the Yu3t formation should be considered an attribute map of the difference in amplitudes of the upper positive (A) and average negative (B) phases of the considered wave packet A, B, C. At the same time, the correlation dependences of the obtained attribute with the values of the thickness of the Yu3t formation in drilled wells should be considered within the areas outside the zone the influence of other elements complicating the wave pattern of the target object (tectonic disturbances and erosive protrusions of the foundation).

Signal quality evaluation of an in-ear EEG device in comparison to a conventional cap system.

Wearable in-ear electroencephalographic (EEG) devices hold significant promise for integrating brain monitoring technologies into real-life applications. However, despite the introduction of various in-ear EEG systems, there remains a necessity for validating these technologies against gold-standard, clinical-grade devices. This study aims to evaluate the signal quality of a newly developed mobile in-ear EEG device compared to a standard scalp EEG system among healthy volunteers during wakefulness and sleep. The study evaluated an in-ear EEG device equipped with dry electrodes in a laboratory setting, recording a single bipolar EEG channel using a cross-ear electrode configuration. Thirty healthy participants were recorded simultaneously using the in-ear EEG device and a conventional EEG cap system with 64 wet electrodes. Based on two recording protocols, one during a resting state condition involving alternating eye opening and closure with a low degree of artifact contamination and another consisting of a daytime nap, several quality measures were used for a quantitative comparison including root mean square (RMS) analysis, artifact quantification, similarities of relative spectral power (RSP), signal-to-noise ratio (SNR) based on alpha peak criteria, and cross-signal correlations of alpha activity during eyes-closed conditions and sleep activities. The statistical significance of our results was assessed through nonparametric permutation tests with False Discovery Rate (FDR) control. During the resting state, in-ear and scalp EEG signals exhibited similar fluctuations, characterized by comparable RMS values. However, intermittent signal alterations were noticed in the in-ear recordings during nap sessions, attributed to movements of the head and facial muscles. Spectral analysis indicated similar patterns between in-ear and scalp EEG, showing prominent peaks in the alpha range (8-12 Hz) during rest and in the low-frequency range during naps (particularly in the theta range of 4-7 Hz). Analysis of alpha wave characteristics during eye closures revealed smaller alpha wave amplitudes and slightly lower signal-to-noise ratio (SNR) values in the in-ear EEG compared to scalp EEG. In around 80% of cases, cross-correlation analysis between in-ear and scalp signals, using a contralateral bipolar montage of 64 scalp electrodes, revealed significant correlations with scalp EEG (p < 0.01), particularly evident in the FT11-FT12 and T7-T8 electrode derivations. Our findings support the feasibility of using in-ear EEG devices with dry-contact electrodes for brain activity monitoring, compared to a standard scalp EEG, notably for wakefulness and sleep uses. Although marginal signal degradation is associated with head and facial muscle contractions, the in-ear device offers promising applications for long-term EEG recordings, particularly in scenarios requiring enhanced comfort and user-friendliness.

Measurement Method of Stress in High-Voltage Cable Accessories Based on Ultrasonic Longitudinal Wave Attenuation.

High-voltage cables are the main arteries of urban power supply. Cable accessories are connecting components between different sections of cables or between cables and other electrical equipment. The stress in the cold shrink tube of cable accessories is a key parameter to ensure the stable operation of the power system. This paper attempts to explore a method for measuring the stress in the cold shrink tube of high-voltage cable accessories based on ultrasonic longitudinal wave attenuation. Firstly, a pulse ultrasonic longitudinal wave testing system based on FPGA is designed, where the ultrasonic sensor operates in a single-transmit, single-receive mode with a frequency of 3 MHz, a repetition frequency of 50 Hz, and a data acquisition and transmission frequency of 40 MHz. Then, through experiments and theoretical calculations, the transmission and attenuation characteristics of ultrasonic longitudinal waves in multi-layer elastic media are studied, revealing an exponential relationship between ultrasonic wave attenuation and the thickness of the cold shrink tube. Finally, by establishing a theoretical model of the radial stress of the cold shrink tube, using the thickness of the cold shrink tube as an intermediate variable, an effective measurement of the stress of the cold shrink tube was achieved.

Propagation characteristics of show sea seismic wave in different underwater media

The propagation characteristics of sea seismic wave (SSSW) in different underwater media are different. This study mainly focuses on the propagation characteristics of SSSW in different underwater media to improve the detection ability of SSSW mines. The propagation of SSSW in different underwater media, including clay, sandy clay, sandstone, mudstone, hard stone, and dolomite, is simulated using the staggered grid finite difference method. The dispersive energy maps of different underwater media are extracted using the f-k dispersive energy extraction method. Compared with the results of Scholte wave dispersion characteristic equations, the simulation results are consistent with the theoretical results. At the same time, the attenuation law of the SSSW train is obtained. The results provide a theoretical basis for developing SSSW mine fuses.

Rayleigh wave propagation in a modified couple stress visco-thermoelastic diffusion medium

The present investigation is devoted to Rayleigh wave propagation in modified couple stress visco-thermoelastic medium with mass diffusion under Lord–Shulman and Green–Lindsay theories of thermoelasticity. After formulating the problem mathematically, the secular equation is derived for stress free, insulated, and impermeable boundary. The wave characteristics like phase velocity and attenuation coefficient have been obtained numerically by developing numerical algorithm. For a particular material, the numerically simulated results are shown graphically to display the physical meaning of the phenomenon. The current inquiry also leads to several specific cases of interest. A comparison has been conducted with the earlier findings that suggested how the additional parameters might affect the phenomena of Rayleigh waves propagating. The results obtained indicate to the strong impact for the diffusivity and viscosity of Rayleigh thermoelastic waves propagation and applicable on the related phenomenon in geology, geophysics, acoustics, astronomy, and geophysics and agreement with the physical meaning of the phenomenon.

The coupled band gap of longitudinal wave in metamaterial-based double-rod containing resonators

This study investigates the coupled band gap and vibration propagation characteristics of elastic waves in a metamaterial elastic double-rod system with attached periodic resonators. We derive the band gap structure and vibration attenuation equations of double-rod structure using the spectral element method, Bloch’s theorem, and the transfer matrix method. The validity of the coupled band gap is confirmed through forced vibration response analysis. Furthermore, we examine the effects of various parameters on the double-rod system, revealing that coupled band gaps exist with the average vibration attenuation rates of −50.23 dB for rod one and −47.87 dB for rod two, respectively. Remarkably, by adjusting the double-rod parameters, both the band gap frequency range and vibration attenuation ability of the coupled band gap can be adjusted to meet specific engineering requirements in low-frequency regions. This research contributes to developing continuous mechanical structures featuring coupled band gaps.

Identification of flame transfer function and mechanism analysis of the influence of boundary impedance characteristics on thermoacoustic instability

Thermoacoustic instability is a common problem in the operation of modern gas turbines. The prediction of thermoacoustic instability and the clarification of its mechanism are the research focus and difficulty in the gas turbine industry. As a response function of flame to acoustic disturbance, flame transfer function is a key parameter in the study of thermoacoustic instability. In this paper, based on the scaled adaptive simulation (SAS) model combined with the eddy dissipation concept (EDC) combustion model, the time-domain flow field data are processed by the system identification method, and the results of flame transfer function extraction are in good agreement with the experimental values. Then, the detailed derivation process of the low-order thermoacoustic network model (LOTAN) is given to capture the behavior characteristics of the acoustic wave in the thermoacoustic system. On this basis, the effects of acoustic boundary conditions and hysteresis time on the thermoacoustic instability of the combustion system are analyzed, and the relationship between the mode shape, pressure, vibration velocity phase, and thermoacoustic instability is explored. It is found that the phase relationship between pressure and vibration mode can be used to determine the thermoacoustic instability of the system. This is of great practical significance for determining the thermoacoustic instability of the system and clarifying the internal mechanism of its generation and provides theoretical support for the subsequent thermoacoustic instability control.