Mechanical Modeling and Analysis of Stability Deterioration of Production Well During Marine Hydrate Depressurization Production

Different from oil and gas production,hydrate reservoirs are shallow and unconsolidated,whose mechanical properties deteriorate with hydrate decomposition.Therefore,the formations will undergo significant subsidence during depressurization,which will destroy the original force state of the production well.However,existing research on the stability of oil and gas production wells assumes the formation to be stable,and lacks consideration of the force exerted on the hydrate production well by formation subsidence caused by hydrate decomposition during production.To fill this gap,this paper proposes an analytical method for the dynamic evolution of the stability of hydrate production well considering the effects of hydrate decomposition.Based on the mechanical model of the production well,the basis for stability analysis has been proposed.A multi-field coupling model of the force state of the production well considering the effect of hydrate decomposition and formation subsidence is established,and a solver is developed.The analytical approach is verified by its good agreement with the results from the numerical method.A case study found that the decomposition of hydrate will increase the pulling-down force and reduce the supporting force,which is the main reason for the stability deterioration.The higher the initial hydrate saturation,the larger the reservoir thickness,and the lower the production pressure,the worse the stability or even instability.This work can provide a theoretical reference for the stability maintaining of the production well.

Effects of connected automated vehicle on stability and energy consumption of heterogeneous traffic flow system

With the development of intelligent and interconnected traffic system,a convergence of traffic stream is anticipated in the foreseeable future,where both connected automated vehicle(CAV)and human driven vehicle(HDV)will coexist.In order to examine the effect of CAV on the overall stability and energy consumption of such a heterogeneous traffic system,we first take into account the interrelated perception of distance and speed by CAV to establish a macroscopic dynamic model through utilizing the full velocity difference(FVD)model.Subsequently,adopting the linear stability theory,we propose the linear stability condition for the model through using the small perturbation method,and the validity of the heterogeneous model is verified by comparing with the FVD model.Through nonlinear theoretical analysis,we further derive the KdV-Burgers equation,which captures the propagation characteristics of traffic density waves.Finally,by numerical simulation experiments through utilizing a macroscopic model of heterogeneous traffic flow,the effect of CAV permeability on the stability of density wave in heterogeneous traffic flow and the energy consumption of the traffic system is investigated.Subsequent analysis reveals emergent traffic phenomena.The experimental findings demonstrate that as CAV permeability increases,the ability to dampen the propagation of fluctuations in heterogeneous traffic flow gradually intensifies when giving system perturbation,leading to enhanced stability of the traffic system.Furthermore,higher initial traffic density renders the traffic system more susceptible to congestion,resulting in local clustering effect and stop-and-go traffic phenomenon.Remarkably,the total energy consumption of the heterogeneous traffic system exhibits a gradual decline with CAV permeability increasing.Further evidence has demonstrated the positive influence of CAV on heterogeneous traffic flow.This research contributes to providing theoretical guidance for future CAV applications,aiming to enhance urban road traffic efficiency and alleviate congestion.

Enhanced High-Temperature Cycling Stability of Garnet-Based All Solid-State Lithium Battery Using a Multi-Functional Catholyte Buffer Layer

The pursuit of safer and high-performance lithium-ion batteries(LIBs)has triggered extensive research activities on solid-state batteries,while challenges related to the unstable electrode-electrolyte interface hinder their practical implementation.Polymer has been used extensively to improve the cathode-electrolyte interface in garnet-based all-solid-state LIBs(ASSLBs),while it introduces new concerns about thermal stability.In this study,we propose the incorporation of a multi-functional flame-retardant triphenyl phos-phate additive into poly(ethylene oxide),acting as a thin buffer layer between LiNi_(0.8)Co_(0.1)Mn_(0.1)O_(2)(NCM811)cathode and garnet electro-lyte.Through electrochemical stability tests,cycling performance evaluations,interfacial thermal stability analysis and flammability tests,improved thermal stability(capacity retention of 98.5%after 100 cycles at 60℃,and 89.6%after 50 cycles at 80℃)and safety characteristics(safe and stable cycling up to 100℃)are demonstrated.Based on various materials characterizations,the mechanism for the improved thermal stability of the interface is proposed.The results highlight the potential of multi-functional flame-retardant additives to address the challenges associated with the electrode-electrolyte interface in ASSLBs at high temperature.Efficient thermal modification in ASSLBs operating at elevated temperatures is also essential for enabling large-scale energy storage with safety being the primary concern.

Interfacial modification using the cross-linkable tannic acid for highly-efficient perovskite solar cells with excellent stability

Although the performance of perovskite solar cells(PSCs)has been dramatically increased in recent years,stability is still the main obstacle preventing the PSCs from being commercial.PSC device instability can be caused by a variety of reasons,including ions diffusion,surface and grain boundary defects,etc.In this work,the cross-linkable tannic acid(TA)is introduced to modify perovskite film through post-treatment method.The numerous organic functional groups(–OH and C=O)in TA can interact with the uncoordinated Pb^(2+)and I^(-)ions in perovskite,thus passivating defects and inhibiting ions diffusion.In addition,the formed TA network can absorb a small amount of the residual moisture inside the device to protect the perovskite layer.Furthermore,TA modification regulates the energy level of perovskite,and reduces interfacial charge recombination.Ultimately,following TA treatment,the device efficiency is increased significantly from 21.31%to 23.11%,with a decreased hysteresis effect.Notably,the treated device shows excellent air,thermal,and operational stability.In light of this,the readily available,inexpensive TA has the potential to operate as a multipurpose interfacial modifier to increase device efficiency while also enhancing device stability.

Significantly enhanced thermal stability of HMX by phase-transition lysozyme coating

A new robust bio-inspired route by using lysozyme aqueous solution for surface modification on 1,3,5,7-tetranitro-1,3,5,7-tetrazocane(HMX)was described in this paper.HMX crystals were coated by in situ phase transition of lysozyme(PTL)molecules.The HMX decorated by PTL was characterized by SEM,XRD,FTIR and XPS,demonstrating a dense core-shell coating layer.The coverage of lysozyme on HMX crystal was calculated by the ratio of sulfur content.The surface coverage increased from 60.5% to 93.5% when the content of PTL was changed from 0.5 wt% to 2.0 wt%,indicating efficient coating.The thermal stability of HMX was investigated by in situ XRD and DSC.The thermal phase transition temperature of HMX(β to δ phase)was delayed by 42℃ with 2.0 wt% PTL coating,which prevented HMX from thermal damage and sensitivity by the effect of PTL coating.After heating at 215℃,large cracks appeared in the naked HMX crystal,while the PTL coated HMX still maintained intact,with the impact energy of HMX dropped dramatically from 5 J to 2 J.However,the impact energy of HMX with 1.0 wt% and 2.0 wt% coating content(HMX@PTL-1.0 and HMX@PTL-2.0)was unchanged(5 J).Present results potentially enable large-scale fabrication of polymorphic energetic materials with outstanding thermal stability by novel lysozyme coating.

Rainfall-triggered waste dump instability analysis based on surface 3D deformation in physical model test

Landslide is the second largest natural disaster after earthquake. It is of significance to study the evolution laws and failure mechanism of landslides based on its surface 3D deformation information. Based on the rainfall-triggered waste dump instability model test, we studied the failure mechanisms of the waste dump by integrating surface deformation and internal slope stress and proposed novel parameters for identifying landslide stability. We developed a noncontact measurement device, which can obtain millimeter-level 3D deformation data for surface scene in physical model test;Then we developed the similar materials and established a test model for a waste dump. Based on the failure characteristics of slope surface, internal stress of slope body and displacement contours during the whole process, we divided the slope instability process in model test into four stages: rainfall infiltration and surface erosion, shallow sliding, deep sliding, and overall instability. Based on the obtained surface deformation data, we calculated the volume change during slope instability process and compared it with the point displacement on slope surface. The results showed that the volume change can not only reflect the slow-ultra acceleration process of slope failure, but also fully reflect the above four stages and reduce the fluctuations caused by random factors. Finally, this paper proposed two stability identification parameters: the volume change rate above the slip surface and the relative velocity of volume change rate. According to the calculation of these two parameters in model test, they can be used for study the deformation and failure mechanism of slope stability.

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

Grassland-type ecosystem stability in China differs under the influence of drought and wet events

Ecological stability is a core issue in ecological research and holds significant implications forhumanity. The increased frequency and intensity of drought and wet climate events resulting from climatechange pose a major threat to global ecological stability. Variations in stability among different ecosystemshave been confirmed, but it remains unclear whether there are differences in stability within the sameterrestrial vegetation ecosystem under the influence of climate events in different directions and intensities.China's grassland ecosystem includes most grassland types and is a good choice for studying this issue.This study used the Standardized Precipitation Evapotranspiration Index-12 (SPEI-12) to identify thedirections and intensities of different types of climate events, and based on Normalized DifferenceVegetation Index (NDVI), calculated the resistance and resilience of different grassland types for 30consecutive years from 1990 to 2019 (resistance and resilience are important indicators to measurestability). Based on a traditional regression model, standardized methods were integrated to analyze theimpacts of the intensity and duration of drought and wet events on vegetation stability. The resultsshowed that meadow steppe exhibited the highest stability, while alpine steppe and desert steppe had thelowest overall stability. The stability of typical steppe, alpine meadow, temperate meadow was at anintermediate level. Regarding the impact of the duration and intensity of climate events on vegetationecosystem stability for the same grassland type, the resilience of desert steppe during drought was mainlyaffected by the duration. In contrast, the impact of intensity was not significant. However, alpine steppewas mainly affected by intensity in wet environments, and duration had no significant impact. Ourconclusions can provide decision support for the future grassland ecosystem governance.

Effects of dietary Clostridium butyricum and rumen protected fat on meat quality,oxidative stability,and chemical composition of finishing goats

Background Clostridium butyricum(CB)is a probiotic that can regulate intestinal microbial composition and improve meat quality.Rumen protected fat(RPF)has been shown to increase the dietary energy density and provide essential fatty acids.However,it is still unknown whether dietary supplementation with CB and RPF exerts beneficial effects on growth performance and nutritional value of goat meat.This study aimed to investigate the effects of dietary CB and RPF supplementation on growth performance,meat quality,oxidative stability,and meat nutritional value of finishing goats.Thirty-two goats(initial body weight,20.5±0.82 kg)were used in a completely randomized block design with a 2 RPF supplementation(0 vs.30 g/d)×2 CB supplementation(0 vs.1.0 g/d)factorial treatment arrangement.The experiment included a 14-d adaptation and 70-d data and sample collection period.The goats were fed a diet consisted of 400 g/kg peanut seedling and 600 g/kg corn-based concentrate(dry matter basis).Result Interaction between CB and RPF was rarely observed on the variables measured,except that shear force was reduced(P<0.05)by adding CB or RPF alone or their combination;the increased intramuscular fat(IMF)content with adding RPF was more pronounced(P<0.05)with CB than without CB addition.The pH24h(P=0.009),a*values(P=0.007),total antioxidant capacity(P=0.050),glutathione peroxidase activities(P=0.006),concentrations of 18:3(P<0.001),20:5(P=0.003)and total polyunsaturated fatty acids(P=0.048)were increased,whereas the L*values(P<0.001),shear force(P=0.050)and malondialdehyde content(P=0.044)were decreased by adding CB.Furthermore,CB supplementation increased essential amino acid(P=0.027),flavor amino acid(P=0.010)and total amino acid contents(P=0.024)as well as upregulated the expression of lipoprotein lipase(P=0.034)and peroxisome proliferator-activated receptorγ(PPARγ)(P=0.012),and downregulated the expression of stearoyl-CoA desaturase(SCD)(P=0.034).The RPF supplementation increased dry matter intake(P=0.005),averaged daily gain(trend,P=0.058),hot carcass weight(P=0.046),backfat thickness(P=0.006),concentrations of 16:0(P<0.001)and c9-18:1(P=0.002),and decreased the shear force(P<0.001),isoleucine(P=0.049)and lysine content(P=0.003)of meat.In addition,the expressions of acetyl-CoA carboxylase(P=0.003),fatty acid synthase(P=0.038),SCD(P<0.001)and PPARγ(P=0.022)were upregulated due to RPF supplementation,resulting in higher(P<0.001)content of IMF.Conclusions CB and RPF could be fed to goats for improving the growth performance,carcass traits and meat quality,and promote fat deposition by upregulating the expression of lipogenic genes of Longissimus thoracis muscle.

Multifunctional interfacial molecular bridge enabled by an aggregation-induced emission strategy for enhancing efficiency and UV stability of perovskite solar cells

The interface defects between the electron transport layer(ETL)and the perovskite layer,as well as the low ultraviolet(UV)light utilization rate of the perovskite absorption layer,pose significant challenges for the commercialization of perovskite solar cells(PSCs).To address this issue,this paper proposes an innovative multifunctional interface modulation strategy by introducing aggregation-induced emission(AIE)molecule 5-[4-[1,2,2-tri[4-(3,5-dicarboxyphenyl)phenyl]ethylene]phenyl]benzene-1,3-dicarboxylic acid(H_(8)ETTB)at the SnO_(2)ETL/perovskite interface.Firstly,the interaction of H_(8)ETTB with the SnO_(2)surface,facilitated by its carboxyl groups,is effective in passivating surface defects caused by noncoord inated Sn and O vacancies.This interaction enhances the conductivity of the SnO_(2)film and adjusts energy levels,leading to enhanced charge carrier transport.Simultaneously,H_(8)ETTB can passivate noncoord inated Pb^(2+)ions at the perovskite interface,promoting perovskite crystallization and reducing the interface energy barrier,resulting in a perovskite film with low defects and high crystalline quality.More importantly,the H_(8)ETTB molecule,can convert UV light into light absorbable by the perovskite,thereby reducing damage caused by UV light and improving the device's utilization of UV.Consequently,the champion PSC based on SnO_(2)-H_(8)ETTB achieves an impressing efficiency of 23.32%and significantly improved photostability compared with the control device after continuous exposure to intense UV radiation.In addition,the Cs_(0.05)(FA_(0.95)MA_(0.05))_(0.95)Pb(I_(0.95)Br_(0.05))_(3)based device can achieve maximum efficiency of 24.01%,demonstrating the effectiveness and universality of this strategy.Overall,this innovative interface bridging strategy effectively tackles interface defects and low UV light utilization in PSCs,presenting a promising approach for achieving highly efficient and stable PSCs.

Stability behavior of the Lanxi ancient flood control levee after reinforcement with upside-down hanging wells and grouting curtain

The stability of the ancient flood control levees is mainly influenced by water level fluctuations, groundwater concentration and rainfalls. This paper takes the Lanxi ancient levee as a research object to study the evolution laws of its seepage, displacement and stability before and after reinforcement with the upside-down hanging wells and grouting curtain through numerical simulation methods combined with experiments and observations. The study results indicate that the filled soil is less affected by water level fluctuations and groundwater concentration after reinforcement. A high groundwater level is detrimental to the levee's long-term stability, and the drainage issues need to be fully considered. The deformation of the reinforced levee is effectively controlled since the fill deformation is mainly borne by the upside-down hanging wells. The safety factors of the levee before reinforcement vary significantly with the water level. The minimum value of the safety factors is 0.886 during the water level decreasing period, indicating a very high risk of the instability. While it reached 1.478 after reinforcement, the stability of the ancient levee is improved by a large margin.

Stability-Considered Lane Keeping Control of Commercial Vehicles Based on Improved APF Algorithm

Regarding the lane keeping system,path tracking accuracy and lateral stability at high speeds need to be taken into account especially for commercial vehicles due to the characteristics of larger mass,longer wheelbase and higher mass center.To improve the performance mentioned above comprehensively,the control strategy based on improved artificial potential field(APF)algorithm is proposed.In the paper,time to lane crossing(TLC)is introduced into the potential field function to enhance the accuracy of path tracking,meanwhile the vehicle dynamics parameters including yaw rate and lateral acceleration are chosen as the repulsive force field source.The lane keeping controller based on improved APF algorithm is designed and the stability of the control system is proved based on Lyapunov theory.In addition,adaptive inertial weight particle swarm optimization algorithm(AIWPSO)is applied to optimize the gain of each potential field function.The co-simulation results indicate that the comprehensive evaluation index respecting lane tracking accuracy and lateral stability is reduced remarkably.Finally,the proposed control strategy is verified by the HiL test.It provides a beneficial reference for dynamics control of commercial vehicles and enriches the theoretical development and practical application of artificial potential field method in the field of intelligent driving.

Construction of core@double-shell structured energetic composites with simultaneously enhanced thermal stability and safety performance

The poor thermal stability and high sensitivity severely hinder the practical application of hexanitrohexaazaisowurtzitane(CL-20).Herein,a kind of novel core@double-shell CL-20 based energetic composites were fabricated to address the above issues.The coordination complexes which consist of natural polyphenol tannic acid(TA) and Fe~Ⅲ were chosen to construct the inner shell,while the graphene sheets were used to build the outer shell.The resulting CL-20/TA-Fe~Ⅲ/graphene composites exhibited simultaneously improved thermal stability and safety performance with only 1 wt% double-shell content,which should be ascribed to the intense physical encapsulation effect from inner shell combined with the desensitization effect of carbon nano-materials from outer shell.The phase transition(ε to γ) temperature increased from 173.70 ℃ of pure CL-20 to 191.87℃ of CL-20/TA-Fe~Ⅲ/graphene composites.Meanwhile,the characteristic drop height(H_(50)) dramatically increased from 14.7 cm of pure CL-20 to112.8 cm of CL-20/TA-Fe~Ⅲ/graphene composites,indicating much superior safety performance after the construction of the double-shell structure.In general,this work has provided an effective and versatile strategy to conquer the thermal stability and safety issues of CL-20 and contributes to the future application of high energy density energetic materials.

Preparation and Thermal Stability of AlMoON Based Solar Selective Absorption Coating

AlMoON based solar selective absorption coatings were deposited on stainless steel substrate by magnetron sputtering.The coatings included infrared reflection layer Mo,absorption layer AlMoN,absorption layer AlMoON and antireflection layer AlMoO from bottom to top.The surface of the deposited coatings is flat without obvious defects.The absorptivity and emissivity are 0.896 and 0.09,respectively,and the quality factor is 9.96.After heat treatment at 500℃-36 h,the surface roughness of the coating increases,a small number of cracks and other defects appear,and the broken part is still attached to the coating surface.A certain degree of element diffusion occurs in the coatings,resulting in the decline of the optical properties of the coatings.The absorptivity and emissivity are 0.883 and 0.131,respectively,the quality factor is 7.06,and the PC value is 0.0335.The coatings do not fail under this condition and have certain thermal stability.

Enhanced stability of nitrogen-doped carbon-supported palladium catalyst for oxidative carbonylation of phenol

Enhancing the stability of supported noble metal catalysts emerges is a major challenge in both science and industry.Herein,a heterogeneous Pd catalyst(Pd/NCF)was prepared by supporting Pd ultrafine metal nanoparticles(NPs)on nitrogen-doped carbon;synthesized by using F127 as a stabilizer,as well as chitosan as a carbon and nitrogen source.The Pd/NCF catalyst was efficient and recyclable for oxidative carbonylation of phenol to diphenyl carbonate,exhibiting higher stability than Pd/NC prepared without F127 addition.The hydrogen bond between chitosan(CTS)and F127 was enhanced by F127,which anchored the N in the free amino group,increasing the N content of the carbon material and ensuring that the support could provide sufficient N sites for the deposition of Pd NPs.This process helped to improve metal dispersion.The increased metal-support interaction,which limits the leaching and coarsening of Pd NPs,improves the stability of the Pd/NCF catalyst.Furthermore,density functional theory calculations indicated that pyridine N stabilized the Pd^(2+)species,significantly inhibiting the loss of Pd^(2+)in Pd/NCF during the reaction process.This work provides a promising avenue towards enhancing the stability of nitrogen-doped carbon-supported metal catalysts.

Stability of the Stratification of Water Bodies in the North Passage of the Yangtze River Estuary Based on the EFDC Model

To study the stratified stability of a water column in the North Passage of the Yangtze River Estuary,a numerical model of the hydrodynamics of this estuary is established using the EFDC model.On the basis of EFDC results,this paper derives and pro-vides the discriminative index of water body stability caused by salinity and analyzes the along-range variation in water body strati-fication stability in the North Passage of the Yangtze River Estuary and the periodic variation at a key location(bend area)based on the simulation results of the numerical model.This work shows that the water body in the bend area varies between mixed and strati-fied types,and the vertical average flow velocity has a good negative correlation with the differential velocity between the surface and bottom layers of the water body.The model simulation results validate the formulae for the stratified stability discriminant during spring tides.

Enhancing capacitive deionization performance and cyclic stability of nitrogen-doped activated carbon by the electro-oxidation of anode materials

Electrode materials with high desalination capacity and long-term cyclic stability are the focus of capacitive deionization(CDI) community. Understanding the causes of performance decay in traditional carbons is crucial to design a high-performance material. Based on this, here, nitrogen-doped activated carbon(NAC) was prepared by pyrolyzing the blend of activated carbon powder(ACP) and melamine for the positive electrode of asymmetric CDI. By comparing the indicators changes such as conductivity, salt adsorption capacity, pH, and charge efficiency of the symmetrical ACP-ACP device to the asymmetric ACP-NAC device under different CDI cycles, as well as the changes of the electrochemical properties of anode and cathode materials after long-term operation, the reasons for the decline of the stability of the CDI performance were revealed. It was found that the carboxyl functional groups generated by the electro-oxidation of anode carbon materials make the anode zero-charge potential(E_(pzc)) shift positively,which results in the uneven distribution of potential windows of CDI units and affects the adsorption capacity. Furthermore, by understanding the electron density on C atoms surrounding the N atoms, we attribute the increased cyclic stability to the enhanced negativity of the charge of carbon atoms adjacent to quaternary-N and pyridinic-oxide-N.

Stability and melting behavior of boron phosphide under high pressure

Boron phosphide(BP)has gained significant research attention due to its unique photoelectric and mechanical properties.In this work,we investigated the stability of BP under high pressure using x-ray diffraction and scanning electron microscope.The phase diagram of BP was explored in both B-rich and P-rich environments,revealing crucial insight into its behavior at 5.0 GPa.Additionally,we measured the melting curve of BP from 8.0 GPa to 15.0 GPa.Our findings indicate that the stability of BP under high pressure is improved within B-rich and P-rich environments.Furthermore,we report a remarkable observation of melting curve frustration at 10.0 GPa.This study will enhance our understanding of stability of BP under high pressure,shedding light on its potential application in semiconductor,thermal,and light-transmitting devices.

Research on the flow stability and noise reduction characteristics of quasi-periodic elastic support skin

To enhance flow stability and reduce hydrodynamic noise caused by fluctuating pressure,a quasiperiodic elastic support skin composed of flexible walls and elastic support elements is proposed for fluid noise reduction.The arrangement of the elastic support element is determined by the equivalent periodic distance and quasi-periodic coefficient.In this paper,a dynamic model of skin in a fluid environment is established.The influence of equivalent periodic distance and quasi-periodic coefficient on flow stability is investigated.The results suggest that arranging the elastic support elements in accordance with the quasi-periodic law can effectively enhance flow stability.Meanwhile,the hydrodynamic noise calculation results demonstrate that the skin exhibits excellent noise reduction performance,with reductions of 10 dB in the streamwise direction,11 dB in the spanwise direction,and 10 dB in the normal direction.The results also demonstrate that the stability analysis method can serve as a diagnostic tool for flow fields and guide the design of noise reduction structures.

Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Self-oscillating systems abound in the natural world and offer substantial potential for applications in controllers,micro-motors,medical equipments,and so on.Currently,numerical methods have been widely utilized for obtaining the characteristics of self-oscillation including amplitude and frequency.However,numerical methods are burdened by intricate computations and limited precision,hindering comprehensive investigations into self-oscillating systems.In this paper,the stability of a liquid crystal elastomer fiber self-oscillating system under a linear temperature field is studied,and analytical solutions for the amplitude and frequency are determined.Initially,we establish the governing equations of self-oscillation,elucidate two motion regimes,and reveal the underlying mechanism.Subsequently,we conduct a stability analysis and employ a multi-scale method to obtain the analytical solutions for the amplitude and frequency.The results show agreement between the multi-scale and numerical methods.This research contributes to the examination of diverse self-oscillating systems and advances the theoretical analysis of self-oscillating systems rooted in active materials.