Critical Speed Research Articles

Wind-induced response and control criterion of the double-layer cable support photovoltaic module system

The cable support photovoltaic module system has obvious characteristics of wind-induced vibration. In order to study the wind-induced vibration response characteristics and mechanism of the double-cable support photovoltaic module systems, and further discuss the stiffness control criterion. The wind-induced vibration response of a new type of cable-truss support photovoltaic module system with a span of 35m is studied through the aeroelastic wind tunnel test. Firstly, the scaled aeroelastic test model was established to meet the aeroelastic test requirements. Then, the effects of wind direction, PV module inclination angle, and stability cable initial prestress on the wind-induced vibration response characteristics under uniform flow and turbulent field are studied. Finally, the wind-induced vibration response mechanism and stiffness control criterion are discussed. The results show that the increase of inclination angle will lead to a decrease in critical wind speed, the 0° wind direction is the most unfavorable, and the increase of initial prestress can increase the critical wind speed but is inefficient. The critical wind speed under the turbulent flow field is about 30% higher than that of the uniform flow field. The instability vibration is the result of multi-mode coupled vibration of vertical bending and torsion. It is suggested that the stiffness control criterion is more appropriate as 1/100. The research results are of great significance for the design and application of the cable support photovoltaic module system.

Stiffness Optimization of Squirrel Cage in Aircraft Engines

squirrel cage is a component used in engine shafts to make the shaft stiffer and able to withstand high cycle fatigue loads continuously for a long time. A squirrel cage can be of many shapes and sizes. The critical speed and the stresses acting on the shaft play a key role in determining the performance of shafts in engines. The squirrel cage in the shaft absorbs stress and extends shaft life. This paper deals with the structural design and analysis of the squirrel cage of an aircraft engine. The design of the squirrel cage was done on SolidWorks, and analysis was carried out on the Ansys workbench. To meet the strength and stiffness, the squirrel cage was optimized by introducing slots in it. Stress analysis of the bearings has been carried out for axial and radial loads from 1 to 20 kg. The radial load is applied to individual bearings, and then the axial load is applied to only one bearing. Then results are plotted into curves, and a slope is obtained based on deformations obtained. The stiffness value is noted, and the same procedure is performed for an optimized slotted squirrel cage. These values are compared, and then the squirrel is proved to be weight optimized and has improved stiffness.

Height Control System for Wind Turbines Based on Critical Wind Speed Calculation

The increasing frequency of wind turbine failures due to extreme weather conditions necessitates the implementation of new solutions to enhance their operational reliability. This paper presents an automatic rotor drop system specifically designed for wind turbines equipped with the Onipko rotor. The system aims to protect turbines from damage caused by critical wind speeds, reducing maintenance costs and extending the equipment’s lifespan. The unique design of the Onipko rotor allows it to operate at wind speeds as low as 0.1 m/s. However, its high drag coefficient and lack of aerodynamic optimization make it susceptible to mechanical stress and structural instability under strong gusts, requiring additional protective measures. The paper presents a calculation of the critical wind speed at which protective measures must be initiated. Through mathematical modeling, this study demonstrates the effectiveness of the rotor drop system in ensuring safe operation at wind speeds reaching 23.5 m/s. The optimization of the PI controller parameters provides a rapid response and stability, significantly enhancing the resilience of wind turbines to adverse weather conditions.

Rub-impact investigation of a bolted joint rotor-bearing system considering hysteresis behavior at mating interface

Hysteresis behavior at the mating interface can induce nonlinear stiffness and frictional dissipation, which may lead to a complex vibration character, self-excited vibration, and even the rubbing fault for the bolted joint rotor system. The present work aims to investigate the effect mechanism of hysteresis behavior on the rotor dynamics and the mechanism of bolted joint performance change induced by a rubbing fault. Firstly, the bolted joint model considering the hysteresis behavior at the mating interface is proposed based on the Iwan model. Then, a non-dimensional dynamic model of the bolted joint rotor system with rubbing fault is established by combining the lumped-mass method and fixed-point rub-impact force model. After that, the nonlinear response of the bolted joint rotor system considering the hysteresis behavior at the mating interface and the effect of rubbing fault on the dynamic performance of such a rotor system is explored. Finally, an experimental verification is carried out by adopting a rotor system test rig with a different stiffness rubbing device. The result shows that the rubbing fault will reduce the critical speed by changing the equivalent average stiffness of the bolted joint and aggravate the self-excited vibration of the system, leading to a stronger nonlinear performance of the rotor system. The outcome of the present work can provide valuable insights into vibration prediction, health detection, and rubbing fault diagnosis for a rotor system with a bolted joint.

Establishment of a dexamethasone-induced zebrafish skeletal muscle atrophy model and exploration of its mechanisms

BackgroundSkeletal muscle atrophy is one of the main side effects of high-dose or continuous use of glucocorticoids (such as dexamethasone). However, there are limited studies on dexamethasone-induced skeletal muscle atrophy in zebrafish and even fewer explorations of the underlying molecular mechanisms. This study aimed to construct a model of dexamethasone-induced skeletal muscle atrophy in zebrafish and to investigate the molecular mechanisms. MethodsZebrafish soaked in 0.01 % dexamethasone solution for 10 days. Loli Track (Denmark) and Loligo Swimming Respirometer were used to observe the effect of dexamethasone on swimming ability. The effects of dexamethasone on zebrafish skeletal muscle were observed by Transmission electron microscopy, H&E, and wheat germ agglutinin techniques. Enriched genes and signaling pathways were analyzed using Transcriptome sequencing. Further, the levels of mitochondrial and endoplasmic reticulum-related proteins were examined to investigate possible mechanisms. Results0.01 % dexamethasone reduced zebrafish skeletal muscle mass (p < 0.05), myofibre size and cross-sectional area (p < 0.001), and increased protein degradation (ubiquitination and autophagy) (p < 0.05). In addition, 0.01 % dexamethasone reduced the swimming ability of zebrafish, as evidenced by the reluctance to move, fewer movement trajectories, decreased total distance traveled (p < 0.001), average velocity of movement (p < 0.001), oxygen consumption (p < 0.001), critical swimming speed (p < 0.01) and increased exhaustive swimming time (p < 0.001). Further, 0.01 % dexamethasone-induced mitochondrial dysfunction (decreased mitochondrial biogenesis, disturbs kinetic homeostasis, increased autophagy) and endoplasmic reticulum stress. Conclusions0.01 % dexamethasone induces skeletal muscle atrophy and impairs the swimming ability of zebrafish through mitochondrial dysfunction and endoplasmic reticulum stress.

The Effect of Dam Break Speed on Flood Evolution in a Downstream Reservoir of a Cascade Reservoir System

The dam break flood is one of the potential causes of catastrophic events in cascade hydropower hub groups. Investigating the movement patterns of dam break flooding among reservoir groups under different dam break speeds is crucial for flood prevention and emergency response. In this study, the evolution characteristics of dam break floods were investigated in a cascading reservoir system, focusing on different break speeds of the upstream dam. The results indicate that the dam break speed determines the concavity or convexity of the water level curve changes in the upstream reservoir. Accordingly, dam breaks are classified into three modes: instant dam break, fast dam break, and slow dam break. An approximate critical speed has been identified to differentiate between the fast dam break and slow dam break. Further investigation into the evolution patterns of dam break floods in downstream reservoirs under different break modes was conducted. Correspondingly, the flood peak discharge and peak arrival time of the dam break floods vary differently with break speed under different break modes. Finally, a theoretical analysis for the flood peak discharge at the dam site during gradual dam break at a certain speed was established, which is able to predict the over-dam flood peak discharge in fast and slow dam break modes. This study is based on a combination of laboratory flume experiments and three-dimensional numerical simulations. This study has theoretical significance for the reinforcement of public infrastructure safety and the prevention of natural disasters.

Comparative Analysis of Boron-Al Metal Matix Composite and Aluminum Alloy in Enhancing Dynamic Performance of Vertical-Axis Wind Turbine

This study aims to assess the dynamic performance of the vertical-axis wind turbine (VAWT) with the help of conventional aluminum (Al) and the boron Al metal matrix composite (MMC). The simulations were conducted using ANSYS software and involved natural frequencies, mode shapes, a mass participation factor, and Campbell plots. The results of static structural analysis show that the boron Al MMC is vastly superior to the aluminum alloy because there is a 65% reduction of equivalent stress with a 70% reduction of deformation compared to the aluminum alloy. These results show that boron Al MMC can withstand higher loads with lesser stress; the structure remains compact and rigid in its working conditions. From the findings, it can be ascertained that employing boron Al MMC improves VAWT power, efficiency, and robustness. However, the critical speed that was established in the dynamic analysis of boron Al MMC requires extraordinary control and the use of dampening systems, thereby avoiding resonance. Overall, boron Al MMC contributes to significant enhancements in the VAWTs’ mechanical and operational characteristics; however, the material’s complete potential can be achieved only with proper maintenance and employing the correct damping techniques. Information about these two materials will allow for a better understanding of their comparative efficacy and their potential application in the further development of VAWTs.

Development of Flexible Rotor Balancing Procedure Using Response Matching Technique

Abstract Purpose The two main methods under use for balancing of flexible rotor know as Influence Coefficient Method (ICM) and Modal Balancing Method (MBM). It needs few trials to arrive at predicting the unbalance mass. In presence of initial bow along with unbalance these methods will fail to give accurate predictions. It becomes further complex when rotors are mounted on flexible supports. To overcome the limitations of these two methods, a new method called response matching method is disused here for flexible rotor balancing. Method The objective of present work is to develop a balancing procedure for flexible rotor balancing, wherein unbalance response of Finite element model (FEM) is matched with experimental response using iterative technique. Unbalance masses, moments and shaft stiffness of FEM model was iterated to match experimental unbalance responses at three distinct speeds below its first flexural critical speed. Further, unbalances mass was estimated iteratively to cross the bending critical speed with lower residual amplitudes at critical speeds. Results Experimental test setup was developed to validate the proposed method. Results show that present method predicts the unbalance masses and moments to compensate the bow more accurately. Conclusion Results shows that with single run, rotor unbalance masses and movements are predicted accurately. Corrected masses are used in experimental test setup to check the rotor amplitudes during its bending critical speeds. It shows rotor passes first bending critical speed without excessive amplitudes.

Power or speed: Which metric is more accurate for modelling endurance running performance on track?

This study aimed to compare the accuracy of the power output, measured by a power meter, with respect to the speed, measured by an inertial measurement unit (IMU) and a global navigation satellite system (GNSS) sport watch to determine the critical power (CP) and speed (CS), work over CP (W') and CS (D'), and long-duration performance (i.e., 60 min). Fifteen highly trained athletes randomly performed seven time trials on a 400m track. The CP/CS and W'/D' were defined through the inverse of time model using the 3, 4, 5, 10, and 20 min trials. The 60 min performance was estimated through the power law model using the 1, 3, and 10 min trials and compared with the actual performance. A lower standard error of the estimate was obtained when using the power meter (CP: 2.7 [2.1-3.3] % and W': 13.8 [10.4-17.3] %) compared to the speed reported by the IMU (CS: 3.4 [2.5-4.3] %) and D': 20.7 [16.6-24.7] %) and GNSS sport watch (CS: 3.4 [2.5-4.3] % and D': 20.6 [16.7-24.7] %). A lower coefficient of variation was also observed for the power meter (4.9 [3.7-6.1] %) Regarding the speed reported by the IMU (10.9 [7.1-14.8] %) and GNSS sport watch (10.9 [7.0-14.7] %) in the 60 min performance estimation, the power meter offered lower errors than the IMU and GNSS sport watch for modelling endurance performance on the track.

Analytical solution of ground vibration of a half-space induced by sub- and super-critical harmonic moving loads: Theory and application

This paper presents an analytical solution to the ground vibration of a half-space subjected to sub- and super-critical moving loads oscillating with the frequency f0 and distributed in different forms. By applying the contour integral combined with the residue theorem, the approximate values of the integrals for the ground response are determined, with a rigorous rationale provided for the exclusive consideration of the Rayleigh waves on the ground. The validity of the present solutions is verified against existing solutions, including Auersch's. Through the parametric analysis, it is observed that the frequency f0 of dynamic loading of the vehicle exhibits significant influence on the critical speed, the magnitude of ground vibrations and their rate of attenuation. In addition, the effect of rail irregularity on the ground vibration was included in some applications of the present theory for high-speed trains under the sub-and super-critical speeds with respect to the Rayleigh waves speed. It was shown that track irregularity can largely amplify the velocity and acceleration responses of the ground, albeit exerting a comparably little effect on the ground displacement. Besides, resonant vibrations are likely to occur when the train is accelerated to the critical speed of the soil.

Evaluation of Selected Factors Affecting the Speed of Drivers at Signal-Controlled Intersections in Poland

In traffic engineering, vehicle speed is a critical determinant of both the risk and severity of road crashes, a fact that holds particularly important for signalized intersections. Accurately selecting vehicle speeds is crucial not only for minimizing accident risks but also for ensuring the proper calculation of intergreen times, which directly influences the efficiency and safety of traffic flow. Traditionally, the design of signal programs relies on fixed speed parameters, such as the posted speed limit or the operational speed, typically represented by the 85th percentile speed from speed distribution data. Furthermore, many design guidelines allow for the selection of these critical speed values based on the designer’s own experience. However, such practices may lead to discrepancies in intergreen time calculations, potentially compromising safety and efficiency at intersections. Our research underscores the substantial variability in the speeds of passenger vehicles traveling intersections under free-flow conditions. This study encompassed numerous intersections with the highest number of accidents, using unmanned aerial vehicles to conduct surveys in three Polish cities: Toruń, Bydgoszcz, and Warsaw. The captured video footage of vehicle movements at predetermined measurement sections was analyzed to find appropriate speeds for various travel maneuvers through these sections, encompassing straight-through, left-turn, and right-turn relations. Our analysis focused on how specific infrastructure-related factors influence driver behavior. The following were evaluated: intersection type, traffic organization, approach lane width, number of lanes, longitudinal road gradient, trams or pedestrian or bicycle crossing presence, and even roadside obstacles such as buildings, barriers or trees, and others. The results reveal that these factors significantly affect drivers’ speed choices, particularly in turning maneuvers. Furthermore, it was observed that the average speeds chosen by drivers at signalized intersections did not reach the permissible speed limit of 50 km/h as established in typical Polish urban areas. A key outcome of our analysis is the recommendation for a more precise speed model that contributes to the design of signal programs, enhancing road safety, and aligning with sustainable transport development policies. Based on our statistical analyses, we propose adopting a more sophisticated model to determine actual vehicle speeds more accurately. It was proved that, using the developed model, the results of calculating the intergreen times are statistically significantly higher. This recommendation is particularly pertinent to the design of signal programs. Furthermore, by improving speed accuracy values in intergreen calculation models with a clear impact on increasing road safety, we anticipate reductions in operational costs for the transportation system, which will contribute to both economic and environmental goals.

Sharp habitat shifts, evolutionary tipping points and rescue: Quantifying the perilous path of a specialist species towards a refugium in a changing environment

Specialist species thriving under specific environmental conditions in narrow geographic ranges are widely recognized as heavily threatened by climate deregulation. Many might rely on both their potential to adapt and to disperse towards a refugium to avoid extinction. It is thus crucial to understand the influence of environmental conditions on the unfolding process of adaptation. Here, I study the eco-evolutionary dynamics of a sexually reproducing specialist species in a two-patch quantitative genetic model with moving optima. Thanks to a separation of ecological and evolutionary time scales and the phase-line study of the selection gradient, I derive the critical environmental speed for persistence, which reflects how the existence of a refugium impacts extinction patterns and how it relates to the cost of dispersal. Moreover, the analysis provides key insights about the dynamics that arise on the path towards this refugium. I show that after an initial increase of population size, there exists a critical environmental speed above which the species crosses a tipping point, resulting into an abrupt habitat switch. In addition, when selection for local adaptation is strong, this habitat switch passes through an evolutionary “death valley”, leading to a phenomenon related to evolutionary rescue, which can promote extinction for lower environmental speeds than the critical one.

АНАЛІЗ ВПЛИВУ КУТА СТРІЛОПОДІБНОСТІ НА ХАРАКТЕРИСТИКИ СТАТИЧНОЇ АЕРОПРУЖНОСТІ КРИЛА НАВЧАЛЬНО-ТРЕНУВАЛЬНОГО ЛІТАКА

The article is dedicated to the analysis of static aeroelastic phenomena in the wing of a trainer aircraft and the general influence of wing sweep on critical speeds. Aeroelasticity studies the interaction between aerodynamic and elastic forces and the impact of this interaction on the aircraft's structure. There are two types of aeroelasticity: static and dynamic. The article reviews and analyzes publications related to this issue. The analysis of the research shows that when designing an aircraft, it is necessary to determine the aeroelastic characteristics of its aerodynamic surfaces. In addition to structural rigidity, the sweep angle also influences these phenomena. The scientific novelty of the study lies in the fact that, unlike the analyzed research, the designed wing structure of a trainer aircraft is considered.For the designed trainer aircraft, the critical speeds of static aeroelastic phenomena were determined. The calculation of the influence of the wing sweep angle on the divergence speeds of the trainer aircraft confirms previously obtained results regarding this influence. When the sweep is increased or decreased for wings with the same span, the torsional rigidity of the wing decreases due to the increase in the length of the line of centers of rigidity. However, the most significant impact on the aeroelastic characteristics is made by the shift of the bending center when the sweep angle changes.With forward sweep, the arm of the aerodynamic forces relative to the bending center increases, thereby reducing the critical divergence speeds. For straight sweep, as the sweep increases, the bending center moves forward, and at a certain point, the bending center is located in front of the aerodynamic center. This means that the wing twist angle decreases as the aerodynamic force increases, which, in the considered planar case, eliminates the occurrence of divergence.The preliminarily determined maximum flight speed does not exceed the critical speeds of divergence and aileron reversal. This result represents the practical value of the study. To achieve higher flight speeds, wings with straight sweep should be used. More precise computational or experimental methods for determining aeroelastic characteristics should be used in the subsequent design stages to prevent aeroelastic phenomena across the entire operational range of speeds and altitudes of the trainer aircraft.

Field observation and cause investigation of low-frequency cable vibrations in a cable-stayed bridge

Considerable levels of stay cable vibration in cable-supported bridges pose significant challenges for safety, operation, and maintenance. An accurate understanding of the specific causes and types of vibration is essential for effectively addressing this problem with an optimal design for mitigation measures. This study aims to investigate the cause of an extraordinary low-frequency vibration that occurred at a stay cable by employing comprehensive methodologies. The modal properties and vibrational characteristics of cable vibrations were first obtained through finite element modeling, operational modal analysis, and vision-based displacement measurements. Subsequently, the primary cause of low-frequency vibrations was investigated using field observations and wind tunnel tests. Field-monitoring data revealed that stay cables were excited by small deck vibrations. The critical wind speeds at which deck vibrations occurred in a wind tunnel experiment were aligned with the ranges of wind speeds that produce low-frequency cable vibrations, which confirmed that these two phenomena are manifested under similar wind conditions. A calculated support excitation amplitude, determined via the use of an empirical equation, exhibited consistency with vision-based measured displacement obtained in field experiments. These findings underscore the potential risk of support excitation between minor deck vibrations and cables, which provides valuable insights that could mitigate cable vibrations.

Simulation method for dynamic characteristics of rotor-support system subjected to environmental loads

An improved finite element method was proposed to investigate the dynamic characteristics of rotor system with environmental loads (temperature and aerodynamic forces) in aeroengines. According to the axial temperature distribution within shaft elements, the polynomials were established for physical properties of material. The derivation for coefficient matrices under thermal loads, and the tensile stiffness matrix considering axial aerodynamic forces were completed, based on the Timoshenko beam theory. A high-pressure rotor was simulated with operating temperature 200∼600∘C, and the magnitude of aerodynamic force is 105N. Furthermore, a squeezed film damper (SFD) was adopted to this rotor-support system, its steady responses were solved by the equivalent coefficient method, and the Newmark-HHT method was utilized to solve the transient responses. The results indicate that the first two critical speeds are reduced by 1.85 % and 2.07 %, which is mainly caused by thermal loads. The rising temperature leads to lower elastic modulus, higher Poisson's ratio and expansion ratio. With the amount of a mass unbalance being 500 g·mm located at the 1st-stage compressor disk (CD1): the 1st resonance peaks at CD1 and turbine disk (TD) increase by 4.56 % and 4.98 %, respectively, and the 2nd resonance peaks at CD1 and TD rise 5.88 % and 5.00 %, separately. Owing to SFD damping, the first two resonance peaks at CD1 and TD decrease by 69 % and 51 %, respectively. Compared to 40 °C, the first two resonance peaks at CD1 increase by 88 % and 55 % at the oil temperature 100 °C. The oil-film damping deteriorates significantly due to the lower oil viscosity in higher temperature. When operating near the first-order critical speed, the transient responses of rotor perform as simple harmonics, circular precession trajectory, dominant rotational frequency, and periodic motions. Overall, the dynamic characteristics of rotor-SFD-support systems exposed to environmental loads can be predicted by the proposed simulation method.

Higher-order nonlinear modeling and multi-modal performance of axially restrained diverse flexible shaft-disk assemblies

Flexible shaft-disk combinations are essential in engines, turbines, and machinery. Understanding their modal characteristics is vital for industry-wide performance, reliability, and safety. This study uses higher-order modeling and multi-modal analysis to grasp complex dynamics, especially with multiple disks of varied sizes. Employing Hamilton’s method and Galerkin’s technique, equations of motion are formulated and then utilized for multi-modal analysis considering structural nonlinearity. Various shaft-disk arrangements are analyzed, including disk number, size, position, and shaft material, to understand their impact on modal behavior. The findings reveal the substantial impact of disk count, sizes, and placements on modal dynamics and intricate vibration characteristics across diverse spinning speeds. This effect is accentuated by integrating higher-order modeling into multi-modal analysis. Notably, higher-order deformation enhances overall resilience capacity and imposes more effective vibration restrictions than the linear approach. Furthermore, the investigation explores how different shaft materials influence modal characteristics, critical speeds, and vibration amplitudes in various shaft-disk combinations. Theoretical findings are validated using numerical results from 3D finite element-based models simulated with ANSYS 3D for accuracy. Ultimately, the study introduces a theoretical framework adaptable to numerous flexible shaft-disk combinations, offering a valuable resource for understanding and enhancing system behavior, benefiting engineers and researchers alike.

A Novel Numerical Approach to Investigate Shaft Diameter Effect on Dynamic Behaviour of Multi-Disc Rotors

In this study, a displacement-based finite element model was developed to investigate the effect of the diameter of rotating shafts on dynamic performance of a multi-disc rotor system with respect to their natural frequencies and critical speeds. The variation in rotor bearing stiffness was considered in this study. A numerical case study that simulating a typical rotating machine was adopted to assess the present methodology. The results obtained show that the diameter of the rotor has a significant effect on the rotor dynamic characteristics. The amount of the influence was found to be highly sensitive to bearing stiffness of the rotating machine. An experimental setup was constructed and tests were performed to validate the applicability of the numerical model. The reasonable agreement found between the results obtained numerically and experimentally validates the proposed numerical model.

Evaluation of the effectiveness of an expressway sand protection system in a gobi region—case study of the Ceke–Ejina expressway, Ejina banner, China

Sand protection systems are widely used to shelter roads from blowing sand. Therefore, it's very important to evaluate their effectiveness. To provide some insights, we used field investigations, measurements of accumulated sand, work logs from sand-removal workers, and wind speed data to analyze a system's performance using China's Ceke–Ejina expressway as a case study. Our results demonstrated that the critical wind speed required to deposit sand on the expressway was 8.6 m s-1 (cumulative frequency 12.1%) before implementing the sand protection system. After implementing the system, the critical wind speed required to deposit sand on the road increased to 14.8 m s-1 (0.3%). However, the critical wind speed decreased to 11.1 m s-1 (3.5%) the next year. Additional work, such as digging ditches, increasing the fence height, and planting shrubs, would help the sand protection system retain its function. Nonetheless, the system continued to function well. The volume of sand removed decreased from ca. 10,000 m3 in 2015 to ca. 100 m3 in 2020. Our results quantify the effectiveness of the sand protection system and reveal how its effectiveness decreases over time. They therefore provide an empirical basis for improving the design and maintenance of sand protection systems.

Minimal wave speed for a two-group epidemic model with nonlocal dispersal and spatial-temporal delay

In this paper, a two-group SIR reaction-diffusion epidemic model with nonlocal dispersal and spatial-temporal delay based on within-group and inter-group transmission mechanisms is investigated. The basic reproduction number R0 is calculated using the method of next-generation matrix. The critical wave speed cm* is determined by analyzing the distribution of roots of the characteristic equation. When R0&amp;gt;1 and wave speed c⩾cm*, the existence of traveling waves connecting disease-free and endemic steady states is obtained by constructing sub- and super-solutions and a Lyapunov functional, and applying Schauder’s fixed-point theorem and a limit argument. When R0&amp;gt;1 and 0&amp;lt;c&amp;lt;cm*, the nonexistence of traveling waves connecting disease-free and endemic steady states is proven by contradiction and two-sided Laplace transform. This indicates that the critical wave speed cm* is exactly the minimum wave speed. Numerical simulations are carried out to illustrate theoretical results. The dependence of the minimal speed cm* on time delay, diffusion rates and contact rates is discussed, showing that the longer the latent period and the lower the diffusion rates of infected individuals and the inter-group transmission rates between groups, the slower the spread of disease.

Research on the Flutter Characteristics of Folding Wings with Variable Swept Angles of the Outer Wing

The critical flutter speed, along with the associated stability and safety of a folding-wing aircraft, has been evaluated for variable wing configurations based on traditional designs. Through theoretical analysis and numerical simulation validation, the contributions of parameters such as the hinge stiffness, sweep angle, and folding angle on the flutter and stability of the folding wing are investigated in detail. It is observed that under a specified safe hinge stiffness, the proposed variable-sweep folding-wing configuration can enhance the critical flutter speed at a dangerous folding angle. Through the joint manipulation of the folding and sweep angles, the aerodynamic drag of the folding wing was reduced, thereby enhancing its flight speed and flutter boundaries. This paper aims to provide novel insights into the design and stability analysis of variable-wing configurations.