This study proposes a novel sandwich beam structure designed for superior low-frequency broadband flexural wave control. The proposed structure synergistically integrates discontinuous sandwich cores with Acoustic Black Holes (ABHs) embedded in the face sheets, demonstrating performance that outperforms conventional designs. To elucidate the coupling mechanisms between the periodic effects of discontinuous cores and ABH effects, two distinct configurations are systematically investigated: the C-ABH and NC-ABH sandwich beams. The sandwich beam with ABHs embedded in the beam segments coupled with the core is designated as C-ABH sandwich beam, while that with ABHs embedded in the segments non-coupled from the core is termed NC-ABH sandwich beam. A wave vector method is employed to establish flexural wave propagation models for both beam configurations, alongside a transmission coefficient model characterizing flexural wave attenuation. Using these models, the influence of four key factors is investigated on the flexural wave attenuation performance of the sandwich beams. Research results show that the proposed NC-ABH sandwich beam delivers superior flexural wave attenuation performance; the attenuation performance is markedly enhanced by embedding ABHs in the face sheet with higher flexural rigidity and by increasing the flexural rigidity asymmetry between the upper and lower face sheets; reducing the ABH minimum thickness and increasing its length and quantity further widen the bandgaps and shift them toward lower frequencies. These findings indicate that the proposed NC-ABH sandwich beam offers an effective strategy for achieving strong flexural wave attenuation in low-frequency broadband applications.

Most autonomous driving accidents are caused by the coupling of multiple factors rather than by a single cause. This makes it essential for the autonomous driving industry to identify coupled risk mechanisms and balance innovation with safety. Using 242 autonomous driving accident cases involving interactions between internal and external factors, this study develops a safety risk factor framework covering personal factors, traditional hardware, autonomous driving technology, management, and environmental conditions. Based on the composite N-K coupling model, this study reveals the coupling effect of autonomous driving safety risks and further quantifies the risk coupling value of secondary risk factors on the risk-causing effect. The results indicate clear multi-factor synergistic risk characteristics, with the coupling of autonomous driving technology, management, and environment ranking as the highest-risk combination. Specifically, the dominant human risks are insufficient driver monitoring and attention failure; the primary technical risks are algorithmic and data deficiencies; the key management weakness lies in gaps in institutional and standard frameworks; and the main environmental catalysts are severe weather and visual/optical interference. These findings provide an evidence base for precise risk prevention and control in autonomous driving, and offer practical implications for vehicle R&D optimization, policy-making, and road operation management.

This study investigates the critical role of resonance capture dynamics in determining the energy dissipation performance of nonlinear energy sinks (NES). A fluid inerter combining mass amplification and damping characteristics is proposed as a core component, based on which two configurations of fractional-order NES (configured in series and parallel) are systematically constructed. The applicability of the complex averaging method in fractional-order systems has been addressed through fractional calculus (such as Leibniz properties), enabling it to be analyzed like integer-order systems. Employing the multi-scale perturbation method, the energy transfer mechanism between the primary oscillator and the NES is derived, leading to the analytical determination of optimal cubic stiffness and maximum energy transfer efficiency. Comparative simulation shows that the parameters of the inerter directly affect the magnitude of critical damping. The optimal cubic stiffness design method is more reliable than traditional methods and can ensure effective target energy transfer triggering. Further analysis of dissipation time shows that the performance of fractional-order NES is superior to integer-order NES; notably, the dissipation time of series fractional-order NES is significantly shorter than that of parallel and traditional NES. In summary, this study provides theoretical guidance for the design of lightweight and high-performance NES and will also promote the application of fractional calculus theory in the field of engineering vibration reduction.

The understanding and application of fluid-type inerters by scholars have been on the rise. However, due to their intricate multiphase mechanical properties, existing models still have considerable room for improvement. This study presents two fractional-order models and conducts parameter identification by integrating them with classical experimental data. The first model is an independent fractional-order model. In comparison with traditional models, it demonstrates significantly higher fitting accuracy in frequency regions beyond the ultra-low frequency range. The second model is a segmented fractional-order model, which determines segments according to critical frequencies. Although this model enhances the overall fitting accuracy, it also leads to increased complexity. To tackle this complexity issue, a rough design strategy is proposed to minimize the critical frequency. Research indicates that under such a strategy, the inertial effect dominates the behavior of the fluid inerter. Even when the independent fractional-order model is used, a high fitting accuracy can be achieved. Consequently, by designing the structural parameters and fluid medium of the fluid inerter based on the rough design strategy, the model can be simplified. Moreover, compared with traditional nonlinear inerter models, the transfer function and eigenvalue analysis methods can be effectively applied. This enables the acquisition of more comprehensive theoretical research results, thereby greatly facilitating theoretical analysis.

In this paper, a generalized acoustic black hole (ABH) beam covered with a viscoelastic layer is proposed to improve the energy dissipation based on the double-parameter Mittag–Leffler (ML) function. Since fractional-order constitutive models can more accurately capture the properties of viscoelastic materials, a fractional dynamic model of an ABH structure covered with viscoelastic film is established based on the fractional Kelvin–Voigt constitutive equation and the mechanical analysis of composite structures. To analyze the energy dissipation of the viscoelastic ML-ABH structures under steady-state conditions, the wave method is introduced, and the theory of vibration wave transmission in such non-uniform structures is extended. The effects of the fractional order, the film thickness and length, and shape function parameters on the dynamic characteristics of the ABH structure are systematically investigated. The study reveals that these parameters have a significant impact on the vibration characteristics of the ABH structure. To obtain the best parameters of the shape function under various parameters, the Particle Swarm Optimization (PSO) algorithm is employed. The results demonstrate that by selecting appropriate ML parameters and viscoelastic materials, the dissipation characteristics of the structure can be significantly improved. This research provides a theoretical foundation for structural vibration reduction in ABH structures.

This article focuses on the study of elastic beams with fractional-order inertial damping structures at both ends, with the aim of exploring their dynamic characteristics, damping effects, and parameter selection rules in depth, providing theoretical and practical support for engineering applications. Firstly, using the generalized Hamilton principle, two dynamic models of an elastic beam are established for two different boundary conditions. Next, using the complex modal analysis method, a design method for the critical damping of the first and second modes of an elastic beam was proposed for the first time, and the accuracy of the critical damping calculation formula was verified. Simulation analysis shows that the higher the derivative order and inertance, the lower the main resonance frequency, and the greater the critical damping. Then, using the main resonance amplitude and frequency attenuation rate (RA and RΩ) as indicators, an analysis was conducted on the impact of damper parameters on vibration suppression effects. The results indicate that the introduction of fractional-order inerter can reduce the main resonance amplitude and frequency, and critical damping plays a significant role in the vibration suppression process. Based on the optimal average RA range (95–98%) and higher cost-effectiveness, selecting a damping value of 0.05~0.6 times the critical damping ensures better overall vibration suppression performance, providing an important reference for the vibration suppression design of elastic beams in practical engineering.

This study investigates a sandwich beam with discrete viscoelastic cores, proposing a novel method to analyze its steady-state vibration response by considering the cores' linear coupling effects on the upper and lower beams. Based on the wave vector method, this study first establishes the reflection and transmission matrices for flexural waves in the sandwich beam with a core, as well as the iterative calculation formulas for the ends of a segment of the sandwich beam. Subsequently, the vibration propagation characteristics are analyzed. Finally, the influence of the coupling strength of periodically arranged cores, the asymmetry of the upper and lower beams and the loss factor of the core on the propagation relationship of flexural waves and their bandgap characteristics is investigated in detail. The results show that for the upper and lower beams of sandwich beams, the beam with higher Young's modulus dominate the energy transfer of flexural waves in sandwich beams; The coupling strength of the core significantly affects the position and width of the bandgap. The asymmetry of the upper and lower beams not only changes the energy transmission relationship, but also promotes the formation of the band gap. The loss factor attenuates vibrational waves, especially near the bandgap, without affecting its position or width. This study provides important theoretical guidance for the structural design and vibration performance optimization of periodic viscoelastic sandwich beams, as well as the control of flexural wave bandgap.

In order to ensure that vehicle can also have good path tracking performance during braking or acceleration process, A fractional order sliding mode controller with two fractional order terms is proposed for path tracking control. First, a three-degree-of-freedom dynamic model is established, and the tire force calculation formula based on Dugoff tire model is given. Based on the kinematic model and the error state equation of vehicle path tracking, a sliding mode controller for vehicle path tracking is designed, the quadratic performance index optimization method is used to obtain the sliding mode surface coefficient. And the fractional calculus is introduced to improve it into fractional order sliding mode surface and fractional order reaching rate sliding mode control, in order to cope with the time-varying characteristics of the system and the change of other parameters in the model when the vehicle changes speed. Finally, MATLAB and Carsim platform are used for co-simulation to verify the double fractional-order sliding mode controller. The results show that compared with the commonly used LQR and MPC controllers, the double fractional-order sliding mode controller has a more ideal path tracking ability under braking and acceleration conditions.

In order to ensure that the autonomous vehicle can predict and taking actions to avoid the collision in time when facing the obstacles with intersection collision risk, an intersection collision risk prediction system is proposed in this paper, and two kinds of active obstacle avoidance strategies are designed according to the system: braking strategy and steering strategy. The position information of the obstacle is predicted by Fractional extended Kalman filter, the collision risk rate is determined by the time difference between the vehicle and the obstacle through the intersection point, and a neural network is trained to quickly give the collision risk of the vehicle and the obstacle. Braking strategy and steering strategy are formulated according to collision risk, the braking deceleration and Sigmoid path parameters are given. Finally, the simulation results of PreScan and MATLAB show that the collision risk prediction system can accurately predict the collision between vehicles and obstacles, the braking and steering strategies can effectively avoid the collision.

This paper aims to study the effects of the non-stationary soil property on the horizontal bearing capacity of three-dimensional monopile in spatially variable soils. The soil undrained shear strength is assumed to obey lognormal distribution and is simulated as non-stationary random fields. The mean value of the undrained shear strength linearly increases with depth, while the standard deviation keeps constant. The random finite-element method is applied to analyze the reliability of the bearing capacity. The influence of the correlations and non-stationary property on the mean and coefficient of variation of the bearing capacity are discussed. It is found that the correlation distance has no obvious effect on the bearing capacity and the bearing capacity increases with the increase of non-stationary coefficient. The results can guide the reliability-based design of horizontally loaded piles embedded in spatially variable soil.

In this paper, we present a generalized model of a viscoelastic beam, which takes into account the influence of axial forces and incorporates a fractional constitutive relationship. In addition, we propose a novel numerical calculation method for analyzing fractional-order viscoelastic beams. This method takes the transverse displacement and bending moment of the beam as state variables, transforms the beam model into a discrete state space equation through the application of the central difference method, and utilizes an improved precise integration algorithm to solve the equation. To evaluate the performance of the method, the responses of the beam under two types of excitations, namely uniformly distributed transverse load and the motion of the support at both ends, are calculated under fixed hinge conditions. The results demonstrate that the present method has excellent accuracy and convergence, and also reveal some nonlinear phenomena of the system.

The porous electrodes have the fractal characteristics of self-similarity and discontinuity at the microscopic scale, which is an important physical condition in the fractional-order system. During the charging and discharging, the multiple heat transfer modes occur simultaneously on the porous electrodes. Due to the different heat transfer rates of various modes, the thermodynamics of batteries is essentially a discontinuous time-delay system, which cannot be ignored. A fractional-order heat transfer model (FOHTM) is proposed to analyze the time-delay effect of the lithium-ion battery module. The fractional derivative order (FDO) of the proposed model is identified. The temperature distribution of the tested battery module is simulated and the cooling system is optimized. The results indicate that the simulation accuracy of FOHTM is higher than that of the classical integer-order heat transfer model (IOHTM). The maximum error of transient temperature of FOHTM under various operating conditions is less than 1.1%. The FOHTM can approach the true temperature faster through updating the historical weighted terms. The FOHTM is a statistical analysis of non-standard thermal diffusion behavior under the action of multiple heat transfer modes, as a result of which, it is more suitable for the modeling of battery thermodynamics.

The soil parameters may obey different types of distribution. However, the lognormal distribution is generally chosen in the probability analysis of pile foundations. The undrained strength of soil is taken as the random variable, and it is assumed to obey Lognormal distribution, Beta distribution and Gamma distribution, respectively. Then the bearing behavior of single pile foundation under vertical and horizontal loads is simulated by stochastic finite element method, in which the different coefficient of variation and correlation distance are considered. The mean value and standard deviation of bearing capacity of single pile are analyzed. The results show that the average vertical bearing capacity of single pile is not affected by the distribution of soil strength. The average horizontal bearing capacity of single pile is the largest when the lognormal distribution is adopted, while the bearing capacity is the smallest when random field obeys the Beta distribution. The standard deviation of bearing capacity obtained by Beta distribution under vertical and horizontal loads is the largest. It is recommended to use Beta distribution to determine the bearing capacity of single pile foundation when the spatial distribution of soil strength is unknown.

The detection and characterization of electrode performance is a key problem of lithium-ion batteries. The physical properties of the electrodes affect the charge density during the life of a battery. The charge density is difficult to monitor because of the complexity of the charge distribution. In this paper, a visualized fractional derivative order (FDO) is used to characterize the charge distribution and to reveal variations in the charge density associated with the physical properties of the electrode. Instantaneous discharge datasets collected at different aging stages of batteries are used to identify the FDO in the fractional derivative model. The results show that the FDO has a strong correspondence with the charge density. As the charge density decreases, the charge mobility gradually increases due to changes in the charge distribution. Moreover, this paper finds that the capacity recovery effect is closely related to the mutation of the charge density and uses the FDO to explain the charge accumulation at the sharp edges of the electrodes. The analysis of the charge density variation caused by the physical properties of the electrodes provides guidance for the detection of the electrode performance and the design of the electrode microstructure.

The existing mathematical model for short-circuit fault diagnosis of management and collaborative system has the problem that the session characteristics of communication link are not clear, resulting in the slow upload speed of fault data. In order to solve this problem, a short-circuit fault diagnosis mathematical model of communication system based on improved SOM neural network and the innovative strategies also management and collaborative system is describe in this paper. Firstly, the early warning information of the system is collected, combined with the repeated information, the session characteristics of the communication link are extracted by using the quasi Newton algorithm, the mutually orthogonal physical resource blocks are transformed, the short-circuit fault diagnosis mode is optimized, the parameters of the components to be detected are estimated, the feature space vector is truncated, and the mathematical model is established by using the improved SOM neural network. Experimental results: the average value of the management and collaborative system short-circuit fault diagnosis mathematical model designed in this paper is 8.244 Mbps, and the average values of the other two management and collaborative system short-circuit fault diagnosis mathematical models are 5.756 Mbps and 5.863 Mbps respectively. The results show that the designed mathematical model for short circuit fault diagnosis of management and collaborative system has high application value.

The general vibration control strategy of beam structures is a global vibration control method based on the principle of modal superposition. However, the vibration wave control of beams can achieve local control of the vibration energy. This paper presents a wave control method for the local vibration control of fractional viscoelastic composite beams based on the operating principle of a piezoelectric sheet. To obtain better control performance, a particle swarm optimization algorithm was adopted to optimize the parameters of the piezoelectric sheet. A linear quadratic regulator control algorithm was designed to verify the validity of the proposed method. In addition, the effects of the piezoelectric sheet number and fractional order on the amplitude response and optimization parameters were investigated. We observed that the proposed method has a good control effect on the local area vibration, and it can control the flow direction of the vibration power. The proposed method can be used to directly design the voltage and phase of a piezoelectric sheet without real-time feedback computation. This method is suitable for reducing local vibration under single repetitive operating conditions in engineering and can provide a theoretical basis for a follow-up study on the acoustic black hole phenomenon.

The fluid inerter described by the fractional derivative model is introduced into the traditional nonlinear energy sink (NES), which is called fractional-order NES in this paper. The slowly varying dynamic equation (SVDE) of the system coupled with fractional-order NES is obtained by the complex averaging method, in which the fractional derivative term is treated using the fractional Leibniz theorem. Then, the discriminants (Δ, Δ1, and Δ2) of the number of equilibrium points are derived. By using the variable substitution method, the characteristic equation for judging the stability is established. The results show: (1) the approximate SVDE is sufficient to reflect the slowly varying characteristics of the system, which shows that the mathematical treatment of the fractional derivative term is reliable; (2) the discriminant conditions (Δ1, Δ2) can accurately reflect the number of equilibrium points, and the corresponding range of nonlinear parameter κ can be calculated when the system has three equilibrium points. The expressions of Δ1, Δ2 are simpler than Δ, which is suitable for analysis and design parameters; (3) the stability discrimination methods of schemes 1 and 2 are accurate. Compared with scheme 2, scheme 1 is more prone to various responses, especially various strongly and weakly modulated responses. In scheme 2, the inertia effect of mass can be completely replaced by integer order inerter. Compared with integer order inerter, the introduction of fractional order inerter, whether in series or in parallel, means that the amplitude of the equilibrium point on the NES vibrator is smaller, but it is also for this reason that it is not easy to produce a modulated response with scheme 2, and the vibration suppression effect of the main structure is not good.

Unlike time-based path tracking controllers, the [Formula: see text]-controller is a spatial path tracking controller. It is a purely geometric path tracking controller and essentially a P-controller to maintain the reasonable spatial distance, [Formula: see text], from the vehicle to the desired path. In this paper, we present some enhancement schemes using the non-conventional PI control laws via optimization. We propose to use a nonlinear term [Formula: see text] for the proportional controller. A fractional-order integral used to achieve a PI[Formula: see text] control. Among the schemes, an optimization search procedure applied to find optimal controller gains by meshing the regions around the values from approximate linear designs. The performance index for parametric optimization is the integration of the absolute purely spatial deviation from the desired path. Three different types of road shape were chosen and the Gazebo-ROS simulation results were presented to show the effectiveness of the proposed enhancement schemes. The results show that in some cases a smaller [Formula: see text] and [Formula: see text] can be achieved by using [Formula: see text] controller, but its disadvantage is there may be some oscillation. For PI[Formula: see text] controller, there is an additional adjustable parameter [Formula: see text], better performance can be achieved without significant disadvantages which is worth in-depth research.

为了研究用含分数阶导数描述的液力惯容器的非线性隔振系统特性,建立无量纲动力学模型.在无阻尼控制时,通过对比力传递率特性指标讨论参数对隔振系统性能的影响.结果表明分数阶惯容器能够反映液力式惯容器的多相特性,既有惯性作用又有一定阻尼作用,相比整数阶惯容器在隔振效果上有一定优势,但同样不能有效抑制非线性效应.在忽略非线性项的前提下,考虑系统含分数导数的特殊情况,详细介绍分数阶临界阻尼设计过程.仿真试验结果表明,所设计临界阻尼可以保证系统在自由振动时单调递减,而且考虑非线性项后,相比整数阶惯容器能够更好抑制非线性效应.

Research on the heat transfer characteristics of lithium-ion batteries is of great significance to the thermal management system of electric vehicles. The electrodes of lithium-ion batteries are composed of porous materials, and thus the heat conduction of the battery is not a standard form of diffusion. The traditional heat conduction model is not suitable for lithium-ion batteries. In this paper, a fractional heat conduction model is used to study the heat transfer properties of lithium-ion batteries. Firstly, the heat conduction model of the battery is established based on the fractional calculus theory. Then, the temperature characteristic test was carried out to collect the temperature of the battery in various operating environments. Finally, the temperature calculated by the fractional heat conduction model was compared with the measured temperature. The results show that the accuracy of fractional heat conduction model is higher than that of traditional heat conduction model. The fractional heat conduction model can well simulate the transient temperature field of the battery. The fractional heat conduction model can be used to monitor the temperature of the battery, so as to ensure the safety and stability of the battery performance.