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.

Auto-parametric resonance of a continuous-beam-bridge model under two-point periodic excitation:an experimental investigation and stability analysis

The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns.The parametric vibration equation is established for the test model using the finite-element method.The auto-parametric resonance stability of the structure is analyzed by using Newmark's method and the energy-growth exponent method.The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model.Compared with the experiment,the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena,and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones.For a continuous beam bridge,when the ratio of multipoint excitation frequency(applied to the columns)to natural frequency of the continuous girder is approximately equal to 2,the continuous beam may undergo a strong auto-parametric resonance.Combined with the present experiment and analysis,a hypothesis of Volgograd Bridge's serpentine vibration is discussed.

Stability analysis of loose accumulation slopes under rainfall:case study of a high‑speed railway in Southwest China

The high and steep slopes along a high-speed railway in the mountainous area of Southwest China are mostly composed of loose accumulations of debris with large internal pores and poor stability,which can easily induce adverse geological disasters under rainfall conditions.To ensure the smooth construction of the high-speed railway and the subsequent safe operation,it is necessary to master the stability evolution process of the loose accumulation slope under rainfall.This article simulates rainfall using the finite element analysis software’s hydromechanical coupling module.The slope stability under various rainfall situations is calculated and analysed based on the strength reduction method.To validate the simulation results,a field monitoring system is established to study the deformation characteristics of the slope under rainfall.The results show that rainfall duration is the key factor affecting slope stability.Given a constant amount of rainfall,the stability of the slope decreases with increasing duration of rainfall.Moreover,when the amount and duration of rainfall are constant,continuous rainfall has a greater impact on slope stability than intermittent rainfall.The setting of the field retaining structures has a significant role in improving slope stability.The field monitoring data show that the slope is in the initial deformation stage and has good stability,which verifies the rationality of the numerical simulation method.The research results can provide some references for understanding the influence of rainfall on the stability of loose accumulation slopes along high-speed railways and establishing a monitoring system.

Research on the Stability Analysis Method of DC Microgrid Based on Bifurcation and Strobe Theory

During the operation of a DC microgrid,the nonlinearity and low damping characteristics of the DC bus make it prone to oscillatory instability.In this paper,we first establish a discrete nonlinear system dynamic model of a DC microgrid,study the effects of the converter sag coefficient,input voltage,and load resistance on the microgrid stability,and reveal the oscillation mechanism of a DC microgrid caused by a single source.Then,a DC microgrid stability analysis method based on the combination of bifurcation and strobe is used to analyze how the aforementioned parameters influence the oscillation characteristics of the system.Finally,the stability region of the system is obtained by the Jacobi matrix eigenvalue method.Grid simulation verifies the feasibility and effectiveness of the proposed method.

Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems:A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

UAV-mounted Ground Penetrating Radar: an example for the stability analysis of a mountain rock debris slope

This paper describes scientific research conducted to highlight the potential of an integrated GPR-UAV system in engineering-geological applications.The analysis focused on the stability of a natural scree slope in the Germanasca Valley,in the western Italian Alps.As a consequence of its steep shape and the related geological hazard,the study used different remote sensed methodologies such as UAV photogrammetry and geophysics survey by a GPR-drone integrated system.Furthermore,conventional in-situ surveys led to the collection of geological and geomorphological data.The use of the UAV-mounted GPR allowed us to investigate the bedrock depth under the detrital slope deposit,using a non-invasive technique able to conduct surveys on inaccessible areas prone to hazardous conditions for operators.The collected evidence and the results of the analysis highlighted the stability of the slope with Factors of Safety,verified in static conditions(i.e.,natural static condition and static condition with snow cover),slightly above the stability limit value of 1.On the contrary,the dynamic loading conditions(i.e.,seismic action applied)showed a Factor of Safety below the stability limit value.The UAV-mounted GPR represented an essential contribution to the surveys allowing the definition of the interface debris deposit-bedrock,which are useful to design the slope model and to evaluate the scree slope stability in different conditions.

Stability analysis for affine fuzzy system based on fuzzy Lyapunov functions

An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.

Stability analysis method of geogrid reinforced expansive soil slopes and its engineering application

The traditional stability analysis method of geogrid reinforced slopes does not consider the effect of lateral swelling,so it is not applicable to reinforced expansive soil slopes.This paper reports a new stability analysis method for geogrid reinforced expansive soil slopes.The additional pullout force of the free zone due to the lateral swelling and the anti-pullout safety factor of each geogrid layer were obtained by ensuring the overall stability of the reinforced slope.The optimum design was carried out to treat an expansive soil cut slope in Hubei Province,China,by changing the spacing and length of geogrid reinforcement.Calculation results show that the additional pullout force caused by lateral swelling has a great influence on the anti-pullout stability of geogrids,and the local stability of the reinforced slope will be overestimated if the swelling effect of soil in the free zone is not considered.

Mechanical response and stability analysis of rock mass in high geostress underground powerhouse caverns subjected to excavation

To investigate the stability of rock mass in high geostress underground powerhouse caverns subjected to excavation,a microseismic(MS)monitoring system was established and the discrete element method(DEM)-based numerical simulation was carried out.The tempo-spatial damage characteristics of rock mass were analyzed.The evolution laws of MS source parameters during the formation of a rock collapse controlled by high geostress and geological structure were investigated.Additionally,a three-dimensional DEM model of the underground powerhouse caverns was built to reveal the deformation characteristics of rock mass.The results indicated that the MS events induced by excavation of high geostress underground powerhouse caverns occurred frequently.The large-stake crown of the main powerhouse was the main damage area.Prior to the rock collapse,the MS event count and accumulated energy release increased rapidly,while the apparent stress sharply increased and then decreased.The amount and proportion of shear and mixed MS events remarkably increased.The maximum displacement was generally located near the spandrel areas.The MS monitoring data and numerical simulation were in good agreement,which can provide significant references for damage evaluation and disaster forecasting in high geostress underground powerhouse caverns.

Stability analysis of ellipse- like suspen-dome structures with low rise-span ratio

To investigate the effects of initial geometric imperfection and material nonlinearity on the stability analysis of the suspen-dome, the steel roof of Jiangsu Culture Sports Center Gymnasium was utilized as a numerical model, and modal analyses were performed. Then, linear buckling analysis,geometric nonlinear stability analysis, geometric nonlinear stability analysis with initial imperfection, and double nonlinear analysis considering material nonlinearity and geometric nonlinearity were discussed in detail to compare the stability performance of the ellipse-like suspen-dome and the single-layer reticulated shell. The results showthat the cable-strut system increases the integrity of the suspen-dome, and moderates the sensibility of the single-layer reticulated shell to initial geometric imperfection. However, it has little influence on integral rigidity, fundamental vibration frequencies, linear ultimate live loads, and geometric nonlinear ultimate live loads without initial imperfection. When considering the material nonlinearity and initial imperfection, a significant reduction occurs in the ultimate stability capacities of these two structures. In this case, the suspen-dome with a lowrise-span ratio is sensitive to the initial imperfection and material nonlinearity. In addition, the distribution pattern of live loads significantly influences the instability modes of the structure, and the uniform live load with full span is not always the most dangerous case.

Stability Analysis of Hybrid-Driven Underwater Glider

Hybrid-driven underwater glider is a new type of tmmanned underwater vehicle, which combines the advantages of autonomous underwater vehicles and traditional underwater gliders. The autonomous underwater vehicles have good maneuverability and can travel with a high speed, while the traditional underwater gliders are highlighted by low power consumption, long voyage, long endurance and good stealth characteristics. The hybrid-driven underwater gliders can realize variable motion profiles by their own buoyancy-driven and propeller propulsion systems. Stability of the mechanical system determines the performance of the system. In this paper, the Petrel-II hybrid-driven underwater glider developed by Tianjin University is selected as the research object and the stability of hybrid-driven underwater glider unitedly controlled by buoyancy and propeller has been targeted and evidenced. The dimensionless equations of the hybrid-driven underwater glider are obtained when the propeller is working. Then, the steady speed and steady glide path angle under steady-state motion have also been achieved. The steady-state operating conditions can be calculated when the hybrid-driven underwater glider reaches the desired steady-state motion. And the steady- state operating conditions are relatively conservative at the lower bound of the velocity range compared with the range of the velocity derived from the method of the composite Lyapunov function. By calculating the hydrodynamic coefficients of the Petrel-II hybrid-driven underwater glider, the simulation analysis has been conducted. In addition, the results of the field trials conducted in the South China Sea and the Danjiangkou Reservoir of China have been presented to illustrate the validity of the analysis and simulations.and to show the feasibility of the method of the composite Lyapunov function which verifies the stability of the Petrel-II hybrid-driven underwater glider.

Discounted Iterative Adaptive Critic Designs With Novel Stability Analysis for Tracking Control

The core task of tracking control is to make the controlled plant track a desired trajectory.The traditional performance index used in previous studies cannot eliminate completely the tracking error as the number of time steps increases.In this paper,a new cost function is introduced to develop the value-iteration-based adaptive critic framework to solve the tracking control problem.Unlike the regulator problem,the iterative value function of tracking control problem cannot be regarded as a Lyapunov function.A novel stability analysis method is developed to guarantee that the tracking error converges to zero.The discounted iterative scheme under the new cost function for the special case of linear systems is elaborated.Finally,the tracking performance of the present scheme is demonstrated by numerical results and compared with those of the traditional approaches.

An Approach to Stability Analysis of Embedded Large-Diameter Cylinder Quay

The large-diameter cylinder structure, which is made of large successive bottomless cylinders placed on foundation bed or partly driven into soil, is a recently developed retaining structure in China. It can be used in port, coastal and offshore works. The method for stability analysis of the large-diameter cylinder structure, especially for stability analysis of the embedded large-diameter cylinder structure, is an important issue. In this paper, an idea is presented that is, embedded large-diameter cylinder quays can be divided into two types, i.e. the gravity wall type and the cylinder pile wall type. A method for stability analysis of the large-diameter cylinder quay of the cylinder pile wall type is developed and a method for stability analysis of the large-diameter cylinder quay of the gravity wall type is also proposed. The effect of significant parameters on the stability of the large-diameter cylinder quay of the cylinder pile wall type is investigated through numerical calculation.

Development of a new type of foam concrete and its application on stability analysis of large-span soft rock tunnel

The long-term stability of large-span soft rock tunnel is influenced greatly by the creep effect of surrounding rock.The development of a new type of foam concrete which has the property of high compressibility and low ductility was introduced.And it was made as filling material of reserved deformation layer between the first lining and the second lining used in large-span soft rock tunnel.The effect of the new type of foam concrete was simulated as filling material of reserved deformation layer using numerical simulation.Through the comparison with the common large-span soft rock tunnel,the vault settlement and surrounding convergence are reduced by about 61% and 45%,respectively,after creep of 100 a.And in the second lining,the plastic zone reduces apparently and the maximum equivalent plastic strain decreases relatively.So,it can be found that the application of the new type of foam concrete as the filling material of reserved deformation layer can relieve the excessive force in second lining induced by rock creep,reduce its deformation and improve the stability of tunnel.

Stability analysis of cohesive soil embankment slope based on discrete element method

In order to study the safety factor and instability process of cohesive soil slope, the discrete element method(DEM) was applied. DEM software PFC2 D was used to simulate the triaxial test to study the influence of the particle micro parameters on the macroscopic characteristics of cohesive soil and calibrate the micro parameters of DEM model on this basis. Embankment slope stability analysis was carried out by strength reduction and gravity increase method, it is shown that the safety factor obtained by strength reduction method is more conservative, and the arc-shaped feature of the sliding surface under the gravity increase method is more obvious. Throughout the progressive failure process, the failure trends, maximum displacements, and velocity changes obtained by the two methods were consistent. When slope was destroyed, the upper part was cracked, the middle part was sheared, and the lower part was destroyed by extrusion. The conclusions of this paper can be applied to the safety factor calculation of cohesive soil slopes and the analysis of the instability process.

Stability Analysis on Rotor Systems Supported by Self-acting Tilting-pad Gas Bearings with Frequency Effects

The recent research on stability of gas bearing-rotor systems still mostly adopts the same method as in oil-lubricated bearing-rotor systems.The dynamic coefficients of gas bearings in the case that the perturbation frequencies are same as the rotating speed are used to carry out the stability analysis of rotor systems.This method does not contact the frequency characteristics of dynamic stiffness and damping coefficients of gas bearings with the dynamical behaviors of rotor systems.Furthermore,the effects of perturbation frequencies on the stability of systems are not taken into account.In this paper,the dynamic stiffness and damping coefficients of tilting-pad gas bearings are calculated by the partial derivative method.On the base of solution of dynamic coefficients,two computational models are produced for stability analysis on rotor systems supported by tilting-pad gas bearings according to whether the degrees of the freedom of pads tilting motions are included in the equations of motion or not.In the condition of considering the frequency effects of dynamic coefficients of tilting-pad gas bearings,the corresponding eigenvalues of the rigid and first five vibration modes of the system with the working speeds of 8-30 kr/min are computed through iteratively solving the equations of motion of rotor-system by using two computational models,respectively.According to the obtained eigenvalues,the stability of rotor system is analyzed.The results indicate that the eigenvalues and the stability of rotor system obtained by these two computational models are well agreement each other.They all can more accurately analyze the stability of rotor systems supported by tilting-pad gas bearings.This research has important meaning for perfecting the stability analysis method of rotor systems supported by gas bearings.

Stability analysis of lead-vehicle control model in cooperative adaptive cruise control platoon within heterogeneous traffic flow

In order to analyze the stability impact of cooperative adaptive cruise control （CACC） platoon, an adaptive control model designed for the lead vehicle in a CACC platoon （LCACC model） in heterogeneous traffic flow with both CACC and manual vehicles is proposed. Considering the communication delay of a CACC platoon, a frequency-domain approach is taken to analyze the stability conditions of the novel lead-vehicle CACC model. Field trajectory data from the next-generation simulation （NGSIM） data is used as the initial condition. To account for car- following behaviors in reality, an intelligent driver model （IDM） is calibrated with the same NGSIM dataset from a previous study to model manual vehicles. The stability conditions of the proposed model are validated by the ring- road stability analysis. The ring-road test results indicate the potential of the LCACC model for improving the traffic flow stability impact of CACC platoons. Sensitivity analysis shows that the CACC fleet size has impact on the parameters of the LCACC model.

Static and dynamic stability analysis using 3D-DDA with incision body scheme

Discontinuous deformation analysis （DDA） provides a powerful numerical tool for the analysis of discontinuous media. This method has been widely applied to the 2D analysis of discontinuous deformation. However, it is hindered from analyzing 3D rock engineering problems mainly due to the lack of reliable 3D contact detection algorithms for polyhedra. Contact detection is a key in 3-D DDA analysis. The limitations and advantages of existing contact detection schemes are discussed in this paper, and a new approach, called the incision body （IB）, is proposed, taking into account the advantages of the existing methods. A computer code 3DIB, which uses the IB scheme as a 3D contact detection algorithm, was programmed with Visual C^＋＋. Static and dynamic stability analysis for three realistic engineering problems has been carried out. Furthermore, the focus is on studying the stability of a gravity dam on jointed rock foundation and dynamic stability of a fractured gravity dam subject to earthquake shaking. The simulation results show that the program 3DIB and incision body scheme are capable of detecting 3D block contacts correctly and hence simulating the open-close and slide process of jointed block masses. In addition, the code 3DIB could provide an effective tool for evaluating the safety of 3D dam structures, which is quite important for engineering problems.

Stability analysis unit and spatial distribution pattern of the terrain texture in the northern Shaanxi Loess Plateau

Terrain texture analysis is an important method of digital terrain analysis in quantitative geomorphological research and in the exploration of the spatial heterogeneity and autocorrelation of terrain features. However, a major issue often neglected in previous studies is the calculation unit of the terrain texture, that is, the stability analysis unit. As the test size increases, the derived terrain textures become increasingly similar so that their differences can be ignored. The test size of terrain texture is defined as the stability analysis unit. This study randomly selected 48 areas within the Loess Plateau in northern Shaanxi in China as the study sites and used the gray level co-occurrence matrix to calculate the terrain texture. The stability analysis unit of the terrain texture was then extracted, and its spatial distribution pattern in the Loess Plateau was studiedusing spatial interpolation method. Four terrain texture metrics, i.e., homogeneity, energy, correlation, and contrast, were extracted on the basis of the stability analysis unit, and the spatial variation patterns of these parameters were studied. Results showed that the spatial distribution pattern and the terrain texture metrics reflected a trend of high–low–high from north to south, which correlated with the spatial distribution of the landforms at the Loess Plateau. In addition, the terrain texture measures was significantly correlated with the terrain factors of gully density and slope, and this relationship showed that terrain texture measures based on the stability analysis unit could reflect the basic characteristics of terrain morphology. The stability analysis unit provided a reasonable analytical scale for terrain texture analysis and could be used as a measure of the regional topography to accurately describe basic terrain characteristics.

Stability Analysis of Bohai Oil-Drilling Ship No. 6 Under Static and Cyclic Loads

This paper presents a procedure to calculate the safety factor against sliding of a marine gravity structure subjected to a combination of static and cyclic loads. This procedure claculates the stress at the sliding surface by the finite element method (FEM) and takes the dynamic properties of clay into account. With this procedure, the stability of a Bohai oil-drilling ship is analyzed. The calculated safety factor is much smaller than 1, indicating that this oil-drilling ship would fail just as what had happened to it.