Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation

This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.

Sensitivity analysis of factors affecting gravity dam anti-sliding stability along a foundation surface using Sobol method

The anti-sliding stability of a gravity dam along its foundation surface is a key problem in the design of gravity dams.In this study,a sensitivity analysis framework was proposed for investigating the factors affecting gravity dam anti-sliding stability along the foundation surface.According to the design specifications,the loads and factors affecting the stability of a gravity dam were comprehensively selected.Afterwards,the sensitivity of the factors was preliminarily analyzed using the Sobol method with Latin hypercube sampling.Then,the results of the sensitivity analysis were verified with those obtained using the Garson method.Finally,the effects of different sampling methods,probability distribution types of factor samples,and ranges of factor values on the analysis results were evaluated.A case study of a typical gravity dam in Yunnan Province of China showed that the dominant factors affecting the gravity dam anti-sliding stability were the anti-shear cohesion,upstream and downstream water levels,anti-shear friction coefficient,uplift pressure reduction coefficient,concrete density,and silt height.Choice of sampling methods showed no significant effect,but the probability distribution type and the range of factor values greatly affected the analysis results.Therefore,these two elements should be sufficiently considered to improve the reliability of the dam anti-sliding stability analysis.

ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS

This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.

Simplified Method of Stability Analysis of Nonlinear Systems without Using of Lyapunov Concept

In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.

Comprehensive Analysis Method of Slope Stability Based on the Limit Equilibrium and Finite Element Methods and Its Application

To study the safety and stability of large slopes, taking the right side slope of the Yuxi’an tunnel of the Yuchu Expressway Bridge in Yunnan Province as an example, limit equilibrium and finite element analysis were applied to engineering examples to calculate the stability coefficient of the slope before and after excavation in the natural state. After comparative analysis, it was concluded that the former had a clear mechanical model and concept, which could quickly provide stability results;the latter could accurately determine the sliding surface of the slope and simulate the stress state changes of the rock and soil mass. The stability coefficients calculated by the two methods were within the stable range, but their values were different. On this basis, combined with the calculation principles, advantages and disadvantages of the two methods, a comprehensive analysis method of slope stability based on the limit equilibrium and finite element methods was proposed, and the rationality of the stability coefficient calculated by this method was judged for a slope case.

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.

THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED PERTURBATIONS

The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.

Inverse reliability analysis and design for tunnel face stability considering soil spatial variability

The traditional deterministic analysis for tunnel face stability neglects the uncertainties of geotechnical parameters,while the simplified reliability analysis which models the potential uncertainties by means of random variables usually fails to account for soil spatial variability.To overcome these limitations,this study proposes an efficient framework for conducting reliability analysis and reliability-based design(RBD)of tunnel face stability in spatially variable soil strata.The three-dimensional(3D)rotational failure mechanism of the tunnel face is extended to account for the soil spatial variability,and a probabilistic framework is established by coupling the extended mechanism with the improved Hasofer-Lind-Rackwits-Fiessler recursive algorithm(iHLRF)as well as its inverse analysis formulation.The proposed framework allows for rapid and precise reliability analysis and RBD of tunnel face stability.To demonstrate the feasibility and efficacy of the proposed framework,an illustrative case of tunnelling in frictional soils is presented,where the soil's cohesion and friction angle are modelled as two anisotropic cross-correlated lognormal random fields.The results show that the proposed method can accurately estimate the failure probability(or reliability index)regarding the tunnel face stability and can efficiently determine the required supporting pressure for a target reliability index with soil spatial variability being taken into account.Furthermore,this study reveals the impact of various factors on the support pressure,including coefficient of variation,cross-correlation between cohesion and friction angle,as well as autocorrelation distance of spatially variable soil strata.The results also demonstrate the feasibility of using the forward and/or inverse first-order reliability method(FORM)in high-dimensional stochastic problems.It is hoped that this study may provide a practical and reliable framework for determining the stability of tunnels in complex soil strata.

A Calculation Method of Double Strength Reduction for Layered Slope Based on the Reduction of Water Content Intensity

The calculation of the factor of safety(FOS)is an important means of slope evaluation.This paper proposed an improved double strength reductionmethod(DRM)to analyze the safety of layered slopes.The physical properties of different soil layers of the slopes are different,so the single coefficient strength reduction method(SRM)is not enough to reflect the actual critical state of the slopes.Considering that the water content of the soil in the natural state is the main factor for the strength of the soil,the attenuation law of shear strength of clayey soil changing with water content is fitted.This paper also establishes the functional relationship between different reduction coefficients.Then,a USDFLD subroutine is programmed using the secondary development function of finite element software.Controlling the relationship between field variables and calculation time realizes double strength reduction applicable to the layered slope.Finally,by comparing the calculation results of different examples,it is proved that the stress and displacement distribution of the critical slope state obtained by the improved method is more realistic,and the calculated safety factor is more reliable.The newly proposedmethod considers the difference of intensity attenuation between different soil layers under natural conditions and avoids the disadvantage of the strength reduction method with uniform parameters,which provides a new idea and method for stability analysis of layered and complex slopes.

Borehole stability in naturally fractured rocks with drilling mud intrusion and associated fracture strength weakening:A coupled DFN-DEM approach

Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.

Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media

In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.

Stabilization meshless method for convection-dominated problems

It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal refinement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all.

Classification and rating of disintegrated dolomite strata for slope stability analysis

Although disintegrated dolomite,widely distributed across the globe,has conventionally been a focus of research in underground engineering,the issue of slope stability issues in disintegrated dolomite strata is gaining increasing prominence.This is primarily due to their unique properties,including low strength and loose structure.Current methods for evaluating slope stability,such as basic quality(BQ)and slope stability probability classification(SSPC),do not adequately account for the poor integrity and structural fragmentation characteristic of disintegrated dolomite.To address this challenge,an analysis of the applicability of the limit equilibrium method(LEM),BQ,and SSPC methods was conducted on eight disintegrated dolomite slopes located in Baoshan,Southwest China.However,conflicting results were obtained.Therefore,this paper introduces a novel method,SMRDDS,to provide rapid and accurate assessment of disintegrated dolomite slope stability.This method incorporates parameters such as disintegrated grade,joint state,groundwater conditions,and excavation methods.The findings reveal that six slopes exhibit stability,while two are considered partially unstable.Notably,the proposed method demonstrates a closer match with the actual conditions and is more time-efficient compared with the BQ and SSPC methods.However,due to the limited research on disintegrated dolomite slopes,the results of the SMRDDS method tend to be conservative as a safety precaution.In conclusion,the SMRDDS method can quickly evaluate the current situation of disintegrated dolomite slopes in the field.This contributes significantly to disaster risk reduction for disintegrated dolomite slopes.

Study on Numerical Comparison Method of Four-bar Straight-line Guidance Mechanism

In order to solve four-bar straight-line guidance mechanism synthesis problem for the arbitrarily given straight-line’s"angle requirement"and"point-position requirement",a numerical comparison synthesis method for single and double straight-line guidance mechanism is presented,which is convenient to realize by computer program.The basic idea of this method is:to select a four-bar linkage whose relative bar length of crank is 1 as a basic four-bar linkage.Then the other three relative bars’length is changed,and a lot of basic four-bar linkage can be obtained.There are many single and double ball-points of each basic four-bar linkage.With the motion of a basic four-bar linkage,there is straight-line segment of each Ball-point’s path.The data of these basic four-bar linkages is saved to a database.When designing a four-bar straight-line guidance mechanism,the design data is compared with the data in database and a satisfactory four-bar linkage can be obtained.The method effectively solves the straight-line guidance mechanism synthesis problem.

Stability Analysis of Nonlinear Models of Nose Landing Gear Shimmy

Shimmy can reduce the service life of the nose landing gear, affect ride comfort, and even cause fuselage damage leading to aircraft crashes. Taking a light aircraft as the research object, the torsional freedom of landing gear around strut axis and lateral deformation of tire are considered. Since the landing gear shimmy is a nonlinear system, a nonlinear mechanical model of the front landing gear shimmy is established. Sobol index method is proposed to analyze the influence of structural parameters on the stability region of the nose landing gear, and Routh-Huritz criterion is used to verify the reliability of the analysis results of Sobol index method. We analyse the effect of torsional stiffness of strut, caster length, rated initial tire inflation pressure, rake angle, and vertical force on the stability region of theront landing gear. And the research shows that the optimization of the torsional stiffness of the strut and the caster length of the nose landing gear should be emphasized, and the influence of vertical force on the stability region of the nose landing gear should be paid attention to.

Slope stability analysis under seismic load by vector sum analysis method

The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.

Control and Stabilization of Chaotic System Based on Linear Feedback Control Method

In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.

Review and comparison of methods and benchmarks for automatic modal identification based on stabilization diagram

Automatic modal identification via automatically interpreting the stabilization diagram provides key technique in bridge structural health monitoring.This paper reviews the progress in the area of automatic modal identification based on interpreting the stabilization diagram.The whole identification process is divided into four steps from establishing the stabilization diagram to removing the outliers in the identification results.The criteria and algorithms used in each step in the existing studies are carefully summarized and classified.Comparisons between typical methods in cleaning and interpreting the stabilization diagram are also conducted.Real structure benchmarks used in the existing studies to validate the proposed automatic modal identification methods are also summarized.Based on the review and comparison,the specific ratio method for cleaning the stabilization diagram,the hierarchical clustering method for interpreting the stabilization diagram and the adjusted boxplot for removing the outliers in the identification results are the most suitable methods for each step.The key point of automatic modal identification based on interpreting the stabilization diagram has also discussed,and it is recommended to pay more attention to cleaning the stabilization diagram.Future study about automatic modal identification under situation with very few sensors deployed should be more concerned.This review aims to help researchers and practitioners in implementing existing automatic modal identification algorithms effectively and developing more suitable and practical methods for civil engineering structures in the future.

Simulation of bluff body stabilized flows with hybrid RANS and PDF method

The motivation of this study is to investigate the turbulence-chemistry interactions by using probability density function （PDF） method. A consistent hybrid Reynolds Averaged Navier-Stokes （RANS）/PDF method is used to simulate the turbulent non-reacting and reacting flows. The joint fluctuating velocity-frequency-composition PDF equation coupled with the Reynolds averaged density, momentum and energy equations are solved on unstructured meshes by the Lagrangian Monte Carlo （MC） method combined with the finite volume （FV） method. The simulation of the axisymmetric bluff body stabilized non-reacting flow fields is presented in this paper. The calculated length of the recirculation zone is in good agreement with the experimental data. Moreover, the significant change of the flow pattern with the increase of the jet-to-coflow momentum flux ratio is well predicted. In addition, comparisons are made between the joint PDF model and two different Reynolds stress models.