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.

The asymptotic stability analysis in stochastic logistic model with Poisson growth coefficient

The asymptotic stability of a discrete logistic model with random growth coefficient is studied in this paper. Firstly, the discrete logistic model with random growth coefficient is built and reduced into its deterministic equivalent system by orthogonal polynomial approximation. Then, the linear stability theory and the Jury criterion of nonlinear deterministic discrete systems are applied to the equivalent one. At last, by mathematical analysis, we find that the parameter interval for asymptotic stability of nontrivial equilibrium in stochastic logistic system gets smaller as the random intensity or statistical parameters of random variable is increased and the random parameter’s influence on asymptotic stability in stochastic logistic system becomes prominent.

Determine Stability Wellbore Utilizing by Artificial Intelligence Systems and Estimation of Elastic Coefficients of Reservoir Rock

Rock elastic properties such as Young’s modulus, Poisson?s ratio, plays an important role in various stages upstream of such as borehole stability, hydraulic fracturing in laboratory scale for observing mechanical properties of the reservoir rock usually using conventional cores sample that obtained from underground in reservoir condition. This method is the most common and most reliable way to get the reservoir rock properties, but it has some weaknesses. Currently, neural network techniques have replaced usual laboratory methods because they can do a similar operation faster and more accurately. To obtain the elastic coefficient, we should have compressional wave velocity (VP), shear wave (Vs) and density bulk due to high cost of (Vs) measurement and low real ability of estimation through the (Vp) and porosity. Therefore in this study, neural networks were used as a suitable method for estimating shear wave, and then elastic coefficients of reservoir rock using different relationships were predicted. Neural network used in this study was not like a black box because we used the results of multiple regression that could easily modify prediction of (Vs) through appropriate combination of data. The same information that were intended for multiple regression were used as input in neural networks, and shear wave velocity was obtained using (Vp) and well logging data in carbonate rocks. The results showed that methods applied in this carbonate reservoir was successful, so that shear wave velocity was predicted with about 92% and 95% correlation coefficient in multiple regression and neural network method, respectively.

INSTABILITY OF SOLUTION FOR THE FOURTH ORDER LINEAR DIFFERENTIAL EQUATION WITH VARIED COEFFICIENT

In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.

Chebyshev Polynomial-Based Analytic Solution Algorithm with Efficiency, Stability and Sensitivity for Classic Vibrational Constant Coefficient Homogeneous IVPs with Derivative Orders n, n-1, n-2

The Chebyshev polynomials are harnessed as functions of the one parameter of the nondimensionalized differential equation for trinomial homogeneous linear differential equations of arbitrary order n that have constant coefficients and exhibit vibration. The use of the Chebyshev polynomials allows calculation of the analytic solutions for arbitrary n in terms of the orthogonal Chebyshev polynomials to provide a more stable solution form and natural sensitivity analysis in terms of one parameter and the initial conditions in 6n + 7 arithmetic operations and one square root.

Intelligent prediction of slope stability based on visual exploratory data analysis of 77 in situ cases

Slope stability prediction research is a complex non-linear system problem.In carrying out slope stability prediction work,it often encounters low accuracy of prediction models and blind data preprocessing.Based on 77 field cases,5 quantitative indicators are selected to improve the accuracy of prediction models for slope stability.These indicators include slope angle,slope height,internal friction angle,cohesion and unit weight of rock and soil.Potential data aggregation in the prediction of slope stability is analyzed and visualized based on Six-dimension reduction methods,namely principal components analysis(PCA),Kernel PCA,factor analysis(FA),independent component analysis(ICA),non-negative matrix factorization(NMF)and t-SNE(stochastic neighbor embedding).Combined with classic machine learning methods,7 prediction models for slope stability are established and their reliabilities are examined by random cross validation.Besides,the significance of each indicator in the prediction of slope stability is discussed using the coefficient of variation method.The research results show that dimension reduction is unnecessary for the data processing of prediction models established in this paper of slope stability.Random forest(RF),support vector machine(SVM)and k-nearest neighbour(KNN)achieve the best prediction accuracy,which is higher than 90%.The decision tree(DT)has better accuracy which is 86%.The most important factor influencing slope stability is slope height,while unit weight of rock and soil is the least significant.RF and SVM models have the best accuracy and superiority in slope stability prediction.The results provide a new approach toward slope stability prediction in geotechnical engineering.

Critical Assessment of Slope Stability: A Case Study on the Toffo-Lalo Road Project

This article systematically delves into a comprehensive analysis of the latest and most advanced techniques for the assessment of slope stability. It particularly focuses on strategies aimed at enhancing slope stability in road construction. In addition to this analysis, the article presents an illustrative case study centered on the Toffo-Lalo Road Project. The core objective of this paper is to scrutinize the stability of large embankments in road construction, with a specific emphasis on the development and asphalt overlay of the Toffo-Lalo road. This scrutiny is conducted through the utilization of stability calculation software, GEOSTUDIO2018, specifically its SLOPE/W module. Within this framework, a detailed model of the cutbank located at KP1+750-2+250 was meticulously developed. This model takes into account the physical-mechanical characteristics of the soil at the site, as well as the topographic layout. Its attributes include a cohesion value of 11.3 Kpa, a density of 16.57 KN/m3, and a friction angle of 27˚. The modeling results, employing the Morgenstern-Price method—an approach renowned for its adherence to equilibrium conditions and provision of precise results—conclude that the safety coefficient (Fs = 1.429) prior to any reinforcement signifies a critical state of slope stability. To address this, the article explores the implementation of reinforcement techniques, particularly focusing on rigid inclusions like nailing and piles. The modeling exercises reveal a noteworthy enhancement in the safety coefficient (Fs) post-reinforcement. Furthermore, the article undertakes a parametric study to optimize the reinforcement strategies. This analysis highlights that anchoring at 0˚ downward relative to the horizontal plane and employing a pile angle of 90˚ represent the most favorable approaches. These measures yield safety coefficients of 3.60 and 2.34, respectively, indicating substantially improved slope stability.

Strategies for Advancing Road Construction Slope Stability: Unveiling Innovative Techniques for Managing Unstable Terrain

This comprehensive review paper explores various aspects of geotechnical engineering, with a focus on the management of unstable terrains, numerical methods for solving complex soil and consolidation problems, rheological analysis of suspensions and muddy soils, and stability analysis of slopes. It begins by examining the unique physicochemical properties of cohesive sediments, including cohesion and specific surface area. The temporal evolution of deposit concentration and average bed concentration in unstable terrains is discussed, along with settling behavior of isolated particles and hindered settling using empirical equations. Key sedimentation theories, such as Kynch’s theory, and geotechnical consolidation theories, including Terzaghi’s consolidation equation and Gibson’s theory, are presented. The investigation interrelates these theories and principles to offer a holistic view of managing unstable terrains. It also addresses the challenges associated with experimental determination of constitutive relationships and presents alternative simplification methods proposed by researchers. Additionally, it delves into numerical methods for solving nonlinear partial differential equations governing soil behavior, emphasizing the need for numerical frameworks and discussing various techniques and associated challenges. The rheological analysis section covers material flow behavior, rheological behavior models, and the rheological properties of water and cohesive sediment mixtures. Fundamental geotechnical calculations, constitutive laws, and failure criteria are explained, highlighting their relevance in geotechnical engineering applications. This paper provides a multidimensional perspective on geotechnical engineering, offering valuable insights into soil properties, consolidation processes, numerical methods, rheological analysis, and slope stability assessment for professionals in the field.

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.

Relation between stabilization energy, crystal field coefficient and the magnetic exchange interaction for Tb^(3+) ion

Based on a single ion model, Hamiltonian of the simplest form about magnetocrystalline anisotropy for Tb3+ ion was solved by using the numerical method. The relation between the stabilization energy, crystal field coefficient B20 and the magnetic exchange interaction was studied as temperature approaches to 0 K. The results show that the stabilization energy contributed by Tb3+ is linear with crystal field coefficient B20 approximately, but it is insensitive to the change of magnetic exchange interaction for the strong magnetic substances such as TbCo5, Tb2Co17 and Tb2Fe14B compounds.

Stability analysis of concrete gravity dam on complicated foundation with multiple slide planes

A key problem in gravity dam design is providing enough stability to prevent slide, and the difficulty increases if there are several weak structural planes in the dam foundation. Overload and material weakening were taken into account, and a .finite difference strength reserve method with partial safety factors based on the reliability method was developed and used to study the anti-slide stability of a concrete gravity dam on a complicated foundation with multiple slide planes. Possible slide paths were obtained, and the stability of the foundation with possible failure planes was evaluated through analysis of the stress distribution characteristics. The results reveal the mechanism and process of sliding due to weak structural planes and their deformations, and provide a reference for anti-slide stability analysis of gravity dams in complicated geological conditions.

Mode stability analysis in the beam-wave interaction process for a three-gap Hughes-type coupled cavity chain

Based on space-charge wave theory, the formulae of the beam-wave coupling coefficient and the beam-loaded conductance are given for the beam-wave interaction in an N-gap Hughes-type coupled cavity chain. The ratio of the nonbeam-loaded quality factor of the coupled cavity chain to the beam quality factor is used to determine the stability of the beam-wave interaction. As an example, the stabilities of the beam-wave interaction in a three-gap Hughes-type coupled cavity chain are discussed with the formulae and the CST code for the operations of the 2π, π, and π/2 modes, respectively. The results show that stable operation of the 2π, π, and π/2 modes may all be realized in an extended-interaction klystron with the three-gap Hughes-type coupled cavity chain.

Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for a Transient Stokes Interface Problem with Jump Coefficients

The distributed Lagrange multiplier/fictitious domain(DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients.The semi-and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface,where the arbitrary Lagrangian-Eulerian(ALE)technique is employed to deal with the moving and immersed subdomain.Stability and optimal convergence properties are obtained for both schemes.Numerical experiments are carried out for different scenarios of jump coefficients,and all theoretical results are validated.

Stability analysis of shallow tunnels subjected to seepage with strength reduction theory

Based on strength reduction theory,the stability numbers of shallow tunnels were investigated within the framework of upper and lower bound theorems of limit analysis. Stability solutions taking into account of water seepage were presented and compared with those without considering seepage. The comparisons indicate that the maximum difference does not exceed 3.7%,which proves the present method credible. The results show that stability numbers of shallow tunnels considering seepage are much less than those without considering seepage,and that the difference of stability numbers between considering seepage and without considering seepage increase with increasing the depth ratio. The stability numbers decrease with increasing permeability coefficient and groundwater depth. Seepage has significant effects on the stability numbers of shallow tunnels.

Modification of Slenderness Coefficient of Angle Steels

To provide information for amendment to Technical Specifications for Power Transmission Towers (SDGJ94-90), the critical loads of typical compressed angle steels was calculated. The correlation of buckling loads and slenderness of compressed angle steels was obtained with regression. A new slenderness coefficient equation was proposed based on the result of the correlation. A practical measure to ensure good result in nonlinear solution using Arch-length method is put forward.

Thermal expansion and dimensional stability of unidirectional and orthogonal fabric M40/AZ91D composites

Unidirectional (60%, volume fraction) and orthogonal (50%, volume fraction) M40 graphite fibre reinforced AZ91D magnesium alloy matrix composites were fabricated by pressure infiltration method. The coefficients of thermal expansion (in the temperature range of 20-350 ℃) and dimensional stability (in the temperature range of 20-150 ℃) of the composites and the corresponding AZ91D magnesium alloy matrix were measured. The results show that coefficients of thermal expansion of the composites in longitudinal direction decrease with elevating temperature. The coefficients of thermal expansion (CTE) for unidirectional M40/AZ91D composites and orthogonal M40/AZ91D composites are 1.24×10-6 ℃-1 and 5.71×10-6 ℃-1 at 20 ℃, and 0.85×10-6 ℃-1 and 2.75×10-6 ℃-1 at 350 ℃, respectively, much lower than those of the AZ91D alloy matrix. Thermal cycling testing demonstrates that the thermal stress plays an important role on residual deformation. Thus, a better dimensional stability is obtained for the AZ91D magnesium alloy matrix composites. More extreme strain hysteresis and residual plastic deformation are observed in orthogonally fabric M40 reinforced AZ91D composite, but its net residual strain after each cycle is similar to that of the unidirectional M40/AZ91D composite.

Analysis on stability of pillar and stiff roof system in the gob area

Based on the open stope method,the stability of the gob area was decided bypillars and stiff roof.Therefore,it was dispensable to leave pillars with long-term strengthand enough size to support the stiff roof during mining activities.Based on the miningconditions of Baixiang wollastonite mine in Changxing County of Zhejiang,while consideringpillars with different shape,irregular size,and distribution,the load imposed on the pillarswas analyzed,and the safety coefficient was calculated in order to determine theirsupport status.The strength of stiff roof was calculated by means of analytical solution-theory of rectangle thin plate rested on elastic foundation.The system stability ofpillar and stiff roof was analyzed according to the proportion of the total cross section areaof pillars to the stiff roof area above the mined area.

Landslide stability for Shuitianba in the Three Gorges area

According to the data of preliminary survey, the authors established a landslide geological model,on the basis of analyses on the sensitivity of landslide, tried to simulate and calculate the landslide stability of Shuitianba with the method of transfer coefficient when it is under different strength parameters, and study the landslide mechanism. The results show that it is sensitive to the effects of shear strength parameters of sliding zone and groundwater level on landslide stability safety coefficient, which provides reliable basis for calculation of landslide stability.

Tribological stability of particle reinforced aluminum matrix composites in braking

The tribological stability of particle reinforced aluminum matrix composites in braking was studied. Considering the requirements of the intention of present transportation field, high braking pressure and high initial braking rotating speed, as well as different reinforcement volume fractions were selected. The results indicate that under a systematic comparison with traditional braking material of cast iron, SiC particulate reinforced aluminum material composites (PRAMC) can retain stable friction coefficient in various braking pressures and rotating speeds. Even in a concrete course of braking, PRAMC can also maintain friction coefficient with little fluctuation. The existence of a uniform mass transfer layer adhering to the contact surface is an important prerequisite for maintaining a stable friction coefficient.

Reliability analysis method for slope stability based on sample weight

The single safety factor criteria for slope stability evaluation, derived from the rigid limit equilibrium method or finite element method （FEM）, may not include some important information, especially for steep slopes with complex geological conditions. This paper presents a new reliability method that uses sample weight analysis. Based on the distribution characteristics of random variables, the minimal sample size of every random variable is extracted according to a small sample t-distribution under a certain expected value, and the weight coefficient of each extracted sample is considered to be its contribution to the random variables. Then, the weight coefficients of the random sample combinations are determined using the Bayes formula, and different sample combinations are taken as the input for slope stability analysis. According to one-to-one mapping between the input sample combination and the output safety coefficient, the reliability index of slope stability can be obtained with the multiplication principle. Slope stability analysis of the left bank of the Baihetan Project is used as an example, and the analysis results show that the present method is reasonable and practicable for the reliability analysis of steep slopes with complex geological conditions.