Insight Into the Separation-of-Variable Methods for the Closed-Form Solutions of Free Vibration of Rectangular Thin Plates

The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.

Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

Synthesis methods and powder quality of titanium monocarbide

Titanium monocarbide(TiC),which is the most stable titanium-based carbide,has attracted considerable interest in the fields of energy,catalysis,and structural materials due to its excellent properties.Synthesis of high-quality TiC powders with low cost and high efficiency is crucial for industrial applications;however major challenges face its realization.Herein,the methods for synthesizing TiC powders based on a reaction system are reviewed.This analysis is focused on the underlying mechanisms by which synthesis methods affect the quality of powders.Notably,strategies for improving the synthesis of highquality powders are analyzed from the perspective of enhancing heat and mass transfer processes.Furthermore,the critical issues,challenges,and development trends of the synthesis technology and application of high-quality TiC powder are discussed.

Structural Modal Parameter Recognition and Related Damage Identification Methods under Environmental Excitations: A Review

Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.

Cascading multi-segment rupture process of the 2023 Turkish earthquake doublet on a complex fault system revealed by teleseismic P wave back projection method

In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back projection analysis.Data in two frequency bands(0.5-2 Hz and 1-3 Hz)are used in the imaging processes.The results show that the rupture of the first event extends about 200 km to the northeast and about 150 km to the southwest,lasting~90 s in total.The southwestern rupture is triggered by the northeastern rupture,demonstrating a sequential bidirectional unilateral rupture pattern.The rupture of the second event extends approximately 80 km in both northeast and west directions,lasting~35 s in total and demonstrates a typical bilateral rupture feature.The cascading ruptures on both sides also reflect the occurrence of selective rupture behaviors on bifurcated faults.In addition,we observe super-shear ruptures on certain fault sections with relatively straight fault structures and sparse aftershocks.

Gas Chromatographic Method for Identification and Quantification of Commonly Used Residual Solvents in Pharmaceuticals Products

Background: Impurities are not expected in the final pharmaceutical products. All impurities should be regulated in both drug substances and drug products in accordance with pharmacopeias and ICH guidelines. Three different types of impurities are generally available in the pharmaceutical’s product specification: organic impurities, inorganic impurities, and residual solvents. Residual solvents are organic volatile chemicals used or generated during the manufacturing of drug substances or drug products. Purpose: The aim of this study is to develop a cost-effective gas chromatographic method for the identification and quantification of some commonly used solvents—methanol, acetone, isopropyl alcohol (IPA), methylene chloride, ethyl acetate, tetrahydrofuran (THF), benzene, toluene, and pyridine—in pharmaceutical product manufacturing. This method will be able to identify and quantify the multiple solvents within a single gas chromatographic procedure. Method: A gas chromatography (GC) equipped with a headspace sampler and a flame ionization detector, and a column DB 624, 30-meter-long × 0.32-millimeter internal diameter, 1,8 μm-thick, Brand-Agilent was used to develop this method. The initial GC oven temperature was 40°C and held for 5 minutes. It was then increase to 80˚C at a rate of 2˚C per minute, followed by a further increase to 225˚C at a rate of 30˚C per minute, with a final hold at 225˚C for 10 minutes. Nitrogen was used as a carrier gas at a flow rate of 1.20 mL per minute. Dimethyl sulfoxide (DMSO) was selected as sample solvent. Results: The developed method is precise and specific. The percent RSD for the areas of six replicate injections of this gas chromatographic method was within 10.0 and the recovery result found within 80.0% to 120.0%.

Numerical Methods for a Class of Quadratic Matrix Equations

Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.

Research on the Extraction of OLR Anomaly Prior to Ms 7.5 Sand Point,Alaska Earthquake based on IPI Method

Based on the understanding that the seismic fault system is a nonlinear complex system,Rundle(1995)introduced the nonlinear threshold system used in meteorology to analyze the ocean-atmosphere interface and the El Ni?o Southern Oscillation into the study of seismic activity changes,and then proposed the PI method(Rundle et al.,2000a,b).Wu et al.(2011)modified the Pattern Informatics Method named MPI to extract the ionospheric anomaly by using data from DEMETER satellites which is suitable for 1–3 months short-term prediction.

Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

Big Data Analysis of Policy Coordination Paths Based on Latent Dirichlet Allocation Model and Fuzzy-Set Qualitative Comparative Analysis Method

The selection and coordinated application of government innovation policies are crucial for guiding the direction of enterprise innovation and unleashing their innovation potential.However,due to the lengthy,voluminous,complex,and unstructured nature of regional innovation policy texts,traditional policy classification methods often overlook the reality that these texts cover multiple policy topics,leading to lack of objectivity.In contrast,topic mining technology can handle large-scale textual data,overcoming challenges such as the abundance of policy content and difficulty in classification.Although topic models can partition numerous policy texts into topics,they cannot analyze the interplay among policy topics and the impact of policy topic coordination on enterprise innovation in detail.Therefore,we propose a big data analysis scheme for policy coordination paths based on the latent Dirichlet allocation(LDA)model and the fuzzyset qualitative comparative analysis(fsQCA)method by combining topic models with qualitative comparative analysis.The LDA model was employed to derive the topic distribution of each document and the word distribution of each topic and enable automatic classi-fication through algorithms,providing reliable and objective textual classification results.Subsequently,the fsQCA method was used to analyze the coordination paths and dynamic characteristics.Finally,experimental analysis was conducted using innovation policy text data from 31 provincial-level administrative regions in China from 2012 to 2021 as research samples.The results suggest that the proposed method effectively partitions innovation policy topics and analyzes the policy configuration,driving enterprise innovation in different regions.

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.

Simplified quantitative analysis method and its application in the insitu synthesized copper-based azide chips

Copper-based azide(Cu(N_(3))2 or CuN_(3),CA)chips synthesized by in-situ azide reaction and utilized in miniaturized explosive systems has become a hot research topic in recent years.However,the advantages of in-situ synthesis method,including small size and low dosage,bring about difficulties in quantitative analysis and differences in ignition capabilities of CA chips.The aim of present work is to develop a simplified quantitative analysis method for accurate and safe analysis of components in CA chips to evaluate and investigate the corresponding ignition ability.In this work,Cu(N_(3))2 and CuN_(3)components in CA chips were separated through dissolution and distillation by utilizing the difference in solubility and corresponding content was obtained by measuring N_(3)-concentration through spectrophotometry.The spectrophotometry method was optimized by studying influencing factors and the recovery rate of different separation methods was studied,ensuring the accuracy and reproducibility of test results.The optimized method is linear in range from 1.0-25.0 mg/L,with a correlation coefficient R^(2)=0.9998,which meets the requirements of CA chips with a milligram-level content test.Compared with the existing ICP method,component analysis results of CA chips obtained by spectrophotometry are closer to real component content in samples and have satisfactory accuracy.Moreover,as its application in miniaturized explosive systems,the ignition ability of CA chips with different component contents for direct ink writing CL-20 and the corresponding mechanism was studied.This study provided a basis and idea for the design and performance evaluation of CA chips in miniaturized explosive systems.

Vibration properties of Paulownia wood for Ruan sound quality using machine learning methods

As an important material for manufacturing resonant components of musical instruments,Paulownia has an important influence on the sound quality of Ruan.In this paper,a model for evaluating the sound quality of Ruan based on the vibration characteristics of wood is developed using machine learning methods.Generally,the selection of materials for Ruan manufacturing relies primarily on manually weighing,observing,striking,and listening by the instrument technician.Deficiencies in scientific theory have hindered the quality of the finished Ruan.In this study,nine Ruans were manufactured,and a prediction model of Ruan sound quality was proposed based on the raw material information of Ruans.Out of a total of 180 data sets,145 and 45 sets were chosen for training and validation,respec-tively.In this paper,typical correlation analysis was used to determine the correlation between two single indicators in two adjacent pairwise combinations of the measured objects in each stage of the production process in Ruan.The vibra-tion characteristics of the wood were tested,and a model for predicting the evaluation of Ruan’s acoustic qualities was developed by measuring the vibration characteristics of the resonating plate material.The acoustic quality of the Ruan sound board wood was evaluated and predicted using machine learning model generalized regression neural net-work.The results show that the prediction of Ruan sound quality can be achieved using Matlab simulation based on the vibration characteristics of the soundboard wood.When the model-predicted values were compared with the tradi-tional predicted results,it was found that the generalized regression neural network had good performance,achieving an accuracy of 93.8%which was highly consistent with the experimental results.It was concluded that the model can accurately predict the acoustic quality of the Ruan based on the vibration performance of the soundboards.

Influence of joint spacing and rock characteristics on the toppling stability of cut rock slope through a simplified limit equilibrium method

Toppling failure of rock mass/soil slope is an important geological and environmental problem.Clarifying its failure mechanism under different conditions has great significance in engineering.The toppling failure of a cutting slope occurred in a hydropower station in Kyushu,Japan illustrates that the joint characteristic played a significant role in the occurrence of rock slope tipping failure.Thus,in order to consider the mechanical properties of jointed rock mass and the influence of geometric conditions,a simplified analytical approach based on the limit equilibrium method for modeling the flexural toppling of cut rock slopes is proposed to consider the influence of the mechanical properties and geometry condition of jointed rock mass.The theoretical solution is compared with the numerical solution taking Kyushu Hydropower Station in Japan as one case,and it is found that the theoretical solution obtained by the simplified analysis method is consistent with the numerical analytical solution,thus verifying the accuracy of the simplified method.Meanwhile,the Goodman-Bray approach conventionally used in engineering practice is improved according to the analytical results.The results show that the allowable slope angle may be obtained by the improved Goodman-Bray approach considering the joint spacing,the joint frictional angle and the tensile strength of rock mass together.

Novel damage constitutive models and new quantitative identification method for stress thresholds of rocks under uniaxial compression

Four key stress thresholds exist in the compression process of rocks,i.e.,crack closure stress(σ_(cc)),crack initiation stress(σ_(ci)),crack damage stress(σ_(cd))and compressive strength(σ_(c)).The quantitative identifications of the first three stress thresholds are of great significance for characterizing the microcrack growth and damage evolution of rocks under compression.In this paper,a new method based on damage constitutive model is proposed to quantitatively measure the stress thresholds of rocks.Firstly,two different damage constitutive models were constructed based on acoustic emission(AE)counts and Weibull distribution function considering the compaction stages of the rock and the bearing capacity of the damage element.Then,the accumulative AE counts method(ACLM),AE count rate method(CRM)and constitutive model method(CMM)were introduced to determine the stress thresholds of rocks.Finally,the stress thresholds of 9 different rocks were identified by ACLM,CRM,and CMM.The results show that the theoretical stress−strain curves obtained from the two damage constitutive models are in good agreement with that of the experimental data,and the differences between the two damage constitutive models mainly come from the evolutionary differences of the damage variables.The results of the stress thresholds identified by the CMM are in good agreement with those identified by the AE methods,i.e.,ACLM and CRM.Therefore,the proposed CMM can be used to determine the stress thresholds of rocks.

Analysis of Extended Fisher-Kolmogorov Equation in 2D Utilizing the Generalized Finite Difference Method with Supplementary Nodes

In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme.Following temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node.These supplementary nodes are distributed along the boundary to match the number of boundary nodes.By incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation.To demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem.

High-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer based on probability density evolution method

This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.

A new approach for pseudo hyperbolic partial differential equations with nonLocal conditions using Laplace Adomian decomposition method

This paper provides a nonlinear pseudo-hyperbolic partial differential equation with non-local conditions.Despite the importance of this problem,the exact solution to this problem is rare in the literature.Therefore,the Laplace-Adomian Decomposition Method(LADM)is used to provide a new approach to solving this problem.Additionally,we give a comparison between the exact and approximate solutions at various points with absolute error.The obtained result showed that the proposed method is effective and accurate for this problem and can be used for many other evolution of nonlinear equations in mathematical physics.

Dynamic Location Method for Shallow Ocean Bottom Nodes Using the Levenberg-Marquart Algorithm

Ocean bottom node(OBN)data acquisition is the main development direction of marine seismic exploration;it is widely promoted,especially in shallow sea environments.However,the OBN receivers may move several times because they are easily affected by tides,currents,and other factors in the shallow sea environment during long-term acquisition.If uncorrected,then the imaging quality of subsequent processing will be affected.The conventional secondary positioning does not consider the case of multiple movements of the receivers,and the accuracy of secondary positioning is insufficient.The first arrival wave of OBN seismic data in shallow ocean mainly comprises refracted waves.In this study,a nonlinear model is established in accordance with the propagation mechanism of a refracted wave and its relationship with the time interval curve to realize the accurate location of multiple receiver movements.In addition,the Levenberg-Marquart algorithm is used to reduce the influence of the first arrival pickup error and to automatically detect the receiver movements,identifying the accurate dynamic relocation of the receivers.The simulation and field data show that the proposed method can realize the dynamic location of multiple receiver movements,thereby improving the accuracy of seismic imaging and achieving high practical value.