Stiffness Characteristics of a Basic Nonlinear Air Spring Model

This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.

Dynamic Behavior and Deformation Analysis of the Fish Cage System Using Mass-Spring Model

Fish cage systems are influenced by various oceanic conditions, and the movements and deformation of the system by the external forces can affect the safety of the system itself, as well as the species of fish being cultivated. Structural durability of the system against environmental factors has been major concern for the marine aquaculture system. In this research, a mathematical model and a simulation method were presented for analyzing the performance of the large-scale fish cage system influenced by current and waves. The cage system consisted of netting, mooring ropes, floats, sinkers and floating collar. All the elements were modeled by use of the mass-spring model. The structures were divided into finite elements and mass points were placed at the mid-point of each element, and mass points were connected by springs without mass. Each mass point was applied to external and internal forces, and total force was calculated in every integration step. The computation method was applied to the dynamic simulation of the actual fish cage systems rigged with synthetic fiber and copper wire simultaneously influenced by current and waves. Here, we also tried to find a relevant ratio between buoyancy and sinking force of the fish cages. The simulation results provide improved understanding of the behavior of the structure and valuable information concerning optimum ratio of the buoyancy to sinking force according to current speeds.

Modeling stress wave propagation in rocks by distinct lattice spring model

In this paper, the ability of the distinct lattice spring model （DLSM） for modeling stress wave propagation in rocks was fully investigated. The influence of particle size on simulation of different types of stress waves （e.g. one-dimensional （1D） P-wave, 1D S-wave and two-dimensional （2D） cylindrical wave） was studied through comparing results predicted by the DLSM with different mesh ratios （It） and those obtained from the corresponding analytical solutions. Suggested values of lr were obtained for modeling these stress waves accurately. Moreover, the weak material layer method and virtual joint plane method were used to model P-wave and S-wave propagating through a single discontinuity. The results were compared with the classical analytical solutions, indicating that the virtual joint plane method can give better results and is recommended. Finally, some remarks of the DLSM on modeling of stress wave propagation in rocks were provided.

On the four-dimensional lattice spring model for geomechanics

Recently, a four-dimensional lattice spring model(4D-LSM) was developed to overcome the Poisson’s ratio limitation of the classical LSM by introducing the fourth-dimensional spatial interaction. In this work, some aspects of the 4D-LSM on solving problems in geomechanics are investigated, such as the ability to reproduce elastic properties of geomaterials, the capability of solving heterogeneous problems,the accuracy on modelling stress wave propagation, the ability to solve dynamic fracturing and the parallel computational efficiency. Our results indicate that the 4D-LSM is promising to deal with problems in geomechanics.

Full Dynamic Model for Liquid Sloshing Simulation in Cylindrical Tank Shape

This study presents a comprehensive full dynamic model designed for simulating liquid sloshing behavior within cylindrical tank structures. The model employs a discretization approach, representing the liquid as a network of interconnected spring-damper-mass systems. Key aspects include the adaptation of liquid discretization techniques to cylindrical lateral cross-sections and the calculation of stiffness and damping coefficients. External forces, simulating various vehicle maneuvers, are also integrated into the model. The resulting system of equations is solved using Maple Software with the Runge-Kutta-Fehlberg method. This model enables accurate prediction of liquid displacement and pressure forces, offering valuable insights for tank design and fluid dynamics applications. Ongoing refinement aims to broaden its applicability across different liquid types and tank geometries.

Stability analysis on tunnels with karst caves using the distinct lattice spring model

The effects of karst caves on tunnel stability were numerically investigated using the distinct lattice spring model(DLSM).The DLSM was validated by investigating the mechanical behavior of Brazilian discs with various sizes of central circular holes.Then,the effects of karst cave on U-shaped tunnel were investigated under various karst caves positions(top,bottom,and right side of the tunnel),tunnelcave distances(0.5-4 times the radius of the tunnel arc),and cave shapes(circular,rectangular flat,and rectangular vertical caves).The failure processes of the tunnel under those various conditions were analyzed and both the failure process and the final failure patterns of the tunnel were discussed.Numerical simulation demonstrated that karst caves around the tunnel could weaken the stability of the tunnel,indicating tunnel-cave distance effects.The closer the cave to the tunnel,the weaker the tunnel under loading.This effect was not significant when the tunnel-cave distance(d)was larger than three times the tunnel arc radius(R).In addition,the final failure pattern of the tunnel and its surrounding rock mass were dependent on both the position and the size of the cave.The larger the cave,the weaker the tunnel and its surrounding rock mass.Furthermore,compared with those cases with top and bottom caves,the tunnel with a right side cave had more impacts on tunnel stability.The main research finding could help engineers carry out stability analysis on tunnels in karst areas and take effective measures to enhance tunnel stability.

Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

We use front tracking data structures and functions to model the dynamic evolution of fabric surface.We represent the fabric surface by a triangulated mesh with preset equilibrium side length.The stretching and wrinkling of the surface are modeled by the mass-spring system.The external driving force is added to the fabric motion through the"Impulse method"which computes the velocity of the point mass by superposition of momentum.The mass-spring system is a nonlinear ODE system.Added by the numerical and computational analysis,we show that the spring system has an upper bound of the eigen frequency.We analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency.This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system.Based on this analysis,we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion.We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.

Elastic Characteristics of Digital Cores from Longmaxi Shale Using Lattice Spring Models

Effective medium methods for the attribution of micro-structures to macro elastic properties of shales are important for the prediction of sweet spots in the shale-gas production.With X-ray micro-computed tomography(XMCT),the micro-structures of shale core samples from Longmaxi Formation are visualized and characterized by 3D digital images.As an efficient alternative to conventional effective medium methods for estimating elastic properties,we propose a consistent workflow of lattice spring modeling(LSM)to emulate the digital cores using three types of lattices.Particular attention is paid to investigate the effective Young’s moduli,Poisson’s ratios,and preferred orientations,by uniaxial compression tests along two directions.Within elastic deformation,the impact of lattice arrangements on the anisotropy is even more than those of stress disturbances and micro-structural features.Compared with analytical approximations and theoretical predictions,the LSM numerical scheme shows general applicability for heterogeneous porous rocks.

Design and Modeling on Stranded Wires Helical Springs

A stranded wires helical spring is formed of a multilayer and coaxial strand of several wires twisted together with the same direction of spiral. Compared with the conventional single wire spring, the stranded wires helical spring has the notable predominance in strength, damping and vibration reduction, which is usually used in aircraft engines, automatic weapons, etc. However, due to its complicated structure, the precise computation of its strength and rigidity need be a correct mathematical model, which then will be imported to finite element analysis software for solutions. Equations on solving geometric parameters, such as external diameters of strands and screw pitches of wires, are put forward in the paper. It also proposes a novel methodology on solving geometric parameters and establishing entity models of the stranded wires helical spring, which provides foundation of computing mechanical parameters by FEA. Then mathematical models on the centre line of the strand and the surface curve of each wire, after closing two ends in a spring, are proposed. Finally, geometric parameters are solved in a case study, and a 3D entity model of a spring with 3 layers and 16 wires is established, which has validated the accuracy of the proposed methodology and the 3D entity mathematical model. The method provides a new way to design stranded wire helical spring.

Electrical triggering of earthquakes:results of laboratory experiments at spring-block models

Recently published results of field and laboratory experiments on the seismic/acoustic response to injection of direct current （DC） pulses into the Earth crust or stressed rock samples raised a question on a possibility of electrical earthquake triggering. A physical mechanism of the considered phenomenon is not clear yet in view of the very low current density （10-7-10-s A/m^2） generated by the pulsed power systems at the epicenter depth （5-10 km） of local earthquakes occurred just after the current injection. The paper describes results of laboratory ＂earthquake＂ triggering by DC pulses under conditions of a spring-block model simulated the seismogenic fault. It is experimentally shown that the electric triggering of the laboratory ＂earthquake＂ （sharp slip of a movable block of the spring-block system） is possible only within a range of subcritical state of the system, when the shear stress between the movable and fixed blocks obtains 0.98-0.99 of its critical value. The threshold of electric triggering action is about 20 A/m^2 that is 7-8 orders of magnitude higher than estimated electric current density for Bishkek test site （Northern Tien Shan, Kirghizia） where the seismic response to the man-made electric action was observed. In this connection, the electric triggering phenomena may be explained by contraction of electric current in the narrow conductive areas of the faults and the corresponding increase in current density or by involving the secondary triggering mechanisms like electromagnetic stimulation of conductive fluid migration into the fault area resulted in decrease in the fault strength properties.

Three-stage Method for Identifying the Dynamic Model Parameters of Stranded Wire Helical Springs

The dynamic behavior of the stranded wire helical spring is described by a modified Bouc-Wen model while the model parameters must be identified using an identification method and experimental data. Existing identification methods usually relies either solely nonlinear iterative algorithms or manually trial and error. Therefore, the identification process can be rather time consuming and effort taking. As a result, these methods are not ideal for engineering applications. To come up with a more practical method, a three-stage identification method is proposed. Periodic loading and identification simulations are carried out to verify the effectiveness of the proposed method. Noises are added to the simulated data to test the performance of the proposed method when dealing with noise contaminated data. The simulation results indicate that the proposed method is able to give satisfying results when the noise levels are set to be 0.01, 0.03, 0.05 and 0.07. In addition, the proposed method is also applied to experimental data and compared with an existing method. The experimental data is acquired through a periodic loading test. The experiment results suggest that the proposed method features better accuracy compared with the existing method. An effective approach is proposed for identifying the model parameters of the stranded wire helical spring.

Relationship between South China Sea Precipitation Variability and Tropical Indo-Pacific SST Anomalies in IPCC CMIP5 Models during Spring-to-Summer Transition

The present study evaluates the precipitation variability over the South China Sea（SCS） and its relationship to tropical Indo-Pacific SST anomalies during spring-to-summer transition（April–May–June,AMJ） simulated by 23 Intergovernmental Panel on Climate Change Coupled Model Intercomparison Project Phase 5 coupled models.Most of the models have the capacity to capture the AMJ precipitation variability in the SCS.The precipitation and SST anomaly（SSTA） distribution in the SCS,tropical Pacific Ocean（TPO）,and tropical Indian Ocean（TIO） domains is evaluated based on the pattern correlation coefficients between model simulations and observations.The analysis leads to several points of note.First,the performance of the SCS precipitation anomaly pattern in AMJ is model dependent.Second,the SSTA pattern in the TPO and TIO is important for capturing the AMJ SCS precipitation variability.Third,a realistic simulation of the western equatorial Pacific（WEP） and local SST impacts is necessary for reproducing the AMJ SCS precipitation variability in some models.Fourth,the overly strong WEP SST impacts may disrupt the relationship between the SCS precipitation and the TPO–TIO SST.Further work remains to be conducted to unravel the specific reasons for the discrepancies between models and observations in various aspects.

Modelling and Optimisation of a Spring-Supported Diaphragm Capacitive MEMS Microphone

Audio applications such as mobile communication and hearing aid devices demand a small size but high performance, stable and low cost microphone to reproduce a high quality sound. Capacitive microphone can be designed to fulfill such requirements with some trade-offs between sensitivity, operating frequency range, and noise level mainly due to the effect of device structure dimensions and viscous damping. Smaller microphone size and air gap will gradually decrease its sensitivity and increase the viscous damping. The aim of this research was to develop a mathematical model of a spring-supported diaphragm capacitive MEMS microphone as well as an approach to optimize a microphone’s performance. Because of the complex shapes in this latest type of diaphragm design trend, analytical modelling has not been previously attempted. A novel diaphragm design is proposed that offers increased mechanical sensitivity of a capacitive microphone by reducing its diaphragm stiffness. A lumped element model of the spring-supported diaphragm microphone is developed to analyze the complex relations between the microphone performance factors and to find the optimum dimensions based on the design requirements. It is shown analytically that the spring dimensions of the spring-supported diaphragm do not have large effects on the microphone performance com pared to the diaphragm and backplate size, diaphragm thickness, and air-gap distance. A 1 mm2 spring-supported diaphragm microphone is designed using several optimized performance parameters to give a –3 dB operating bandwidth of 10.2 kHz, a sensitivity of 4.67 mV/Pa (–46.5 dB ref. 1 V/Pa at 1 kHz using a bias voltage of 3 V), a pull-in voltage of 13 V, and a thermal noise of –22 dBA SPL.

Modelling the meteorological influence on the yellowing of spring wheat leaves

The yellowed-leaf rate is one of the important variables in simulation models for thegrowth of spring wheat. Based on the field experiments (1985-1988), the evolution of yellowed-leafrate of spring wheat is analyzed. The functional relationship between the yellowing process of greenleaves and the development stages of spring wheat is established. Based on modelling and correctingfor the yellowing proass of green leaves affected by temperature and moisture, the synthetic modelfor simulating the dynaniical evolution of yellowed-leaf rate is constructed. The numerical experi-inents show that the result of the modelling is satisfactory.

Impacts of Upper Tropospheric Cooling upon the Late Spring Drought in East Asia Simulated by a Regional Climate Model

Responses of late spring （21 April 20 May） rainfall to the upper tropospheric cooling over East Asia are investigated with a regional climate model based on Laboratoire de M6t6orologie Dynamique Zoom （LMDZ4-RCM）. A control experiment is performed with two runs driven by the mean ERA-40 data during 1958-1977 and 1981 2000, respectively. The model reproduces the major decadal-scale circulation changes in late spring over East Asia, including a cooling in the upper troposphere and an anomalous meridional cell. Accordingly, the precipitation decrease is also captured in the southeast of the upper-level cooling region. To quantify the role of the upper-level cooling in the drought mechanism, a sensitivity experiment is further conducted with the cooling imposed in the upper troposphere. It is demonstrated that the upper-level cooling can generate the anomalous meridional cell and consequently the drought to the southeast of the cooling center. Therefore, upper tropospheric cooling should have played a dominant role in the observed late spring drought over Southeast China in recent decades.

Modelling and Inversion of Ground Magnetic and Electromagnetic Data for Delineation of Subsurface Structures at Siloam Hot Spring in the Soutpansberg Basin

Geophysical surveys utilising magnetic and electromagnetic techniques were carried out at the Siloam hot spring. The spring is in the Soutpansberg Basin in the northern part of South Africa. The research was to investigate groundwater bearing structures at the hot spring. Magnetic survey results showed that the spring occurs between two north dipping dykes. The two dykes could be faulted segments of a single dyke or sill. Magnetic susceptibility results highlighted the presence of metamorphic and volcanic rocks. Electromagnetic survey results showed that the hot spring was within a roughly east to west trending, zone with high electrical conductivity values. Based on the survey results, water is exploiting fractures in the dyke or sill.

A preliminary study on simplified simulation model of spring wheat growth

In the model developed in this paper, taking the characters and requirements of meteorological services into account, some conventional meteorological observations which are easy to be obtained have been ch.osen, and mathematical equations describing micro-growth processes of crops have been established on the basis of the field experiments, laboratorial analysis and computer's modelling tests with time interval of ten-days for several years (1987-1989), in accordance with the known biological and physical rules and corresponding reference literatures. It is a preliminary simplified simulation model of spring wheat growth in optimal water and nutrient conditions. The field experiments show that simulation results of this simplified model are satisfactory. The potential operational application and theoretical sense are significant in the meteorological forecast of yield and in the assessment of influences of climatic change on agriculture.

Mass-Spring-Damper Model with Steady State Parameters for Predicting the Movement of Liquid Column and Temperature Oscillation in Loop Heat Pipe

In order to investigate the mechanism of the temperature oscillation in loop heat pipes,this paper investigated the movement of the phase interface as the changed input power by a mass-spring-damper model.The model was solved with MATLAB and was used to explain the high-frequency and low-amplitude temperature oscillation.Temperature variation with the input power from 20 W to 75 W was investigated based on a LHP prototype in a literature.The model agreed well with the experimental data in the literature.The simulation results suggested that the movement of the liquid column was caused by the fluctuation of pressure difference applied on the liquid column and the stiffness coefficients of the vapor springs increasing with the input power.According to parameter analyses,the temperature oscillation at the outlet of the condenser can be weakened by increasing the mass of the liquid column and keeping the temperature at the outlet of the condenser steady.

考虑环间接头影响的盾构隧道纵向变形简化解

为反映外荷载下盾构隧道相邻环间张开和错台,提出考虑环间接头影响的盾构隧道纵向变形简化解答。首先,引入纵向梁-弹簧模型模拟盾构隧道纵向受力变形,其中采用Timoshenko短梁考虑隧道环段变形,引入转动和剪切弹簧分别模拟环间接头转动与错台。其次,构建弹性地基上纵向梁-弹簧模型的有限差分方程,以解决环间接头-管环非连续变形求解问题,并推导外荷载下既有盾构隧道的纵向变形公式。最后,建立新建隧道上穿和下穿引起既有盾构隧道的纵向变形解答,并与新建隧道上、下穿越工程案例及现有理论方法对比验证。研究结果表明:所提方法预测的隧道位移与Timoshenko连续梁模型,协同变形模型和实测数据均具有较好的一致性,但所提方法得到的环间错台略低于Timoshenko梁模型和协同变形模型;所提方法可考虑环间接头的影响,得到的隧道位移曲线呈现既不光滑也不连续的特征,其中环段变形以刚体位移为主,而环间接头主要发生转动和错台;而基于现有理论所得盾构隧道纵向位移均为连续曲线,无法反映环间接头的真实转动与错台位移。

Voronoi-RBSM耦合的混凝土细观建模方法研究

为解决已有混凝土细观数值模拟方法计算效率低、对象尺寸受限的问题,提出一种基于Voronoi网格拓扑和刚体弹簧模型(RBSM)的混凝土细观建模新思路。该模型将混凝土视为由骨料、水泥砂浆组成的二相材料,骨料通过Voronoi单胞描述,视为刚性体,水泥砂浆简化为Voronoi单胞交界面的均布弹簧,弹簧刚度依据局部砂浆的实际情况自动定义。无需对骨料和水泥砂浆进行网格细化,可大大减少单元数量,允许Voronoi单胞在界面处侵入和分离,描述混凝土的变形、开裂等。为验证该文模型的有效性和适用性,开展了室内试验与数值模拟的对比研究,并分析了骨料占比等参数的敏感性。结果表明:基于Voronoi-RBSM的混凝土细观模型,可以较为高效、准确预测混凝土构件在加载过程中细观力学响应,对于尺寸较小的混凝土试件、尺寸较大钢筋混凝土简支梁均有较好的细观模拟效果,尤其是当网格尺寸与骨料平均粒径接近时,预测结果与试验结果最为接近。此外,模型的预测精度受骨料体积占比影响,骨料体积占比越小精度越低,因此,并不适用于浆体占比高的混凝土材料细观数值模拟。