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.

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.

A Simplified Model with Soil Water Limitation on Spring Wheat Growth

The authors constructed a simplified model of spring wheat (Triticum aestivum L.) carbon assimilation and dry matter accumulation (DMA) process which consisted of two independent variables, day length (L) and total daily radiation (TDR). Leaf water potential (Ψ) was incorporated into the simplified growth model based on the assumption that both light use efficiency (α) and CO 2 conductance of assimilation (g c) were depressed by water limitation. Finally,Ψ was estimated from a regression equation in which the independent variables were relative soil water content in the upper 80 cm (θ R,80 ), ambient temperature (T a), vapor pressure deficit (VPD), the cumulative leaf water potential below thresholds of -1.5 MPa (Ψ c,1.5 ). Some applications in research program of field experiment of atmosphere_land surface processes in Heihe River region were tested. The simulated data agreed well with the data observed at Linze oasis in 1989 for various levels of water supply and at Zhangye oasis in 1992 in the field. The analysis and simulation using the model demonstrated that the simplified growth model could describe very well the DMA process of spring wheat with and without water limitation in the region of HEIFE (Heihe field experiment).

Basic Soil Productivity of Spring Maize in Black Soil Under Long-Term Fertilization Based on DSSAT Model

Increasing basic farmland soil productivity has significance in reducing fertilizer application and maintaining high yield of crops. In this study, we defined that the basic soil productivity （BSP） is the production capacity of a farmland soil with its own physical and chemical properties for a specific crop season under local environment and field management. Based on 22-yr （1990-2011） long-term experimental data on black soil （Typic hapludoll） in Gongzhuling, Jilin Province, Northeast China, the decision support system for an agro-technology transfer （DSSAT）-CERES-Maize model was applied to simulate the yield by BSP of spring maize （Zea mays L.） to examine the effects of long-term fertilization on changes of BSP and explore the mechanisms of BSP increasing. Five treatments were examined： （1） no-fertilization control （control）; （2） chemical nitrogen, phosphorus, and potassium （NPK）; （3） NPK plus farmyard manure （NPKM）; （4） 1.5 time of NPKM （1.5NPKM） and （5） NPK plus straw （NPKS）. Results showed that after 22-yr fertilization, the yield by BSP of spring maize significantly increased 78.0, 101.2, and 69.4% under the NPKM, 1.5NPKM and NPKS, respectively, compared to the initial value （in 1992）, but not significant under NPK （26.9% increase） and the control （8.9% decrease）. The contribution percentage of BSP showed a significant rising trend （P〈0.05） under 1.5NPKM. The average contribution percentage of BSP among fertilizations ranged from 74.4 to 84.7%, and ranked as 1.5NPKM〉NPKM〉NPK〉NPKS, indicating that organic manure combined with chemical fertilizers （I.5NPKM and NPKM） could more effectively increase BSP compared with the inorganic fertilizer application alone （NPK） in the black soil. This study showed that soil organic matter （SOM） was the key factor among various fertility factors that could affect BSP in the black soil, and total N, total P and/or available P also played important role in BSP increasing. Compared with the chemical fertilization, a balanced chemical plus manure or straw fertilization （NPKM or NPKS） not only increased the concentrations of soil nutrient, but also improved the soil physical properties, and structure and diversity of soil microbial population, resulting in an iincrease of BSP. We recommend that a balanced chemical plus manure or straw fertilization （NPKM or NPKS） should be the fertilization practices to enhance spring maize yield and improve BSP in the black soil of Northeast China.

SIMPLE ECOSYSTEM MODEL OF THE CENTRAL PART OF THE EAST CHINA SEA IN SPRING

This paper’s simple ecological model to simulate the ecosystem variation and the vertical carbon flux in the central part of the East China Sea in spring, inter-reated the phytoplankton, zooplankton,autotrophic and heterotrophic bacterioplankton, nitrate, and dissolved organic carbon (DOC) in a run lasting 90 days. Except for DOC, because of poor observation precision,the major seasonal features of the vertical distribution for these components can be simulated by this model. The results show that spring bloom is just a short period of 1-2 weeks and that deposit carbon flux at the bottom interface is about 200 mg /m2 ·d in the first 20 days and then reaches its maximum of 1500mg/m2·d about 2 months later after the spring bloom.

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.

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.

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.

A STATISTICAL PREDICTION MODEL FOR SPRING RAINFALL OVER NORTHERN CHINA BASED ON THE INTERANNUAL INCREMENT APPROACH

The spring (March-April-May) rainfall over northern China (SPRNC) is predicted by using the interannual increment approach. DY denotes the difference between the current year and previous years. The seasonal forecast model for the DY of SPRNC is constructed based on the data that are taken from the 1965-2002 period (38 years), in which six predictors are available no later than the current month of February. This is favorable so that the seasonal forecasts can be made one month ahead. Then, SPRNC and the percentage anomaly of SPRNC are obtained by the predicted DY of SPRNC. The model performs well in the prediction of the inter-annual variation of the DY of SPRNC during 1965-2002, with a correlation coefficient between the predicted and observed DY of SPRNC of 0.87. This accounts for 76% of the total variance, with a low value for the average root mean square error (RMSE) of 20%. Both the results of the hindcast for the period of 2003-2010 (eight years) and the cross-validation test for the period of 1965-2009 (45 years) illustrate the good prediction capability of the model, with a small mean relative error of 10%, an RMSE of 17% and a high rate of coherence of 87.5% for the hindcasts of the percentage anomaly of SPRNC.

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.

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.

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.

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.

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.

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.

Modeling and Simulation of Diaphragm Spring Clutch

A model was developed to simulate a vehicle diaphragm spring clutch with the evaluation indicators of jerk degree and friction work.First,the pressing load characteristic of the driven plate of the diaphragm spring clutch was analyzed.Then,the clutch dynamic characteristic under each state was studied according to the basic principles of tribology.Finally,the mathematical model of the clutch was developed.Based on the model,the performance of a vehicle was simulated.The simulation results show that the model can predict the dynamic characteristic of the clutch correctly and evaluate the performance of the clutch engagement effectively.The model can be used for theoretical research of automatic clutch control and can be easily applied to simulate vehicle longitudinal dynamics.

Mathematical Model of the Geothermal Water Resources in the South Hot Spring System in Chongqing

The geothermal waters of south hot spring, small hot spring and Qiaokouba in Chongqing, are all part of the south hot spring geothermal water system. Exploitation has caused a decline in the water levels of the south and small hot springs, which have not flowed naturally for 15 years. Now, bores pump geothermal water to the springs. If the water level drops below the elevation of the rivers, river-water will replenish the geothermal water, destroying this resource. It is therefore an urgent task to model the geothermal water system, to enable sustainable development and continued use of the geothermal water in Qiaokouba. A numerical simulation of the geothermal water system was adopted and a quantitative study on the planning scheme was carried out. A mathematical model was set up to simulate the whole geothermal water system, based on data from the research sites. The model determined the maximum sustainable water yield in Qiaokouba and the two hot springs, and the south hot spring and small hot spring sustainable yields are 1 100 m^3/d and 700 m^3/d from 2006 to 2010, 1 300 m^3/d and 1 000 m^3/d from 2011 to 2015, and 1 500 m^3/d and 1 200 m^3/d from 2016 to 2036. The maximum exploitable yield is 3 300 m^3/d from 2006 to 2036 in Qiaokouba. The model supplies a basis to adequately exploit and effectively protect the geothermal water resources, and to continue to develop the geothermal water as a tourist attraction in Chongqing.

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.

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 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.