Physical Modeling Method Research Articles

Robot physical modeling based on matlab/simulink

Robots play an irreplaceable role in the manufacturing industry. The use of machines instead of humans‘activing. It is a long-term development trend, but it is difficult to realize the research of real robots, and the data that the robot can collect is less. In response to the above problems, this article mainly proposes a method of physical modeling using matlab/simulink. This method can realize research without robots, and can obtain more robot-related data. This method includes robot physical modeling, importing into simulink and packaging in simulink. This article is mainly aimed at IRB6700 robot to complete the simulation platform construction.

Data-driven predictive control for the swing process of a cutter suction dredger

The working process of cutter suction dredger is complex, so it is difficult to establish accurate model by traditional physical modeling method. The final yield of cutter suction dredger is directly related to the density of the slurry in the pipeline, while the density is controlled by the swing process. Therefore, by analyzing the measured data of the dredger, it establishes the swing process mathematical model based on subspace theory. The algorithm is based on input–output data, simulation results show the algorithm is effective for the control application.

Development of pumps with improved anti-cavitation characteristics

When considering the creation of pumps with improved anti-cavitation characteristics, the results of an in-depth analysis of the problem of pumping viscous liquids at high temperatures are presented. On the example of the technological process of evaporation of sugar syrup on a film evaporator of the latest type, the problem of the occurrence of cavitation when pumping viscous liquids at high temperatures was revealed. After analyzing the existing machines used for the specified operating conditions, critical design and operating parameters were identified that affect the appearance of cavitation. Namely, the appearance of cavitation is influenced by the reduced diameter of the impeller inlet, the diameter of the impeller inlet, the number of blades, the width of the blades and the rotor speed. To study the level of influence of these parameters, a method of physical modeling was chosen, an experimental stand was designed and manufactured. Studies have been carried out on the operation of the pump with and without a reducer. The work with a two- and three-blade inducer is analyzed, the work with an open and closed impeller, with one and two-level blade system is investigated. As a result of the analysis of experimental data, the optimal design of the hydraulic part with a three-blade reducer and a semi-open impeller with a two-level blade system was chosen. In turn, this made it possible to reduce the compression of the flow at the inlet to the impeller without loss of energy efficiency; the angles of inclination of the inducer and impeller blades were synchronized. The experience gained made it possible to design and manufacture an industrial sample of a cantilever pump with an inducer and a semi-open impeller. Thus, allowing to solve the problem of pumping thick syrup on a film evaporating unit of the Teofipol sugar plant (Khmelnytskyi region, Ukraine), with a cavitation reserve of 1.5 m.

Research of hydrodynamics of gas flow filtration through a stationary layer of crushed cotton stalks (wild cotton)

The object of this research is the hydrodynamics of the stationary layer of crushed cotton stalks. One of the most problematic areas is the influence of the physical and mechanical characteristics of the stationary layer of crushed cotton stalks on the hydrodynamics of filtration drying. In the course of research, methods of physical and mathematical modeling are used. Sieve analysis is used to determine the granulometric composition of the polydisperse mixture of crushed cotton stalks. The granulometric composition of the crushed stalks of cotton is determined and the graphical dependence of the percentage of each fraction is presented. The hydrodynamics of gas flow filtration through a stationary layer of crushed cotton stalks are experimentally investigated, and a graphical dependence of pressure losses on the fictitious rate of gas flow filtration is presented. It is found that pressure losses in the stationary layer of crushed cotton stalks are parabolic, which indicates the influence of both inertial and viscous components on pressure losses. The unknown coefficients of the modified Ergun equation are determined on the basis of experimental data. The correlation dependence between the experimental and theoretically calculated values is presented and it is shown that the maximum relative error is 9.6 %, which is quite acceptable for practical calculations. The results of experimental studies are also presented in the form of a graphical dependence of the Euler number on the Reynolds number. Based on the generalization of the experimental data, the calculated dependences are obtained in the form of dimensionless complexes, which describe the hydrodynamics of the gas flow filtration through a stationary layer of crushed cotton stalks. This makes it possible to predict the energy costs for creating a differential pressure, with an accuracy sufficient for practical calculations. The ratio of the experimental values of pressure losses to the theoretically calculated ones, depending on the Reynolds number, is graphically presented. It is shown that the maximum relative error does not exceed 8 %. The proposed generalizations of experimental data will make it possible to determine the energy consumption for creating a pressure drop at the design stage of the drying equipment, as well as to calculate the optimal process parameters and predict its economic feasibility.

100-years’ story of success: photoelasticity — LSR–MICE – MSUCE

Introduction. The 100-years’ history of MICE – MSUCE is also a history of establishment and flourishing of one of the world’s most powerful experimental school of development and application of the photoelasticity method in the investigation of the stress state of civil and special structures. Reliable forecast of the stress state of buildings and structures under static, thermal and dynamic impacts is an indispensable prerequisite of safe operation provision of civil structures during the construction and the operation. The photoelasticity method, allows, along with the analytical methods of the mechanical science, for continual study of the stress state of the object under test, being an experimental method efficiently used both in “standalone” mode and in conjunction with numerical methods. The goal and the objectives hereof: a retrospective development review of the photoelasticity method, in particular, of the contribution of LSR of MICE, and the assessment of the contemporary state of the method in terms of its actuality, novelty and practical significance of mechanical problem solutions, of stress-strain state studies of structures and buildings.
 
 Materials and methods. The subject hereof is the polarized light method or the photoelasticity method: development, problematics, solution methods of mechanical problems and studies of structures, applications.
 
 Results. The paper describes solution examples of vital problems by the photoelasticity method: stress analysis in the wedge-shaped notch zone of the area boundary, stress state problem under forced deformation in the block-basement contact area, stress state study of underground hydropower plant tunnel with the weir erected by pinpoint blasting. The performed analysis of the photoelasticity method and its contemporary level illustrates the opportunities provided by the method in solving of mechanical problems and in structural studies.
 
 Conclusions. Is the experimental school of the photoelasticity method of LSR–MICE – MSUCE really the sunk Atlantis? The development of the experimental mechanics of deformable solid bodies is characterized by progressive proximity of experimental and numerical analysis research methods. The physical modelling, in particular, the polarized light method, allows for obtaining stress-strain state diagrams of structures, or solutions of mechanical problems, feasible for assessment or for calculation result corrections, that is why the polarized light method retains actuality and practical significance. The development of the deformable solid body mechanics determines the significance of the physical modelling, including the polarized light method. The benefit of the polarized light method is the continuity of mechanical problem solutions which is especially important when local areas with specific features of the stress strain behaviour are considered. Modern technologies of material property studies, invention of new materials lead to creation of new mechanical models, for adequacy assessment of which physical modelling methods are required, in particular, the polarized light method.

Physical modeling of unsteady electromagnetic processes in power transformer under sharp load fluctuations

Purpose. To develop and experimentally confirm the method of physical modeling of non-stationary electromagnetic processes in a powerful power transformer operating under variable loads by combining similarity criteria and equivalence coefficients. Methodology. Theoretical provisions of mathematical and computer modeling, theoretical electrical engineering were used in the research, as well as the theory of experiment with the application of equivalence coefficients. Findings. Methods of experimental research were developed, which include the formation and registration of a set of external and internal parameters of physical models, prototypes and real equipment. Criteria for similarity of nonstationary electromagnetic processes excited by sharply changing scattering fields in special purpose power transformers are obtained. . Originality. The theory and practice of physical modeling, as well as the similarity theory applied to unsteady electromagnetic processes in powerful transformer equipment for special purposes were further developed. A set of distinctive features of test conditions and their registration were formed. Practical value. Application of physical modeling of unsteady electromagnetic processes at the design and manufacture stages of power transformers for power supply systems of electric arc furnaces, rolling mill drives, etc., as well as during the refinement of general-purpose power transformers.

Исследование теплового состояния металла с использованием методов физического и математического моделирования

Исследование теплового состояния металла с использованием методов физического и математического моделирования

A Novel Simulation Method for Analyzing Diode Electrical Characteristics Based on Neural Networks

Based on the equivalent circuit model and physical model, a new method for analyzing diode electrical characteristics based on a neural network model is proposed in this paper. Although the equivalent circuit model is widely used, it cannot effectively reflect the working state of diode circuits under the conditions of large injection and high frequency. The analysis method based on physical models developed in recent years can effectively resolve the above shortcomings, but it faces the problem of a low simulation efficiency. Therefore, the physical model method based on neural network acceleration is used to improve the traditional, equivalent circuit model. The results obtained from the equivalent circuit model and the physical model are analyzed using the finite-difference time-domain method. The diode model based on a neural network is fitted with training data obtained from the results of the physical model, then it is summarized into a voltage–current equation and used to improve the traditional, equivalent circuit method. In this way, the improved equivalent circuit method can be used to analyze the working state of a diode circuit under large injection and high frequency conditions. The effectiveness of the proposed model is verified by some examples.

Coriolis force impact on lump kinematics in a grinder workspace

Research relevance. Currently produced rotary grinders are not efficient enough, while their efficiently is mainly characterized by the degree of fineness. This is due to sparse knowledge of the processes occurring in the counter-impact labyrinth rotor when the material is being ground, and therefore insufficient scientific substantiation of the design methods. The grinding member’s geometry and rotation speed have been set empirically according to the similarity principle, which inevitably results in grinding fineness and efficiency deviation from the set values. It seems impossible to improve the design and therefore the running efficiency of the equipment unless the kinematics of a lump in the channel of the grinder is analyzed. Particular attention should be paid to the Coriolis force impact on the kinematics of a lump. It will make it possible to scientifically substantiate the dependence between equipment design and technological parameters. Methods of research included the factor analysis, data synthesis, and methods of mathematical and physical modeling. Object of research is a rotary grinder preparing rocks for sampling. Subject of research is the workflow of the counter-impact rotary grinder. Research objective is to increase the efficiency of the ore rotary grinder by analyzing particles movement in the rotor channels. Methods of research includes the analysis of particles motion in the rotor channels using the provisions of theoretical mechanics and the theory of impact. The differential calculus acts as a mathematical apparatus. Results and summary. Based on the proposed particle motion theory analysis and qualitative representations of the processes in the rotor of the counter-impact grinder, it is essential to form the foundation to obtain quantitative dependencies for design calculations. This will improve the methods of design and construction of a new type of rotary grinder. It was found that the Coriolis force reduces the relative speed of a lump by not more than 20.3% depending on the assumptions made

The atmospheric nitrogen fixation thermodynamic probability study depending on the mixed mineral fertilizers composition

The mixed mineral fertilizers component composition effect on the binding atmospheric nitrogen thermodynamic probability in soils was studied. The studies were carried out by the physical and chemical modelling method based on the Selector software package. The systems following final indicators were calculated: the Gibbs system energy, the corresponding independent components chemical potentials, the solution components amount, the evolved gases amount, the solution pH, and the system redox potential. The results obtained in this work make it possible to conclude that the atmospheric nitrogen fixation in a nitrate ion form is thermodynamically resolved, and the problem lies in finding conditions conducive to this process implementation. It was revealed that the thermodynamic probability of atmospheric nitrogen oxidation depends both on the mineral fertilizer main component and on this component form, in particular, on its redox or acid-base characteristics. According to the modelling results, limestone as a mixed mineral fertilizers component contributes to a significant increase in the binding atmospheric nitrogen thermodynamic probability with the most oxidized form formation. The nitrogen presence in mixed mineral fertilizers in the most oxidized form (the nitrogen oxidation state is +5) can contribute to the conditions’ creation favorable for fixing atmospheric nitrogen. An increase in the urea and ammonium hydrate content in ammonia water, where nitrogen is in the maximum reduced oxidation state of -3, on the contrary, leads to a decrease in the atmospheric nitrogen binding thermodynamic probability to form oxide forms.

Accuracy of the independent atom approximation in digital tomosynthesis Monte Carlo simulations

Monte Carlo (MC) codes serve as the gold standard simulation tool during design and optimisation of x-ray imaging systems. Such simulations often model Rayleigh scattering based on the Independent Atom Approximation Model (IAM). This model neglects the low range molecular interference (MI) effects of non-crystalline materials such as human tissues. Previous work has found discrepancies in the simulated images of planar x-ray images between IAM and MI models. However, insignificant differences were found for computed tomography (CT) reconstructions. In this work we present Geant4 MC simulations of a flat panel source digital tomosynthesis (DT) system for human extremities. Results show that with a 1:9 scatter to primary ratio (SPR) in the x-ray projections, the DT reconstructions are insensitive to the differences of the IAM and MI models. Therefore, MC codes that use the IAM model are sufficient for the study of DT systems. That is because DT algorithms have a larger effect on image quality than the few percent change in the noise due to a physical model and noise suppression methods make this change even less important. Dependency of this conclusion on SPR must be considered in other DT modalities where SPR might be larger.

Audio Enhancement of Physical Models of Musical Instruments Using Optimal Correction Factors: The Recorder Case

A simulation of a musical instrument is considered to be a successful one when there is a good resemblance between the model’s synthesized sound and the real instrument’s sound. In this work, we propose the integration of physical modeling (PM) methods with an optimization process to regulate a generated digital signal. Its goal is to find a new set of values of the PM’s parameters’ that would lead to a synthesized signal matching as much as possible to reference signals corresponding to the physical musical instrument. The reference signals can be: (a) described by their acoustic characteristics (e.g., fundamental frequencies, inharmonicity, etc.) and/or (b) the signals themselves (e.g., impedances, recordings, etc.). We put this method into practice for a commercial recorder, simulated using the digital waveguides’ PM technique. The reference signals, in our case, are the recorded signals of the physical instrument. The degree of similarity between the synthesized (PM) and the recorded signal (musical instrument) is calculated by the signals’ linear cross-correlation. Our results show that the adoption of the optimization process resulted in more realistic synthesized signals by (a) enhancing the degree of similarity between the synthesized and the recorded signal (the average absolute Pearson Correlation Coefficient increased from 0.13 to 0.67), (b) resolving mistuning issues (the average absolute deviation of the synthesized from the recorded signals’ pitches reduced from 40 cents to the non-noticeable level of 2 cents) and (c) similar sound color characteristics and matched overtones (the average absolute deviation of the synthesized from the recorded signals’ first five partials reduced from 41 cents to 2 cents).

Effect of submerged entry nozzle wall surface morphologies on boundary layer structure and alumina inclusions transport

During the Al-killed steel continuous casting process, the molten steel corrosion and the accumulation of alumina inclusion deposits affect the submerged entry nozzle (SEN) wall surface, including the surface morphologies of the smooth wall, porous refractory wall, and clogged wall. The SEN wall surface morphology affects the boundary layer structure and alumina inclusions transport. In this study, a physical modeling method was adopted, and the surface morphologies simulation was realized by filling up the natural porous refractory material and inserting the real clog material in the polymethyl methacrylate SEN model. The velocity in the boundary layer was measured using the particle image velocimetry (PIV) technology, and the alumina inclusions transport path in the boundary layer was calculated by MATLAB software. The MATLAB codes combined the velocity data from the PIV measurement results and the inclusion transport equation. The four-quadrant analysis showed that sweep and ejection events existed in the boundary layer. The fluctuations of the velocity and the turbulent kinetic energy in the normal direction were increased in the porous refractory and the clogged wall boundary layer when the sweep and ejection events existed. The transport of the alumina inclusions with a diameter of 1–15 μm was affected by the ejection and the sweep events. The alumina inclusions moved toward the boundary in the sweep event. During the sweep event, the transport path of alumina inclusions with 1 μm diameter was close to the boundary; the alumina inclusions were more easily attached to the boundary. The alumina inclusions escaped from the boundary in the ejection event. In the porous refractory and the clogged walls, the alumina inclusion transport path in the normal direction was increased. When the SEN wall’s morphologies changed from smooth wall to porous refractory wall and clogged wall, the sweep event area proportion increased from 10.17% to 39.77%, and the ejection event area proportion decreased from 32.96% to 9.24%. Moreover, the sweep event’s probability increased from 25.83% to 28.24% when the morphologies of the SEN wall changed from smooth wall to porous refractory wall and clogged wall, which will increase the alumina inclusion deposition rate in the porous refractory wall and the clogged wall boundary.

Physical modeling of a skip pneumatic winder

Introduction. The analytical phase of research on mine skip pneumatic winders has been passed, so the theoretical provisions have to be tested by the methods of physical modeling which is aimed at confirming the mathematical model adequacy and assessing the effectiveness of different types of sealing devices. Research methods. Physical modeling phases have been formulated, including modeling by geometric and aerodynamic similarity criteria, constructing aerodynamic characteristics of the installation, carrying out experiments with non-contacting and combined seals, and calculating the values of the installation volumetric efficiency based on the experimental data obtained. Research results. The lifting time of the skip model with different masses of material and seal types has been determined. The installation working points in the “flow rate–pressure” coordinate system have been identified, and the values of the volumetric efficiency have been calculated for each working point. Analysis of the results. A satisfactory convergence of calculated and experimental parameters of the physical model has been established. The model's volumetric efficiency has reached a technically acceptable level. The expected value of the experimental model’s volumetric efficiency has been calculated according to the similarity constants. Conclusions. The model's study revealed the convergence of the experimentally obtained volumetric efficiency of the model with its calculated values and proved the applicability of the mathematical model to experimental sample parameters calculation. The volumetric efficiency of the installation with both non-contacting and combined seals is quite high allowing to recommend the studied sealing devices for mine pneumatic winders.

Devising manufacturing techniques to control the process of zonal segregation in large steel ingots

A method of physical modeling was applied to study the effect of external actions on the processes of crystallization and the formation of the structure of ingots. A brief review of existing hypotheses about the evolution of physical, structural, and chemical heterogeneities in large steel ingots is given. The parameters of the structure and the two-phase zone have been determined, as well as the nature of the distribution of segregated materials along the cross-section of ingots, depending on the conditions of their curing. The decisive importance of convective and capillary mass transfer in the interdendritic channels of hardening ingots on the formation of a zonal heterogeneity at their cross-section has been proven. Experimentally, when crystallizing a model environment (camphene), it has been visually confirmed that the flow of segregated materials in interdendritic channels occurs when a certain amount of impurities accumulates in them. A clear dependence of the speed of this flow on the rate of melt crystallization has been established. With an increase of the hardened part of the melt, the rate of segregated material movement (Vl) increases while the rate of crystallization (R) decreases due to worsening heat release conditions. At a certain distance from the ingot’s surface, these rates become equal, and impurities are carried to the curing border, which is the main cause of the formation of zonal segregation. The results reported here show that the evolution of zonal segregation in ingots can be controlled using various techniques involving external influence on the hardening melt. This study has demonstrated that the adjustable intensity of heat removal from an ingot, as well as the addition of external excess pressure on the hardening melt, could be used as such tools. In the study, to obtain ingots with a minimum level of chemical heterogeneity, it would suffice to provide the following conditions for the curing of the alloy: a value of the alloy crystallization speeds at the level of Rcr ≥ 9·10–2 mm/s, or external pressure on the free surface of ingots Рext. ≥ 135 kPa. The industrial implementation of the reported results could make it possible to improve the technology of obtaining large blacksmith ingots, provide savings in materials and energy resources, increase the yield of a suitable metal, and improve its quality

Brain trauma characteristics for lightweight and heavyweight fighters in professional mixed martial arts

ABSTRACT Mixed martial arts (MMA) is a sport where the fighters are at high risk of brain trauma, with characteristics, such as the frequency, magnitude, and interval of head impacts influencing the risk of developing short- and long-term negative brain health outcomes. These characteristics may be influenced by weight class as they may have unique fighting styles. The purpose of this research was to compare frequency, magnitude, and interval of head impacts between lightweight and heavyweight fighters in professional MMA. Frequency, interval, event type, velocity, and location of head impacts were documented for 60 fighters from 15 Lightweight and 15 Heavyweight professional MMA fights. Head impact reconstructions of these events were performed using physical and finite element modelling methods to determine the strain in the brain tissues. The results found that LW and HW fighters sustained similar head impact frequencies and intervals. The LW fighters sustained a significantly higher frequency of very low and high magnitude impacts to the head from punches; HW a larger frequency of high category strains from elbow strikes. These brain trauma profiles reflect different fight strategies and may inform methods to manage and mitigate the long-term effects of repetitive impacts to the head.

Assessment of the technical condition of intercoolers for turbocharged internal combustion engines

The presented work considers the analysis of methods and means for assessing the technical condition of charge air coolers in vehicles in operation. Metallographic studies of the fragments of samples, identified local sections of the heat exchanger, have been carried out. Various defects of the internal heat transfer surface, caused by the influence of operational factors, have been revealed. The article also touches upon the problem of imperfection of methods and means of instrumental control of the operating parameters of the heat exchange equipment of road transport. It is proposed to carry out diagnostics of the technical condition of heat exchangers at specialized stands equipped with an instrumentation and apparatus complex. The prospects of new developments in the field of diagnostic equipment for determining the operating characteristics of heat exchangers with the ability to measure the most important parameter - heat transfer are noted. An important addition, confirming the relevance of the chosen direction of research, is the substantiation of the value of the described developments not only as a tool for measuring the parameters of the state of heat exchangers, but also to solve the problem of predicting their residual resource. The results of the conducted research are presented. Using the method of physical modeling, an algorithm has been developed for diagnosing the technical condition of the charge air cooler in operation. Issues of provision with methods and means of diagnosing parameters of heat exchangers of vehicles in operation and repair are considered.

Summary of the Prediction Methods of Tool Remaining Life Based on Data Collection

According to different starting principles, this article has advanced the prediction methods of tool remaining life in FMS. It focuses on the physical model method and the method of collecting data based on specific signals and using it as the tool life prediction feature quantity. Then they showed their research status and summarized the corresponding advantages and disadvantages.

IMPROVEMENT OF THE THREE-DIMENSIONAL VISUALIZATION METHODS FOR DETERMINATION OF MORPHOLOGICAL FEATURES OF PHASE MICROOBJECTS

The use of methods of physical and mathematical three-dimensional modelling of phase microobjects, in particular blood erythrocytes, was proposed in order to determine morphological changes. The method of digital signal processing based on double Fourier transform, with the imposition of a band pass filter, the method of restoring the three-dimensional shape of objects from two-dimensional images and the method of spectral analysis were considered in detail improved performance. On the basis of dimensional and aberration calculations, the optimal elements in terms of optical parameters were selected and an experimental stand was assembled. Interference digital images of normal human erythrocytes and altered under the action of osmotic pressure, images of peripheral blood cells for illumination by three types of coherent radiation were obtained. To implement three-dimensional modelling developed a program in Python using Numpy and Open CV libraries and a program that allows to build and visualize three-dimensional models of two-dimensional images, running Windows, written in C ++. A DirectX library and a graphics accelerator are used to display 3D models. The method of visualization of three-dimensional models on two-dimensional images makes it possible to change the scale of the surface and the type of projection used, to work in real time in interactive mode. The method of spectral analysis with processing of images of erythrocytes for enlightenment obtained in three frequency bands of coherent light, after further correlation of the obtained results will significantly improve the accuracy of determining its morphological parameters. The proposed improved methods allow using them to determine the state of the plasma membranes of erythrocytes in order to assess possible pathologies, which will increase the effectiveness of laboratory diagnostic methods.

Numerical Investigation of the Effect of Heterogeneous Pore Structures on Elastic Properties of Tight Gas Sandstones

Strong heterogeneity of pore microstructures leads to complicated velocity-porosity relationships in tight sandstone that cannot be well explained by conventional empirical formulas. To better understand the effect of complex pore structures on elastic properties of tight gas sandstone, we compared three rock physics models. In the first model, we used a single aspect ratio value to quantify varied pore geometry in the tight sands. In the second model, complex pore space was equivalent to the combination of high-aspect-ratio round pores (stiff pores) and low-aspect-ratio compliant microcracks (soft pores). In the third multiple pore-aspect-ratio model, pore spaces are represented using a set of pores with varied values of aspect ratio following statistical normal distribution. Modeling results showed that complex velocity-porosity relationships could be interpreted by the variations in pore aspect ratio in the first model, by the fraction of soft pores in the second model, and by the mean value and variance in the third statistical model. For a given mean value in the third model, higher variance of the multiple pore-aspect-ratio indicated stronger heterogeneity of pore spaces. Further studies on rock physical inversion showed that, compared with the first single pore-aspect-ratio model, the second dual-pore model gave better prediction in shear wave velocity by regarding the soft pore fraction as a fitting parameter. This finding revealed that the dual-pore model could be a more realistic representation of tight sandstone. The third statistical model showed comparable precision in the prediction of shear wave velocity compared with the dual-pore model; however, uncertainty existed for simultaneously determining mean value and variance of pore aspect ratio. On the basis of the dual-pore model, we evaluated the elastic modulus of dry frames of the tight sandstone using logging data in a borehole. Compared with empirical formulas, such as the Krief methods, the method in this paper provided a more rigorous way to determine elastic properties of dry frames for the tight sandstone. Comparisons of rock physical modeling methods offer a better understanding of the microstructures controlling the elastic behaviors of tight gas sandstone.