scholarly journals ABOUT THE ANALYTICAL SOLUTION OF THE EQUATION OF IMPACT FORCE OF TWO ELASTIC BODIES

2021 ◽  
pp. 34-42
Author(s):  
Vasyl Olshanskiy ◽  
Maksym Slipchenko ◽  
Olena Solona ◽  
Ihor Kupchuk
Keyword(s):  
Analytical Solution ◽  
Impact Force ◽  
Raw Materials ◽  
Theory Of Elasticity ◽  
Numerical Results ◽  
Elementary Functions ◽  
Elastic Bodies ◽  
Centers Of Mass ◽  
Analytical Time ◽  
The Impact

A nonlinear differential equation of the force of direct central impact of elastic bodies of revolution, which have a singular point on the boundary contact surface, where its curvature is infinite, is compiled. To determine the coefficients of the equation and the order of its power nonlinearity, the well-known solution of the axisymmetric contact problem of the theory of elasticity, constructed by I. Ya. Shtaermann, is used. In the formulation of the dynamic problem, the classical assumptions of the theory of quasi-static impact proposed by H. Hertz were also used. The constituted equation of impact force is reduced to the Bernoulli equation and its closed analytical solution is constructed, which is expressed in terms of the Ateb-sine. Analytical time dependences of the impact force and the convergence of the centers of mass of elastic bodies are obtained. Compact formulas have been derived for calculating the maxima of these quantities, as well as the durations of the process of compression and impact of bodies. Compact approximations of Ateb-sine by elementary functions are proposed. Thanks to these approximations, it was possible to obtain a fairly simple analytical sweep in time of a fast-flowing mechanical process. Traditionally, in other works such a scan was obtained by numerical solution of the corresponding integral equations that determine the force of an impact. Examples of calculations are given in which the influence of various factors on the main characteristics of a body impact with a small initial velocity is investigated. The limitation on the collision rate is due to the elastic formulation of the problem, where the possibility of plastic deformations is excluded. As a result of this formulation, the need to determine the rate of recovery rate has disappeared, for it is equal to one. Comparison of numerical results is carried out, to which the obtained analytical solutions and the numerical integration of the impact force equation on a computer lead. Small divergences of the results confirmed the accuracy of the derived calculation formulas. Numerical results relate to the impact of a steel body on a fixed rubber half-space, the analogue of which is observed in practice when falling pieces of mineral raw materials on the rolls of a vibration classifier lined with rubber.

scholarly journals SOLUTION OF THE EQUATION OF IMPACT THE ELASTIC BODY, ONE OF WHICH CONE

2019 ◽  
pp. 43-49
Author(s):  
Vasyl Olshanskiy ◽  
Stanislav Olshanskiy
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Impact Force ◽  
Raw Materials ◽  
Theory Of Elasticity ◽  
Elementary Functions ◽  
Elastic Bodies ◽  
Static Contact ◽  
The Impact ◽  
Good Agreement

The impact interaction of elastic bodies with a small initial velocity is considered, when one of them is limited in the contact zone with another conical surface of revolution. Using the well-known solution of the static contact problem of the theory of elasticity, which found I. Shtaermann, and the assumptions of G. Hertz, which he made when creating his own theory of quasistatic impact of solids, compiled a nonlinear differential equation of impact force as a function of time. His closed analytical solution, which describes the process of dynamic interaction of bodies in time, is expressed through the periodic Ateb-sine. To simplify the use of the obtained analytical solution in the calculations, a separate table of the specified special function has been compiled and its approximation with elementary functions has been proposed, the relative error of which is less than one percent. In order to confirm the reliability of the constructed solutions, the integration of the equation of impact force on the computer was carried out in parallel. A good agreement is established between the results obtained by the constructed analytical solution and the numerical integration of the nonlinear Cauchy problem on a computer for a second-order differential equation. Compact formulas for the maxima of the impact force and the magnitude of the compression of bodies, as well as the formula for the duration of the impact process are derived. It is noted that the obtained results can be used in determining the dynamic loads acting on the rubber-lined rolls of the vibration classifier when pieces of solid raw materials fall on them. Examples of calculations are given and a comparative analysis of the results is carried out.

scholarly journals Modeling and analysis of impact based on numerical and experimental approaches

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881306
Author(s):  
Xupeng Wang ◽  
Yan Zhang ◽  
Zhu Gao ◽  
Xiaomin Ji ◽  
Lin Li
Keyword(s):  
Mechanical System ◽  
Contact Force ◽  
Impact Force ◽  
Numerical Results ◽  
Experimental Results ◽  
Force Model ◽  
Restitution Coefficient ◽  
Contact Force Model ◽  
Improved Model ◽  
The Impact

Impact is a universal phenomenon and has serious influences on the dynamic characteristics of mechanical system, so it is critical to accurately describe the effects of impact. In this work, a numerical and comprehensive method is presented to calculate the impact force in clearance joint during impact process, which has higher effectiveness and accuracy than the most popular used L-N model. Different from traditional contact models, where the coefficient of restitution is assumed to be a constant value nearly to 1 during impact process, the improved model in this work sets up the model of restitution coefficient related to two important parameters for impact phenomenon, which are initial impact velocity and the yield strength of the materials in clearance joints. A great number of numerical and experimental results are introduced and compared to validate the improved contact force model; it needs to be highlighted that the numerical results are based on the improved model and the most popular impact force model presented by Lankarani and Nikravesh, and the experimental results are based on two typical pendulum experimental test rigs. It can be concluded that (1) when compared to the experimental results, the numerical results based on the improved model are in better agreement than those based on Lankarani and Nikravesh impact force model; (2) the numerical results based on the improved model are in reasonable agreement with the experimental results, and the relative errors of impact force and restitution coefficient are all no more than 10% between numerical and experimental results; and (3) the improved contact force model is effective and can exactly describe the impact effects between two bodies in mechanical system.

scholarly journals Analytical solution of the longitudinal wave propagation due to the single impact

2018 ◽  
Vol 37 (4) ◽  
pp. 849-858
Author(s):  
M Akhondizadeh
Keyword(s):  
Wave Propagation ◽  
Analytical Solution ◽  
Longitudinal Wave ◽  
Impact Force ◽  
Initial Condition ◽  
Simple Assumption ◽  
Longitudinal Wave Propagation ◽  
The Common ◽  
The Impact ◽  
Sinusoidal Function

In the present work, the rod response due to the impact of a ball is studied in order to analyze the longitudinal wave propagation during the impact and evaluate the velocity of points over the rod length at the end of impact. An analytical solution is given for the governing equation of rod vibration by assuming the impact force as an equivalent sinusoidal function of time. The impact force is defined by a Fourier series to be zero at the rod length except at the impacted end. An analysis of wave propagation will give information about the rod–ball interaction. The evaluated velocity profile at the end of impact can be used as the initial condition for after-impact solution of the rod vibration. It will modify the common simple assumption of constant initial velocity for impacted end.

scholarly journals Determining The Factors Affecting Fruit Hardness of Different Peach Types with Meta Analysis

2014 ◽  
Vol 3 (2) ◽  
pp. 98
Author(s):  
Hande Küçükönder ◽  
Kazım Kubilay Vursavuş ◽  
Fath Üçkardeş
Keyword(s):  
Effect Size ◽  
Contact Time ◽  
Impact Force ◽  
Meta Analysis ◽  
Theory Of Elasticity ◽  
Shock Acceleration ◽  
Significance Level ◽  
The Mean ◽  
The Impact ◽  
The Relationship

The aim of this study is to determine the factor effective in determining the hardness of Caterina, Suidring, Royal Glory and Tirrenia peach types using meta analysis. In the study, the impact force (Fi) and the contact time (tc) were detected and the impulse values (I) that are expressed as independent variable in the area under the curve were calculated in the measurements performed using the technique of a low-mass lateral impactor multiplicated with peach. Using the theory of elasticity, the independent variables were determined as Fmax (maximum impact force), contact time (tmax), Fmax/tmax, 1/tmax, 1/tmax2,5, Fmax/tmax 1.25 and Fmax2.5 parameters. The correlation coefficient values showing the relationship between these parameters and the dependent variable Magness-Taylor force (MT) were calculated and were combined with meta-analysis by using the Hunter-Schmid and Fisher’s Z methods. The Cohen’s classification criterion was used in evaluating the resulting mean effect size (combined correlation value) and in determining its direction. As a result of the meta-analysis, the mean effect size according to Hunter-Schmid method was found 0.436 (0.371-0.497) positively directed in 95% confidence interval, while it was found 0.468 (0.390-0.545) according to Fisher’s Z method. The effect sizes in both methods were determined “mid-level” according to the Cohen’s classification. When the significance level of the studies was analyzed with the Z test, all of the ones that taken into the meta analysis has been found statistically significant. As a result of the meta analysis in this study evaluating the relationship of peach types with the fruit hardness, the mean effect size has been found to reach “strong level”. Consequently, “maximum shock acceleration” was found to be a more effective factor comparing to the other factors in determining the the fruit hardness according to the results of meta analysis applied in both methods.

An analytical model to predict the impact response of one-dimensional structures

2016 ◽  
Vol 22 (12) ◽  
pp. 2253-2268 ◽  
Author(s):  
Mohammad Tahaye Abadi
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Impact Loading ◽  
Impact Force ◽  
Displacement Function ◽  
Impact Response ◽  
Elastic Rod ◽  
Base Function ◽  
One Dimensional ◽  
The Impact

An analytical solution method is presented for the transient axial response of one-dimensional structures subjected to impact loading. The transient structural response is expressed as a series of the impact loading function and its progressive shifting values depending on both material position and time scale. The governing differential equation on the impact force is derived considering the general solution and constitutive equation of the contact interface. The analytical solution of differential equation yields a recursive function describing the impact force and displacement function of the total geometry. Depending on the contact surface roughness and the material properties, an impact function is introduced as a base function for impact response. The procedure is implemented to determine the shock waves generated at the collision of the elastic rod on the rigid surface and two elastic rods. The analytical solution also derives the steady-state response of the structure after the impact loading.

Some thought on the Estimating of the Impact Force by an Experiment

2019 ◽  
Vol 7 (2) ◽  
pp. 205-213
Author(s):  
Yong-Doo Kim ◽  
Seung-Jae Lim ◽  
Hyun-Ung Bae ◽  
Kyoung-Ju Kim ◽  
Chin-Ok Lee ◽  
...  
Keyword(s):  
Impact Force ◽  
The Impact

Оrganic Meat Production of Broiler Chickens Hubbard Redbro Cross

2020 ◽  
Keyword(s):  
Broiler Chickens ◽  
Raw Materials ◽  
Animal Health ◽  
Meat Products ◽  
Poultry Meat ◽  
Meat Production ◽  
Significant Difference ◽  
Environmentally Safe ◽  
The Impact

This article presents the results of studying the impact of housing and feeding conditions on broiler chickens of Hubbard RedBro cross, as well as the quality of products obtained when using floor and cage content, in a farm. It established that when receiving a mixed feed of own production using feed raw materials grown on a farm without the use of pesticides, a statistically significant decrease in potentially dangerous substances for animal health is recorded. Compared with factory feed, it has reduced the content of pesticides by 14 times, and mercury and arsenic by 24 times, cadmium by five times, and lead by ten times. The results of the study of economic indicators of growing Hubbard RedBro cross broiler chickens, as well as the chemical composition and quality of carcasses, indicated that there was no significant difference between the floor and cell conditions of keeping. Still, the use of a diet based on eco-feeds contributed to a statistically significant decrease in the concentration of toxic metals in the muscles of the poultry of the experimental groups. As a result, it found that the use of the studied compound feed in the diets of broiler chickens increased the indicators of Biosafety and ensured the production of environmentally safe ("organic") poultry meat products.

Impact of Raw Materials and Processing Techniques on The Microbiological Quality of Egyptian Domiati Cheese

2020 ◽  
Keyword(s):  
Raw Materials ◽  
Microbiological Quality ◽  
Raw Milk ◽  
Plate Count ◽  
E Coli ◽  
Fresh Cheese ◽  
Processing Techniques ◽  
The Impact ◽  
Total Yeast

Domiati cheese is the most popular brand of cheese ripened in brine in the Middle East in terms of consumed quantities. This study was performed to investigate the impact of the microbiological quality of the used raw materials, the applied traditional processing techniques and ripening period on the quality and safety of the produced cheese. Three hundred random composite samples were collected from three factories at Fayoum Governorate, Egypt. Collected samples represent twenty-five each of: raw milk, table salt, calf rennet, microbial rennet, water, environmental air, whey, fresh cheese, ripened cheese & swabs from: worker hands; cheese molds and utensils; tanks. All samples were examined microbiologically for Standard Plate Count (SPC), coliforms count, Staphylococcus aureus (S. aureus) count, total yeast & mould count, presence of E. coli, Salmonellae and Listeria monocytogenes (L. monocytogenes). The mean value of SPC, coliforms, S. aureus and total yeast & mould counts ranged from (79×102 CFU/m3 for air to 13×108 CFU/g for fresh cheese), (7×102 MPN/ cm2 for tank swabs to 80×106 MPN/ml for raw milk), (9×102 CFU/g for salt to 69×106 CFU/g for fresh cheese) and (2×102 CFU/cm2 for hand swabs to 60×104 CFU/g for fresh cheese), respectively. Whereas, E. coli, Salmonella and L. monocytogenes failed to be detected in all examined samples. There were significant differences in all determined microbiological parameters (p ≤0.05) between fresh and ripened cheese which may be attributed to different adverse conditions such as water activity, pH, salt content and temperature carried out to improve the quality of the product.

Cloud computing demand elasticity algorithm based on ant colony algorithm

2020 ◽  
Vol 13 ◽  
Author(s):  
Chunyu Liu ◽  
Fengrui Mu ◽  
Weilong Zhang
Keyword(s):  
Ant Colony Algorithm ◽  
Theory Of Elasticity ◽  
Ant Colony ◽  
Demand Elasticity ◽  
Network Efficiency ◽  
Elasticity Of Demand ◽  
Operating Profit ◽  
Network Load ◽  
Network Utilization ◽  
The Impact

Background: In recent era of technology, the traditional Ant Colony Algorithm (ACO) is insufficient in solving the problem of network congestion and load balance, and network utilization. Methods: This paper proposes an improved ant colony algorithm, which considers the price factor based on the theory of elasticity of demand. The price factor is denominated in the impact on the network load which means indirect control of network load, congestion or auxiliary solution to calculate the idle resources caused by the low network utilization and reduced profits. Results: Experimental results show that the improved algorithm can balance the overall network load, extend the life of path by nearly 3 hours, greatly reduce the risk of network paralysis, and increase the profit of the manufacturer by 300 million Yuan. Conclusion: Furthermore, results shows that the improved method has a great application value in improving the network efficiency, balancing network load, prolonging network life and increasing network operating profit.

scholarly journals 2-Piece Cork Stoppers as Alternative for Valorization of Thin Cork Planks: Analysis by LCA Methodology

Foods ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 873
Author(s):  
Francisco Javier Flor-Montalvo ◽  
Agustín Sánchez-Toledo Ledesma ◽  
Eduardo Martínez Cámara ◽  
Emilio Jiménez-Macías ◽  
Jorge Luis García-Alcaraz ◽  
...  
Keyword(s):  
Life Cycle Assessment ◽  
Life Cycle ◽  
Raw Materials ◽  
Lca Methodology ◽  
Significant Difference ◽  
Different Dimensions ◽  
The Impact ◽  
Different Thickness ◽  
Cork Stoppers ◽  
Wine Bottle

Natural stoppers are a magnificent closure for the production of aging wines and unique wines, whose application is limited by the availability of raw materials and more specifically of cork sheets of different thickness and quality. The growing demand for quality wine bottle closures leads to the search for alternative stopper production. The two-piece stopper is an alternative since it uses non-usable plates in a conventional way for the production of quality caps. The present study has analyzed the impact of the manufacture of these two-piece stoppers using different methodologies and for different dimensions by developing an LCA (Life Cycle Assessment), concluding that the process phases of the plate, its boiling, and its stabilization, are the phases with the greatest impact. Likewise, it is detected that the impacts in all phases are relatively similar (for one kg of net cork produced), although the volumetric difference between these stoppers represents a significant difference in impacts for each unit produced.

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