scholarly journals Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Grzegorz Mikułowski ◽  
Rafał Wiszowaty
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Experimental Verification ◽  
Load Capacity ◽  
Mechanical Energy ◽  
Specific Situation ◽  
Engineering Structures ◽  
Piston Cylinder ◽  
Proposed Model ◽  
Energy Absorbers

Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA), which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

Effect of Thread Profile Angle and Geometry Clearance on the Loosening Performance of a Preloaded Bolt-Nut System Under Harmonic Transverse Excitation

2011 ◽  
Author(s):  
Xianjie Yang ◽  
Sayed A. Nassar
Keyword(s):  
Mathematical Model ◽  
Analytical Model ◽  
Experimental Verification ◽  
Good Accuracy ◽  
Profile Angle ◽  
Bolt Preload ◽  
Transverse Excitation ◽  
Proposed Model ◽  
Thread Profile ◽  
Number Of Cycles

A mathematical model is proposed for investigating the effect of the thread profile angle, thread and hole clearances on the loosening behavior of a preloaded bolt-nut system that is subjected to cyclic transverse excitation. Experimental verification of the analytical model results is provided for various levels of the initial bolt preload and frictional characteristics. Comparison of the experimental and analytical results on the clamp load decay with the number of cycles verifies that the proposed model predicts the loosening performance with good accuracy.

scholarly journals On Mathematical Modelling of the Indian Human Hair Industry in the Post-COVID-19 Era

2021 ◽  
Vol 8 (3) ◽  
pp. 447-452
Author(s):  
Shibam Manna ◽  
Tanmay Chowdhury ◽  
Asoke Kumar Dhar ◽  
Juan Jose Nieto
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Human Hair ◽  
Control Parameter ◽  
Employment Opportunities ◽  
Alternative Employment ◽  
Job Opportunities ◽  
Proposed Model ◽  
The Stability ◽  
The Impact

An attempt to model the human hair industry in the post-COVID-19 pandemic situation using mathematical modelling has been the goal of this article. Here we introduce a novel mathematical modelling using a system of ordinary differential equations to model the human hair industry as well as the human hair waste management and related job opportunities. The growth of human hair in the months of nationwide total lockdown has been taken into account and graphs have been plotted to analyze the effect of Lockdown in this model. The alternative employment opportunities that can be created for collecting excessive hair in the post-pandemic period has been discussed. A probable useful mathematical model and mechanism to utilize the migrant labours who became jobless due to the pandemic situation and the corresponding inevitable lockdown situation resulting out of that crisis has been discussed in this paper. We discussed the stability analysis of the proposed model and obtained the criteria for an optimal profit of the said model. Graphs have also been plotted to analyze the impact of the control parameter on the optimal profit.

scholarly journals Mathematical modelling of heat transfer in liquid flat-plate solar collector tubes

2010 ◽  
Vol 31 (2) ◽  
pp. 45-62 ◽  
Author(s):  
Wiesław Zima ◽  
Piotr Dziewa
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Flux ◽  
Mathematical Modelling ◽  
Flat Plate ◽  
Solar Collector ◽  
Tube Wall ◽  
Step Function ◽  
Proposed Model ◽  
Flat Plate Solar Collector

Mathematical modelling of heat transfer in liquid flat-plate solar collector tubesThe paper presents a one-dimensional mathematical model for simulating the transient processes which occur in the liquid flat-plate solar collector tubes. The proposed method considers the model of collector tube as one with distributed parameters. In the suggested method one tube of the collector is taken into consideration. In this model the boundary conditions can be time-dependent. The proposed model is based on solving the equation describing the energy conservation on the fluid side. The temperature of the collector tube wall is determined from the equation of transient heat conduction. The derived differential equations are solved using the implicit finite difference method of iterative character. All thermo-physical properties of the operating fluid and the material of the tube wall can be computed in real time. The time-spatial heat transfer coefficient at the working fluid side can be also computed on-line. The proposed model is suitable for collectors working in a parallel or serpentine tube arrangement. As an illustration of accuracy and effectiveness of the suggested method the computational verification was carried out. It consists in comparing the results found using the presented method with results of available analytic solutions for transient operating conditions. Two numerical analyses were performed: for the tube with temperature step function of the fluid at the inlet and for the tube with heat flux step function on the outer surface. In both cases the conformity of results was very good. It should be noted, that in real conditions such rapid changes of the fluid temperature and the heat flux of solar radiation, as it was assumed in the presented computational verification, do not occur. The paper presents the first part of the study, which aim is to develop a mathematical model for simulating the transient processes which occur in liquid flat-plate solar collectors. The experimental verification of the method is a second part of the study and is not presented in this paper. In order to perform this verification, the mathematical model would be completed with additional energy conservation equations. The experimental verification will be carry out in the close future.

scholarly journals Mathematical modelling of molecule evolution in protocells

2013 ◽  
Vol 23 (1) ◽  
pp. 213-229 ◽  
Author(s):  
Dariusz Myszor ◽  
Krzysztof A. Cyran
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Biological System ◽  
Rna World ◽  
Early Stage ◽  
Phosphodiester Bond ◽  
Bond Breakage ◽  
Proposed Model ◽  
Primordial Earth ◽  
Model Point

In this article, we analyse the process of the emergence of RNA polynucleotides located in an enclosed environment, at an early stage of the RNA world. Therefore we prepared a mathematical model, composed of a set of differential equations, which simulates the behaviour of an early biological system bounded by a protocell membrane. There is evidence that enclosed environments were available on the primordial Earth. There are also experimental proofs that RNA strands can develop in these formations. The proposed model allows analysis of the influence of membrane permeability on the composition of internal material. It takes into account phenomena that lead to the elongation of an RNA strand (ligation), fission of molecules (phosphodiester bond breakage) and replication of polynucleotides. Results obtained from the model point out that the existence of protocells might support concentration of material and creation of longer molecules.

scholarly journals Effects of Refuge Prey on Stability of the Prey-Predator Model Subject to Immigrants: A Mathematical Modelling Approach

2021 ◽  
Vol 47 (4) ◽  
pp. 1376-1391
Author(s):  
Mussa Amos Stephano ◽  
Il Hyo Jung
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Functional Response ◽  
Volterra Model ◽  
Predator Population ◽  
Type I ◽  
Proposed Model ◽  
Predator Model ◽  
Model Subject ◽  
Type Ii Functional Response

Prey-predator system is enormously complex and nonlinear interaction between species. Such complexity regularly requires development of new approaches which involves more factors in analysis of its population dynamics. In this paper, we formulate a modified Lotka-Volterra model that incorporates factors such as refuge prey and immigrants. We investigate the effects of refuge prey and immigrants by varying the refuge factor, with and without immigrants. The results show that with Holling’s type I functional response, the proposed model is asymptotically convergent when a refuge prey factor is introduced. Moreover, with Holling’s type II functional response, the proposed mathematical model is unstable and does not converge. However, with Holling’s type III functional response in a system, the proposed mathematical model is asymptotically stable. These results point out the following remarks: The effects of refuge prey on stability of the dynamical system vary depending on the type of functional response, and when the predator population increases, the likelihood of prey extinction declines when the proportion of preys in refuge population increases. Hence, the factor of refuge prey is crucial for controlling the population of the predator and obtaining balances between prey and predator in the ecosystem. Keywords: Refuge prey, stability, prey-predator, immigrants, Mathematical modelling

scholarly journals Mechanics of air-inflated 3D distance fabric

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Vlastimil Votrubec ◽  
Josef Žák
Keyword(s):  
Mathematical Model ◽  
Mechanical Behaviour ◽  
Experimental Verification ◽  
Load Capacity ◽  
Tensile Tests ◽  
Unit Weight ◽  
Inflatable Structures ◽  
Cylindrical Bending ◽  
Fail Safe ◽  
The Mathematical Model

3D distance fabrics are modern and promising material for lightweight inflatable structures. The applications are used in sport, boats, tents, construction, military etc. Its advantages are large load capacity per unit weight, stiffness dependent on pressurized air, fail-safe structure. However, the mechanics of inflated fabric panel is not still described enough. This paper gives basic theory and its experimental verification about mechanical behaviour of distance fabrics. The mathematical model of air-inflated distance fabric panel is created based on analytical theory of cylindrical bending of plates. Material data of the fabric required for performing computations of the model are determined from tensile tests. The reliability of the analytical model is experimentally verified. For that purpose the air-inflated fabric panel was made and tested. Results obtained both experimentally and analytically are compared and discussed. The experiment proves the validity of the mathematical model and allows us to predict the behaviour of distance fabrics.

scholarly journals Analysis of the mitigation strategies for COVID-19: from mathematical modelling perspective

2020 ◽  
Author(s):  
S. M. Kassa ◽  
H.J.B. Njagarah ◽  
Y. A. Terefe
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Backward Bifurcation ◽  
Mitigation Strategies ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Proposed Model ◽  
The Future ◽  
Parameter Values ◽  
Disease Free

AbstractIn this article, a mathematical model for the transmission of COVID-19 disease is formulated and analysed. It is shown that the model exhibits a backward bifurcation at ℛ0 = 1 when recovered individuals do not develop a permanent immunity for the disease. In the absence of reinfection, it is proved that the model is without backward bifurcation and the disease free equilibrium is globally asymptotically stable for ℛ0 < 1. By using available data, the model is validated and parameter values are estimated. The sensitivity of the value of ℛ0 to changes in any of the parameter values involved in its formula is analysed. Moreover, various mitigation strategies are investigated using the proposed model and it is observed that the asymptomatic infectious group of individuals may play the major role in the re-emergence of the disease in the future. Therefore, it is recommended that in the absence of vaccination, countries need to develop capacities to detect and isolate at least 30% of the asymptomatic infectious group of individuals while treating in isolation at least 50% of symptomatic patients to control the disease.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

A Mathematical Model for the Anaerobic Digestion Process Applied to a Mixture of Night Soil and Septic Tank Sludge

1986 ◽  
Vol 18 (7-8) ◽  
pp. 239-248 ◽  
Author(s):  
Sung Ryong Ha ◽  
Dwang Ho Lee ◽  
Sang Eun Lee
Keyword(s):  
Mathematical Model ◽  
Anaerobic Digestion ◽  
Biomass Concentration ◽  
Gas Production ◽  
Septic Tank ◽  
Volatile Acid ◽  
Hydraulic Residence Time ◽  
Anaerobic Digestion Process ◽  
Digestion Process ◽  
Proposed Model

Laboratory scale experiments were conducted to develop a mathematical model for the anaerobic digestion of a mixture of night soil and septic tank sludge. The optimum mixing ratio by volume between night soil and septic tank sludge was found to be 7:3. Due to the high solids content in the influent waste, mixed-liquor volatile suspended solids (MLVSS) was not considered to be a proper parameter for biomass concentration, therefore, the active biomass concentration was estimated based on deoxyribonucleic acid (DNA) concentration in the reactor. The weight ratio between acidogenic bacteria and methanogenic bacteria in the mixed culture of a well-operated anaerobic digester was approximately 3:2. The proposed model indicates that the amount of volatile acid produced and the gas production rate can be expressed as a function of hydraulic residence time (HRT). The kinetic constants of the two phases of the anaerobic digestion process were determined, and a computer was used to simulate results using the proposed model for the various operating parameters, such as BOD5 and volatile acid concentrations in effluent, biomass concentrations and gas production rates. These were consistent with the experimental data.

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