Fore-Aft Stiffness Characteristics Of Pneumatic Tires

1974 ◽  
Vol 2 (2) ◽  
pp. 79-101 ◽  
Author(s):  
R. N. Dodge ◽  
S. K. Clark
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Structural Data ◽  
Close Correlation ◽  
Elastic Stiffness ◽  
Elastic Tube ◽  
Simple Mathematical Model ◽  
Proposed Model ◽  
Stiffness Characteristics ◽  
Pneumatic Tires

Abstract A simple mathematical model is proposed for estimating the fore-aft elastic stiffness of pneumatic tires. This model is based upon two idealized solutions, the first being that for the extensional stiffness of a pressurized tube reinforced with inextensible cords, while the second solution is that for the shear deformation of an unpressurized elastic tube. The combination of these two elements allows one to estimate fore-aft stiffness characteristics of pneumatic tires. The validity of the proposed model was tested by static measurements at different inflation pressures of the fore-aft spring rates of four tires varying in size and construction. Additional structural data required for the analytical solution of the model were also obtained from these tires. Comparison of the calculated and experimental results indicates that the trends are generally correct, although close correlation between experiment and calculation is difficult to obtain.

scholarly journals A Biological Model of Acupuncture and its Derived Mathematical Modeling and Simulations

2015 ◽  
Vol 18 (4) ◽  
pp. 831-849 ◽  
Author(s):  
Marc Thiriet ◽  
Yannick Deleuze ◽  
Tony Wen-Hann Sheu
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Numerical Simulations ◽  
Blow Up ◽  
Biological Model ◽  
Mesh Adaptivity ◽  
Simple Mathematical Model ◽  
Global Knowledge ◽  
Small Width ◽  
The Brain

Abstract(Aims) Acupuncture was employed since 2 millenaries, but the underlying mechanisms are not globally handled. The present study is aimed at proposing an explanation by pointing out involved processes and a convincing modeling to demonstrate its efficiency when carried out by trained practitioners.(Method) In the absence of global knowledge of any mechanism explaining the acupuncture process, a biological model is first developed, based on stimulation in a given domain around the needle tip of a proper mastocyte population by a mechanical stress, electrical, electromagnetic, or heat field. Whatever the type of mechanical or physical stimuli, mastocytes degranulate. Released messengers either facilitate the transfer of main mediators, or target their cognate receptors of local nerve terminals or after being conveyed by blood their receptors on cerebral cells. Signaling to the brain is fast by nervous impulses and delayed by circulating messengers that nevertheless distribute preferentially in the brain region of interest due to hyperemia. The process is self-sustained due to mastocyte chemotaxis from the nearby dense microcirculatory circuit and surrounding mastocyte pools, which are inadequate for acupuncture, but serve as a signal relay. A simple mathematical model is solved analytically. Numerical simulations are also carried out using the finite element method with mesh adaptivity.(Results) The analytical solution of the simple mathematical model demonstrates the conditions filled by a mastocyte population to operate efficiently. A theorem gives the blow-up condition. This analytical solution serves for validation of numerical experiments. Numerical simulations show that when the needle is positioned in the periphery of the acupoint or outside it, the response is too weak. This explains why a long training is necessary as the needle implantation requires a precision with a magnitude of the order of 1mm.(Conclusion) The acupoint must contain a highly concentrated population of mastocytes (e.g., very-high–amplitude, small-width Gaussian distribution) to get an initial proper response. Permanent signaling is provided by chemotaxis and continuous recruitment of mastocytes. Therefore, the density and distribution of mastocytes are crucial factors for efficient acupuncture as well as availability of circulating and neighboring pools of mastocytes.

scholarly journals Shape control of hybrid functionally graded plate through smart application of piezoelectric material using simple plate theory

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
K. M. Bajoria ◽  
S. A. Patare
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Piezoelectric Material ◽  
Functionally Graded Material ◽  
Shape Control ◽  
Functionally Graded ◽  
Simple Mathematical Model ◽  
Graded Material ◽  
Flexural Analysis

AbstractThe present study takes its inspiration from notable work in the literature related to the flexural analysis of functionally graded material (FGM) plate along with a smart application of piezoelectric material but maintains its novelty in terms of simple approach, an analytical solution with a wide scope of application. Coupling the plate element with piezoelectric smart material can control deflection, vibration thereby increasing the safety, stability, and life of these elements. Plates made up of functionally graded material further enhances the applicability as two different materials are fused. Analysis of such a system is challenging especially for a closed form mathematical solution along with complex boundary conditions. In the present study, it is proposed to develop a simple analytical model for bending analysis of FGM plate coupled with piezoelectric layers. Polynomial based shear deformation function taken from literature is applied to develop a simple mathematical model. A complete flexural analysis is performed for FGM plate to validate the governing simple mathematical model. Through the smart application of piezoelectric material, the deflection of the FGM plate is controlled in as closed loop feedback system. Analytical solution valid over the entire plate domain is obtained incorporating fixed and simple support types of boundary conditions. The initial part of the study details complete mathematical formulation for the plate under consideration, followed by numerical validation in which results of the present model are compared with notable studies in the literature. Lastly, the smart application through shape control of the FGM plate is demonstrated graphically and numerically. The development and application of the discussed mathematical model presented in this study are complete in all aspects of its mathematical form, solution, and numerical validation.

scholarly journals A simple mathematical model for Coronavirus (COVID-19)

2020 ◽  
Author(s):  
Said Melliani ◽  
Abdelati El Allaoui ◽  
Lalla Saadia Chadli
Keyword(s):  
Mathematical Model ◽  
Death Rate ◽  
Infected Individual ◽  
Viral Pneumonia ◽  
Contact Rate ◽  
Simple Mathematical Model ◽  
Proposed Model ◽  
The World ◽  
Per Capita ◽  
Novel Coronavirus

AbstractA novel coronavirus (COVID-19) was identified in Wuhan, China in the end of 2019, it causing an outbreak of viral pneumonia. It caused to the death rate of 4.63% among 571, 678 confirmed cases around the world to the March 28th, 2020. In this brief currentstudy, we will present a simple mathematical model where we show how the probability of successfully getting infected when coming into contact with an infected individual and the per-capita contact rate affect the healthy and infected population with time. The proposed model is used to offer predictions about the behavior of COVID-19 for a shorter period of time.

scholarly journals DESENVOLVIMENTO DE MODELAGEM MATEMÁTICA PARA O PROCESSO DE PURIFICAÇÃO DE HIDROGÊNIO POR ADSORÇÃO EM COLUNAS DE RECHEIO POROSO

e-xacta ◽  
2016 ◽  
Vol 9 (2) ◽  
Author(s):  
Paôlla Chrystine Pinheiro Patrício ◽  
Márcio Ribeiro Vianna Neto ◽  
Andréa Oliveira Souza da Costa ◽  
Marcelo Cardoso
Keyword(s):  
Mathematical Model ◽  
Adsorption Process ◽  
Training System ◽  
Hydrogen Purification ◽  
Simple Mathematical Model ◽  
Purification Process ◽  
Operator Training ◽  
Time Modeling ◽  
Proposed Model ◽  
Operator Training System

<p>O Sistema de treinamento de Operadores (OTS) permite um treinamento sem riscos de acidentes e sem perdas de insumos e de tempo. A modelagem e simulação da operação associada aos dados de entrada no modelo, que são as variáveis manipuladas pelos operadores, geram resultados virtuais com comportamento similar aos que seriam gerados se o treinamento estivesse sendo feito nos equipamentos. O objetivo deste trabalho foi desenvolver um modelo matemático simples para o processo de purificação de hidrogênio em uma coluna de adsorção. Tal modelo poderá ser empregado na proposta de OTSs sem a necessidade de lidar com modelos com significativa complexidade matemática. O modelo proposto foi validado empregando-se dois casos reportados na literatura. Assim, foi possível concluir que esse descreve o processo de adsorção satisfatoriamente e poderá ser utilizado posteriormente no desenvolvimento de um OTS para todo o processo de purificação de hidrogênio.</p><p>ABSTRACT </p><p>Operator Training System allows training without risk of accident and no loss of material and time. Modeling and simulation of operation associated with inputs, which are manipulated variables by operators, generate virtual results with similar behavior to that would be generated if the training was being done on the equipment. The aim of this work was to develop a simple mathematical model for the adsorption process for hydrogen purification. This model can be used in the proposal for OTSs without having to handle models with significant mathematical complexity. The proposed model has been validated employing two reported cases in the literature. Thus, it was concluded that this model describes the adsorption process satisfactorily and it can be used for a future development of an OTS for the entire hydrogen purification process.</p>

In-Plane Bending and Shear Deformation of Belt Contributions on Tire Cornering Stiffness Characteristics

2020 ◽  
Author(s):  
Gibin Gil ◽  
Sujin Lee
Keyword(s):  
Mathematical Model ◽  
Shear Deformation ◽  
Beam Theory ◽  
Slip Angle ◽  
Wear Properties ◽  
Angle Change ◽  
Foundation Model ◽  
Plane Bending ◽  
Stiffness Characteristics ◽  
Brush Model

ABSTRACT In radial tires, belt structure plays a role of minimizing the lateral deflection of carcass, which has a significant influence on the cornering and wear properties of a tire. The deflection of carcass affects the magnitude of tread block deformation when the tire is under the slip angle. As a result, it can change the cornering stiffness characteristics of the tire, especially when the vertical load is high. During tire development, a tire design engineer tries to find the optimal belt ply angle that satisfies the various performance requirements simultaneously, but it is not an easy task because the effect of belt angle change is different depending on the size of the tire. There have been many attempts to construct a mathematical model that represents the structural properties of the belt package, including the string-based model and the beam on elastic foundation model. But, in many cases, only the in-plane bending of belt is considered and the shear deformation is not taken into consideration. In this study, the effect of belt angle change on belt stiffness is analyzed using a mathematical model based on the Timoshenko beam theory. This model can account for the in-plane bending and shear deformation of the belt structure at the same time. The results of the analysis show how the contribution of bending and shear is changed depending on a tire design parameter, herein the belt cord angle. The effect of belt ply angle change on cornering stiffness is investigated by means of the brush model including belt flexibility. The prediction by the brush model is compared with the measurement using a Flat-trac machine, and the validity of the model is discussed.

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.

scholarly journals On the Dragging Trajectory of Anchors in Clay for Merchant Ships

2021 ◽  
Vol 9 (2) ◽  
pp. 118
Author(s):  
Xinqing Zhuang ◽  
Keliang Yan ◽  
Pan Gao ◽  
Yihua Liu
Keyword(s):  
Mathematical Model ◽  
Structural Integrity ◽  
Indirect Measurement ◽  
Test System ◽  
Flow Rule ◽  
Burial Depth ◽  
Proposed Model ◽  
Depth Increase ◽  
Two Parameters ◽  
The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

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