Modeling the Flexural Properties of SLG Reinforced Phenol Formaldehyde Composites Using Langrage’s Method

2011 ◽  
Vol 410 ◽  
pp. 305-308
Author(s):  
Harry Ku ◽  
Hong Zhou ◽  
Peter Wong ◽  
Gang Su ◽  
Jayant Vadher
Keyword(s):  
Mathematical Model ◽  
Fracture Toughness ◽  
Tensile Strength ◽  
Polynomial Interpolation ◽  
Phenol Formaldehyde ◽  
Flexural Properties ◽  
Simple Mathematical Model ◽  
The Mathematical Model ◽  
Conventional Oven ◽  
Lagrange’S Method

The flexural properties of SLG filled phenolic composites have been determined in previous study. It is time consuming to prepare the samples for the tests. In addition, it is even more time consuming to carry out the tests and analyze the results. It is therefore necessary to develop a mathematical model that will predict the flexural properties of particulate filled phenolic composites. Mathematical models for tensile strength, Young’s modulus are available but not for impact strength, flexural strength and fracture toughness. There is no sign that it can be built up from simple mathematical model; polynomial interpolation using Lagrange’s method was therefore employed to generate the flexural properties model using the data obtained from experiments. From experiments, it was found that the trend of the flexural properties of the samples post-cured conventionally was similar to that post-cured in microwaves; it is therefore possible to predict the flexural properties of the samples post-cured in microwaves from the mathematical model generated for flexural properties of samples post-cured in a conventional oven. The workload is therefore halved as the process of generating the mathematical was much faster and simpler.

scholarly journals Mathematical Modeling of the Fracture Toughness of Phenol Formaldehyde Composites Reinforced with E-Spheres

2009 ◽  
Vol 79-82 ◽  
pp. 1165-1168
Author(s):  
H. Ku ◽  
W. Xiang ◽  
N. Pattarachaiyakoop
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Fracture Toughness ◽  
Tensile Strength ◽  
Polynomial Interpolation ◽  
Phenol Formaldehyde ◽  
Simple Mathematical Model ◽  
The Mathematical Model ◽  
Conventional Oven ◽  
Lagrange’S Method

The fracture toughness of SLG filled phenolic composites have been determined by short bar tests. It is expensive to prepare the samples for the tests. Therefore, it is necessary to develop a mathematical model that will predict the fracture toughness of particulate filled phenolic composites. Mathematical models for tensile strength, Young’s modulus are available but not for impact strength and fracture toughness. There is no sign that it can be built up from simple mathematical model; polynomial interpolation using Lagrange’s method was therefore employed to generate the fracture toughness model using the data obtained from experiments. From experiments, it was found that the trend of the fracture toughness of the samples cured conventionally was similar to that cured in microwaves; it is therefore possible to predict the fracture toughness of the samples cured in microwaves from shifting the mathematical model generated for fracture toughness of samples post-cured in conventional oven. The shifted model represented the fracture toughness of the samples cured in microwaves vey well.

scholarly journals Hybrid Secondary Suspension Systems

2009 ◽  
Vol 16 (5) ◽  
pp. 467-480 ◽  
Author(s):  
Nader Vahdati ◽  
Mehdi Ahmadian
Keyword(s):  
Mathematical Model ◽  
Vibration Absorbers ◽  
Simple Mathematical Model ◽  
System Behavior ◽  
Engine Mounts ◽  
Suspension Systems ◽  
Tuned Vibration Absorbers ◽  
Simulation Results ◽  
Secondary Suspension ◽  
The Mathematical Model

Passive fluid mounts are used in the fixed wing applications as engine mounts. The passive fluid mount is placed in between the engine and the fuselage to reduce the cabin's structure- borne noise and vibration generated by the engine.To investigate the benefits of passive fluid mounts used in conjunction with tuned vibration absorbers (TVA), a simple mathematical model is developed. This mathematical model includes the mathematical model of a passive fluid mount, a TVA, and a spring representing the fuselage structure. The simulation results indicate that when passive fluid mounts are used in conjunction with TVAs, an active suspension system behavior is nearly created.

scholarly journals A simple mathematical model for Batesian mimicry

2005 ◽  
Vol 2005 (1) ◽  
pp. 87-92 ◽  
Author(s):  
Terence R. Blows ◽  
Barry J. Wimmer
Keyword(s):  
Mathematical Model ◽  
Full Range ◽  
Logistic Map ◽  
Period Doubling ◽  
Species Interaction ◽  
Batesian Mimicry ◽  
Simple Mathematical Model ◽  
Predator Prey ◽  
The Mathematical Model ◽  
Period Doubling Bifurcations

A simple mathematical model is presented for Batesian mimicry, which occurs when a harmless species (mimic) is morphologically similar to another species (model) that is noxious or distasteful to predators, thus gaining a measure of protection. Although mathematical models for species interaction, such as predator-prey or competition, are well known, there is no similar literature on mimicry. The mathematical model developed here is a one-dimensional iterated map which has the full range of dynamic behavior present in the logistic map, depending on the values of its parameters. The dynamics ranges from a stable fixed point and stable cycles through chaotic dynamics achieved through a sequence of period doubling bifurcations.

scholarly journals Optimisation of a clam bunk skidder from the emission production point of view

2012 ◽  
Vol 58 (No. 4) ◽  
pp. 136-141
Author(s):  
A. Janeček ◽  
R. Adamovský
Keyword(s):  
Mathematical Model ◽  
Production System ◽  
Operating Performance ◽  
Point Of View ◽  
Optimal Rate ◽  
Simple Mathematical Model ◽  
Operation Performance ◽  
The Mathematical Model

This article presents a proposal of a simple mathematical model for minimisation of the production of extraneous substances as a function of the rate of operation performance of a production system. The model is then verified by operation tests of the Terri 2040 clam bunk skidder and by determining the system&rsquo;s optimal rate of performance from the point of view of production of SO<sub>2</sub>, HC and NO<sub>x </sub>emissions. The operation tests conducted to verify the mathematical model have confirmed that conditions can be determined for the production system at which it produces minimum emissions. Min. values of SO<sub>2</sub>, and HC were achieved at approximately the same rate of performance of the clam bunk skidder. Minimum values of NO<sub>x </sub>were achieved at significantly higher rate of performance of the equipment. At the calculated optimal rate of operating performance of the Terri 2040 clam bunk skidder, the values of the produced emissions were determined per m<sup>3</sup> of timber: SO<sub>2</sub> = 1.00035 g/m<sup>3</sup>, HC = 7.796 g/m<sup>3</sup> and NO<sub>x</sub> = 0.277 g/m<sup>3</sup>.

PERIODIC DRAFT TILLAGE FORCES IN SOIL WORKING PROCESSES OF AGRICULTURAL EQUIPMENT

2021 ◽  
Author(s):  
Cardei Petru ◽  
Oprescu Remus Marius ◽  
Muraru Vergil ◽  
Muraru Sebastian ◽  
Muraru-Ionel Cornelia
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Tensile Strength ◽  
Traction Force ◽  
Component Model ◽  
Dynamic Component ◽  
Agricultural Equipment ◽  
Dynamics Problems ◽  
The Mathematical Model ◽  
Agricultural Machines

The article presents results of the mathematical modelling of the tensile strength for equipment for opening and compartmentalizing watering furrows. This agricultural machine develops a less common traction force, with two components, one of which with oscillates behavior. The mathematical model given in the paper provides calculation formulas for the static component and for the dynamic component. Model constants are used to calibrate the model using existing experimental data for this type of machine. The paper it is specified the dynamics problems of agricultural machines in which such models are needed

The Mathematical Model of Online Quenching for Extruding Bar of 6061 Aluminum Alloy

2011 ◽  
Vol 117-119 ◽  
pp. 1798-1801
Author(s):  
Yi Lin ◽  
De Zhi Li ◽  
Jian Min Zeng ◽  
Ping Chen ◽  
Li Hua Liang
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Aluminum Alloy ◽  
Simple Mathematical Model ◽  
Extrusion Speed ◽  
6061 Aluminum Alloy ◽  
Different Temperatures ◽  
Set Up ◽  
The Mathematical Model ◽  
Quenching Apparatus

A simple mathematical model that correlates the temperature and extrusion speed of a 6061 aluminum bar extruded from the die has been established based on the principle of heat transfer in this paper. The 6061 alloy bar is extruded from the die orifice and is cooled through heat exchanged between the bar and ambient. The temperature of the bar decreases as the distance increases away from the die orifice. The more rapidly the temperature drops, the slower the extrusion speed is. A flexible online quenching apparatus has been set up before the critical quenching position to guarantee good supersaturation of alloying elements. The calculations have shown that at the extrusion speeds of 10m/min, 15 m/min and 20 m/min, the critical quenching positions are 0.44m, 0.88m and 1.30m from the die orifice, respectively for the temperature of 520°C; and for the different temperatures, the critical quenching positions from the die orifice are 0.66m, 1.31m, 1.95m at 530°C and 0.88m, 1.75m, 2.6m at 540°C, respectively.

Dynamic analysis of the mathematical model of COVID-19 with demographic effects

2020 ◽  
Vol 75 (11-12) ◽  
pp. 389-396 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan ◽  
E. F. Doungmo Goufo ◽  
Amna Anjum ◽  
Ali Anjum
Keyword(s):  
Mathematical Model ◽  
Perturbation Method ◽  
Effective Treatment ◽  
Homotopy Perturbation Method ◽  
Simple Mathematical Model ◽  
Safety Measures ◽  
Seir Model ◽  
Homotopy Perturbation ◽  
The Mathematical Model ◽  
Demographic Effects

AbstractThe coronavirus is currently extremely contagious for humankind, which is a zoonotic tropical disease. The pandemic is the largest in history, affecting almost the whole world. What makes the condition the worst of all is no specific effective treatment available. In this article, we present an extended and modified form of SIR and SEIR model, respectively. We begin by investigating a simple mathematical model that describes the pandemic. Then we apply different safety measures to control the pandemic situation. The mathematical model with and without control is solved by using homotopy perturbation method. Obtained solutions have been presented graphically. Finally, we develop another mathematical model, including quarantine and hospitalization.

The Mathematical Model of the Relation among the Resistance, the Distortion Temperature and the Rate of the Steel in the Plastic Deformation

2012 ◽  
Vol 502 ◽  
pp. 184-188
Author(s):  
Hong Li ◽  
Xiao Lin You
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Tensile Strength ◽  
Basic Theory ◽  
Deformation Resistance ◽  
Deformation Degree ◽  
Plastic Processing ◽  
Hardening Curve ◽  
Fundamental Equations ◽  
The Mathematical Model

the hardening curve of the steel in the plastic deformation only considers the influence of the deformation degree on the resistance. This paper, according to the basic theory of plastic processing, proposes out the respective relation between the deformation resistance and the deformation degree, the temperature, as well as the rate. This paper gets the curves of these relations by experiments, summarizes the fundamental equations by simulation and finally deduces the plastic conditional equations relating to the material performance----the tensile strength.

scholarly journals Stability analysis of a simple mathematical model for school bullying

2022 ◽  
Vol 7 (4) ◽  
pp. 4936-4945
Author(s):  
H. A. Ashi ◽  
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
School Bullying ◽  
Drop Out ◽  
Simple Mathematical Model ◽  
Globally Asymptotically Stable ◽  
School Drop Out ◽  
New Criterion ◽  
The Mathematical Model ◽  
Commit Suicide

<abstract><p>School bullying is a highly concerned problem due to its effect on students' academic achievement. The effect might go beyond that to develop health problems, school drop out and, in some extreme cases, commit suicide for victims. On the other hand, adolescents who continuously bully over time are at risk of becoming involved in gang membership and other types of crime. Therefore, we propose a simple mathematical model for school bullying by considering two variables: the number of victims students and the number of bullies students. The main assumption employed to develop the mathematical model is that school policy bans bullying and expels students who practice this behavior to maintain a constructive educational environment within the school. We show that the model has two equilibrium points, and that both equilibrium points are locally and globally asymptotically stable under certain conditions. Also, we define a threshold parameter with a new criterion called the bullying index. Furthermore, we show that the model exhibits the phenomena of transcritical bifurcation subject to the bullying index. All the findings are supported with numerical simulations.</p></abstract>

scholarly journals THE FIVE PARAMETER LOGISTIC (5PL) FUNCTION AND COVID-19 EPIDEMIC IN ICELAND

2021 ◽  
Author(s):  
Pinaki Pal
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Linear Regression ◽  
Linear Regression Analysis ◽  
Cumulative Number ◽  
Simple Mathematical Model ◽  
Non Linear ◽  
The Mathematical Model ◽  
Epidemiological Parameters

Right now, investigations are rigorously carried out on modeling the dynamic progress of (Covid-19) pandemic around the globe. Here we introduce a simple mathematical model for analyzing the dynamics of the Covid-19, considering only the number of cumulative cases. In the present work, the 5PL function is applied to study the Covid-19 spread in Iceland. The cumulative number of infected persons C(t) has been accurately fitted with the 5PL equation, giving rise to different epidemiological parameters. The result of the current examination reveals the effectiveness and efficacy of the 5PL function for exploring the Covid 19 dynamics in Iceland. The mathematical model is simple enough such that practitioners knowing algebra and non-linear regression analysis can employ it to examining the pandemic situation in different countries.

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