Abstract: This paper presents the static and cyclic stresses in combination with fatigue analysis resultant of loads applied on the friction discs usually utilized on industrial clutches. The material chosen to simulate the friction discs under load is aluminum. The numerical simulation was done by software COMSOLTM Multiphysics. The results obtained for static loads showed enough stiffness for both geometries and the material utilized. On the other hand, in the fatigue standpoint, failure is clearly verified, what demonstrates the importance of both approaches, mainly dynamical analysis. The results and the conclusion are based on the stresses on disc, counted stress cycles, and fatigue usage factor.
Abstract: In this work, we propose and analyze a model of
Phytoplankton-Zooplankton interaction with harvesting considering
that some species are exploited commercially for food. Criteria for
local stability, instability and global stability are derived and some
threshold harvesting levels are explored to maintain the population
at an appropriate equilibrium level even if the species are exploited
continuously.Further,biological and bionomic equilibria of the system
are obtained and an optimal harvesting policy is also analysed using
the Pantryagin’s Maximum Principle.Finally analytical findings are
also supported by some numerical simulations.
Abstract: Large rotating systems, especially gear drives and gearboxes, occur as parts of many mechanical devices transmitting the torque with relatively small loss of power. With the increased demand for high speed machinery, mathematical modeling and
dynamic analysis of gear drives gained importance. Mathematical description of such mechanical systems is a complex task evolving for several decades. In gear drive dynamic models, which include flexible shafts, bearings and gearing and use the finite elements, nonlinear effects due to gear mesh and bearings are usually ignored, for such models have large number of degrees of freedom (DOF) and it is computationally expensive to analyze nonlinear systems with large number of DOF. Therefore, these models are not suitable for simulation of nonlinear behavior with amplitude jumps in frequency response. The contribution uses a methodology of nonlinear large rotating system modeling which is based on degrees of freedom (DOF) number reduction using modal synthesis method (MSM).
The MSM enables significant DOF number reduction while keeping
the nonlinear behavior of the system in a specific frequency range.
Further, the MSM with DOF number reduction is suitable for
including detail models of nonlinear couplings (mainly gear and
bearing couplings) into the complete gear drive models. Since each
subsystem is modeled separately using different FEM systems, it
is advantageous to parameterize models of subsystems and to use
the parameterization for optimization of chosen design parameters.
Final complex model of gear drive is assembled in MATLAB and
MATLAB tools are used for dynamical analysis of the nonlinear
system. The contribution is further focused on developing of a
methodology for investigation of behavior of the system by Nonlinear
Normal Modes with combination of the MSM using numerical
continuation method. The proposed methodology will be tested using
a two-stage gearbox including its housing.
Abstract: This paper presents the mathematical description of the high-speed rotating system taking into account the influence of internal and external damping. The mathematical model is obtained by using the finite element method. The analyzed system is an automotive turbocharger understood as a rotor-bearing system. The circular cross-section shaft is equipped with one compressor wheel, one turbine wheel and is supported by two floating ring bearings. Based on the model, the dynamical analysis of a turbocharger is performed and stability conditions are evaluated.
Abstract: We used mathematical model to study the
transmission of dengue disease. The model is developed in which
the human population is separated into two populations, pregnant and
non-pregnant humans. The dynamical analysis method is used for
analyzing this modified model. Two equilibrium states are found and
the conditions for stability of theses two equilibrium states are
established. Numerical results are shown for each equilibrium state.
The basic reproduction numbers are found and they are compared by
using numerical simulations.
Abstract: Microarrays technique allows the simultaneous measurements of the expression levels of thousands of mRNAs. By mining this data one can identify the dynamics of the gene expression time series. By recourse of principal component analysis, we uncover the circadian rhythmic patterns underlying the gene expression profiles from Cyanobacterium Synechocystis. We applied PCA to reduce the dimensionality of the data set. Examination of the components also provides insight into the underlying factors measured in the experiments. Our results suggest that all rhythmic content of data can be reduced to three main components.
Abstract: Malaria is transmitted to the human by biting of
infected Anopheles mosquitoes. This disease is a serious, acute and
chronic relapsing infection to humans. Fever, nausea, vomiting, back
pain, increased sweating anemia and splenomegaly (enlargement of
the spleen) are the symptoms of the patients who infected with this
disease. It is caused by the multiplication of protozoa parasite of the
genus Plasmodium. Plasmodium falciparum, Plasmodium vivax,
Plasmodium malariae and Plasmodium ovale are the four types of
Plasmodium malaria. A mathematical model for the transmission of
Plasmodium Malaria is developed in which the human and vector
population are divided into two classes, the susceptible and the
infectious classes. In this paper, we formulate the dynamical model
of Plasmodium falciparum and Plasmodium vivax malaria. The
standard dynamical analysis is used for analyzing the behavior for
the transmission of this disease. The Threshold condition is found
and numerical results are shown to confirm the analytical results.
Abstract: Adopting the measured constitutive relationship of
stress-strain of river ice, the finite element analysis model of
percussive force of river ice and pier is established, by the explicit
dynamical analysis software package LS-DYNA. Effects of element
types, contact method and arithmetic of ice and pier, coupled modes
between different elements, mesh density of pier, and ice sheet in
contact area on the collision force are studied. Some of measures for
the collision force analysis of river ice and pier are proposed as
follows: bridge girder can adopt beam161 element with 3-node; pier
below the line of 1.30m above ice surface and ice sheet use solid164
element with 8-node; in order to accomplish the connection of
different elements, the rigid body with 0.01-0.05m thickness is defined
between solid164 and beam161; the contact type of ice and pier adopts
AUTOMATIC_SURFACE_TO_SURFACE, using symmetrical
penalty function algorithms; meshing size of pier below the line of
1.30m above ice surface should not less than 0.25×0.25×0.5m3. The
simulation results have the advantage of high precision by making a
comparison between measured and computed data. The research
results can be referred for collision force study between river ice and
pier.
Abstract: Dengue virus is transmitted from person to person
through the biting of infected Aedes Aegypti mosquitoes. DEN-1,
DEN-2, DEN-3 and DEN-4 are four serotypes of this virus. Infection
with one of these four serotypes apparently produces permanent
immunity to it, but only temporary cross immunity to the others. The
length of time during incubation of dengue virus in human and
mosquito are considered in this study. The dengue patients are
classified into infected and infectious classes. The infectious human
can transmit dengue virus to susceptible mosquitoes but infected
human can not. The transmission model of this disease is formulated.
The human population is divided into susceptible, infected, infectious
and recovered classes. The mosquito population is separated into
susceptible, infected and infectious classes. Only infectious
mosquitoes can transmit dengue virus to the susceptible human. We
analyze this model by using dynamical analysis method. The
threshold condition is discussed to reduce the outbreak of this
disease.
Abstract: The presence of cold air with the convergent
topography of the Lut valley over the valley-s sloping terrain can
generate Low Level Jets (LLJ). Moreover, the valley-parallel
pressure gradients and northerly LLJ are produced as a result of the
large-scale processes. In the numerical study the regional MM5
model was run leading to achieve an appropriate dynamical analysis
of flows in the region for summer and winter. The results of this
study show the presence of summer synoptical systems cause the
formation of north-south pressure gradients in the valley which could
be led to the blowing of winds with the velocity more than 14 ms-1
and vulnerable dust and wind storms lasting more than 120 days.
Whereas the presence of cold air masses in the region in winter,
cause the average speed of LLJs decrease. In this time downslope
flows are noticeable in creating the night LLJs.
Abstract: Dengue fever is an important human arboviral disease. Outbreaks are now reported quite often from many parts of the world. The number of cases involving pregnant women and infant cases are increasing every year. The illness is often severe and complications may occur. Deaths often occur because of the difficulties in early diagnosis and in the improper management of the diseases. Dengue antibodies from pregnant women are passed on to infants and this protects the infants from dengue infections. Antibodies from the mother are transferred to the fetus when it is still in the womb. In this study, we formulate a mathematical model to describe the transmission of this disease in pregnant women. The model is formulated by dividing the human population into pregnant women and non-pregnant human (men and non-pregnant women). Each class is subdivided into susceptible (S), infectious (I) and recovered (R) subclasses. We apply standard dynamical analysis to our model. Conditions for the local stability of the equilibrium points are given. The numerical simulations are shown. The bifurcation diagrams of our model are discussed. The control of this disease in pregnant women is discussed in terms of the threshold conditions.