Thesis in Mathematics

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Computational Modeling of Crack Detection for a Beam using the Finite Element Method
(CUET, 15-Apr-2024) Karmaker, Rajib
Nowadays the presence of crack in different engineering structures becomes a serious threat to performance. Since most of the civil and mechanical structures may be damaged due to material fatigue, mechanical vibration, environmental attack and long-term service. Cracks in structural bodies lead to local changes in their stiffness, flexibility and consequently their static and dynamic behavior is affected. Moreover, dynamical systems of a beam usually possess non-linear characteristics, which causes practical difficulties on the model-based damage detection techniques. So it becomes essential to study the dynamic response characteristics in order to avoid any catastrophic failures and to follow structural integrity and performance. In the present study, a numerical simulation using the Finite Element Method (FEM) is carried out on a simply supported concrete beam of length 0.12m and width 0.015m with two open transverse cracks, to analyze the response characteristics for which the parameters considered are crack depth and its location. Its natural frequency and mode shapes are determined by applying suitable boundary conditions. A vibration-based model is employed to simulate the results by using COMSOL Multiphysics. By performing the computational analysis it is observed that, after applying load the frequencies of the cracked beam changes with the variation of the location of the crack for the all modes of vibration. It also found that frequencies are proportional to the increase in load and maximum frequency (around 2304.3 Hz) reserved at the cracked stage. Finally, it also revealed that the effects of crack are closer to the fixed end than at the free end, and by following this approach, very small sizes of crack (near 0.05 mm) can be identified in any structural beam.
NONLINEAR ACOUSTIC WAVE PHENOMENA IN MAGNETIZED COLLISIONLESS RELATIVISTIC PLASMAS
(CUET, 1-Sep-2024) Barua, Sagar
The thesis investigates the nonlinear propagation of ion-acoustic solitons (IASs) within a
Numerical Investigation of Single and Double Differential Cross-Section for the Ionization of Metastable 2S State Hydrogen Atom by Electron Impact
(CUET, 19-Dec-2023) Chowdhury, Md. Thowhidul Hoque
This thesis focuses on the ionization of hydrogen atoms by electrons in an asymmetric coplanar geometry, which plays a crucial role in atomic ionization problems. The Double Differential Cross Sections (DDCS) from the ionization of hydrogen atoms with different kinematic conditions offer valuable insights into various fields, including Applied Mathematics, Applied Physics, Atomic Physics, Astrophysics, Plasma Physics, and Fusion Technology.
PROPAGATION OF ION ACOUSTIC SOLITON AROUND THE CRITICAL VALUES OF ANY SPECIFIC PARAMETER IN UNMAGNETIZED COLLISIONLESS RELATIVISTIC PLASMAS
(CUET, 1-Sep-2024) Rahman, Md. Obaidur
The main purpose of the present work is to investigate how electrostatic plasma parameters
Radiation induced structural and electric properties of Al-Substituted NiCuCd nanoparticles
(CUET, 24-Feb-2024) Sharma, Bishakar
The effect of gamma (γ) irradiations on the physical, magnetic and electrical properties of nanoferrites samples with a chemical formula of Ni0.5Cu0.2Cd0.3Fe2-xAlxO4 have studied. These samples have prepared by sol-gel auto combustion method. The synthesized samples have irradiated for γ rays from 60Co source at room temperature with a dose of 1 and 3 MRad, at a dose rate of 1.067 MRad/h. X-ray diffraction (XRD) parameters, magnetization, dielectric constant, dielectric loss factor, electric modulus, impedance and ac conductivity have analyzed for the irradiated samples. XRD patterns show that the irradiation has caused a change in the lattice constant due to ions redistribution. The lattice constant of the investigated samples has increased with the increase in irradiation (gamma) due to the conversion of Fe3+ (0.67Å) to Fe2+ (0.76Å). Moreover, the cation redistribution play an important role in increasing the values of ac conductivity with increasing the irradiation (gamma) dose.
Shock Wave Excitation in Unmagnetized Multi-Component Plasmas.
(CUET, 19-Jan-2024) Akter, Parvin
This thesis deals with the nonlinear propagation of shock wave excitations by
Similarity solution of unsteady MHD boundary layer flow of a nanofluid for free and forced convection around an inclined plate.
(CUET, 9-Jun-2024) Gani, S. M. Osman
This study investigates the unsteady magnetohydrodynamic (MHD) boundary layer flow of electrically conducting nanofluids over an inclined plate, considering both forced and free convection. This flow situation is relevant to various engineering applications, including solar water heaters, inclination sensors, heat removal in industrial processes, and even deterrence, power generation in nuclear reactors, and biomedical applications. The governing equations are transformed into ordinary differential equations using similarity solutions. These equations are then solved numerically with the sixth-order Runge-Kutta method and the Nachtsheim-Swigert iteration technique. The effects of various parameters, such as the buoyancy ratio, magnetic field strength, Brownian motion, thermophoresis, and unsteadiness, on the velocity, temperature, and concentration profiles are analyzed in detail through graphical representations and discussions.
The Effect of the Angle of Perforation on Inserts in a Pipe Flow for Heat Transfer Analysis
(CUET, 21-Aug-2024) Acherjee, Simul
A numerical simulation study of heat transfer analysis is considered with perforated inserts using a different angle of perforation in a circular pipe. In our simulation, we have used 0°, 5°, 10°, 15°, 16°, 17°, 20°, 30°, 40°, 50°, 60°, 65°, 68° and 70° angles of perforation respectively in a perforated axial insert considering the non-isothermal laminar flow. The inserts are used perpendicular to the fluid flow inside a pipe. A uniform heat-flux around the circular tube is assumed for our simulations. The temperature and pressure distribution are measured for a different angle of perforation. The relation between heat transfer rate and wall temperature is observed and found that the heat transfer rate increases inversely with the wall temperature. The effect of Nusselt number and friction factor are the diagnosis for all including angles and Reynolds numbers. The Thermal Performance Evaluation Criterion (PEC) is also analyzed in this study.