Optimal Homotopy Asymptotic Solution for Thermal Radiation and Chemical Reaction Effects on Electrical MHD Jeffrey Fluid Flow Over a Stretching Sheet through Porous Media with Heat Source

In this paper, the problem of thermal radiation and chemical reaction effects on electrical MHD Jeffrey fluid flow over a stretching surface through a porous medium with the heat source is presented. We obtained the approximate analytical solution of the nonlinear differential equations governing the problem using the Optimal Homotopy Asymptotic Method (OHAM). Comparison of results has been made with the numerical solutions from the literature, and a very good agreement has been observed. Subsequently, effects of governing parameters of the velocity, temperature and concentration profiles are presented graphically and discussed

Approximate Analytical Methods For Solving Fredholm Integral Equations

Persamaan kamiran memainkan peranan penting dalam banyak bidang sains seperti matematik, biologi, kimia, fizik, mekanik dan kejuruteraan. Oleh yang demikian,pelbagai teknik berbeza telah digunakan untuk menyelesaikan persamaan jenis ini. Kajian ini, memfokus kepada analisis secara matematik dan berangka bagi beberapa kes persamaan kamiran Fredholm yang linear dan bukan linear. Kes-kes ini termasuklah persamaan kamiran Fredholm satu dimensi jenis pertama dan kedua, persamaan kamiran Fredholm dua dimensi jenis pertama dan kedua dan sistem persamaan kamiran Fredholm satu dimensi dan dua dimensi. Integral equations play an important role in many branches of sciences such as mathematics, biology, chemistry, physics, mechanics and engineering. Therefore, many different techniques are used to solve these types of equations. This study focuses on the mathematical and numerical analysis of some cases of linear and nonlinear Fredholm integral equations. These cases are one-dimensional Fredholm integral equations of the first kind and second kind, two-dimensional Fredholm integral equations of the first kind and second kind and systems of one and two-dimensional Fredholm integral equations

A Computational Method for Solving a Class of Fractional-Order Non-Linear Singularly Perturbed Volterra Integro-Differential Boundary-Value Problems

In this thesis, we present a computational method for solving a class of fractional singularly perturbed Volterra integro-differential boundary-value problems with a boundary layer at one end. The implemented technique consists of solving two problems which are a reduced problem and a boundary layer correction problem. The reproducing kernel method is used to the second problem. Pade’ approximation technique is used to satisfy the conditions at infinity. Existence and uniformly convergence for the approximate solution are also investigated. Numerical results provided to show the efficiency of the proposed method

Nanotalade võnkumise numbriline analüüs

Väitekirja elektrooniline versioon ei sisalda publikatsiooneKäesolevas väitekirjas uuritakse nanomaterjalist valmistatud talade omavõnkumisi mitmesuguste kinnitusviiside korral. Väitekirjas on välja töötatud meetodid nanotalade omavõnkesageduse määramiseks astmelise nanotala jaoks erinevate kinnitustingimuste korral; kusjuures astmete nurkades asuvad stabiilsed praod või prao-tüüpi defektid. Prao mõju võnkesagedusele modelleeritakse nn kaalutu väändevedru meetodil. Selle meetodi kohaselt tuleb reaalne astmega tala asendada kahest elemendist koosneva süsteemiga, kus elemendid on omavahel ühendatud väändevedruga, mille jäikus on pöördvõrdeline pinge intensiivsuse koefitsiendiga prao tipu juures. Kuna pinge intensiivsuse koefitsiendi väärtused on leitavad kataloogidest, siis see meetod võimaldab omavahel siduda nanotala omavõnkesageduse ning prao pikkuse ja laiuse. Väitekiri koosneb sissejuhatusest, viiest peatükist ning kirjanduse loetelust, mis sisaldab 82 nimetust. Sissejuhatus kujutab endast esimest peatükki. Teises peatükis on toodud põhivõrrandid ning põhieeldused. Esimesed kaks peatükki on referatiivsed, ülejäänutes esitatakse originaalseid tulemusi. Kolmandas peatükis esitatakse nanotalade võnkumise võrrandid, mis arvestavad tala elementide pöördeinertsi. Need on Euler-Bernoulli võrrandite üldistuseks juhule, kui pöördeinertsi arvestamine on kohustuslik. See süsteem on lahendatav ka muutujate eraldamise teel. Neljandas peatükis lahendatakse põhivõrrandite süsteem numbriliselt. Näidatakse muuhulgas, et süsteemi saab hõlpsasti lahendada Maclaurini rea abil. Viies peatükk on pühendatud nanotalade võnkumise uurimisele juhul, kui nanotala on kinnitatud elastsete tugede abil st. toed ei ole jäigad. Kuuendas peatükis uuritakse pragudega nanotalade võnkumisi arvestades termilisi mõjutusi st. temperatuuripingeid. Väitekirjas saadud tulemusi on võrreldud erijuhtudel kirjandusest leitavate tulemustega ning veendutud, et väitekirjas esitatud tulemused on heas kooskõlas teiste uurijate poolt saadud tulemustega. Väitekirjas saadud tulemuste põhjal on avaldatud koos juhendajaga 10 teadusartiklit.In this dissertation, an analysis of the dynamic behavior of nanobeams with different physical and geometrical properties using several numerical techniques is presented. Euler-Bernoulli beam theory and nonlocal theory of elasticity are used to simulate the nanobeam. Nanobeams are considered with some special requirements such as tapered, axially graded, and double beams. First of all, in a tapered beam, the width of the beam is varying exponentially along the x-axis from one end to another end. The properties of the tapered beam are to reduce material consumption and provide the cross-sectional area according to the moment distribution. Secondly, in an axially graded beam, material properties such as elasticity and density are varying exponentially from one end to another end. The axially graded beam can be considered as a non-homogeneous as well as a composite beam. In this beam, the material properties can be distributed according to the requirement. The axially graded beam overcomes the limitation of conventional composite. Finally, in a double beam, two identical nanobeams are connected by a Winkler-type spring layer. Double beams are used for absorbing the vibration. It reduces deflection and vibration. The double beam is modeled by the coupled differential governing equations. Some adverse effects such as cracks and the influence of the temperature are considered. Cracks are common defects in nanostructures. Single and multiple cracks are considered in this analysis. According to the model, the crack is replaced by a rotational spring where the crack divides the beam into two segments that are connected to each other by the spring at the crack position. Cracks reduce the overall stiffness of the beam. The effect of temperature is significant for the vibration of nanobeams. The thermal load is compatible with the mechanical load where the thermal load is modeled as an axial load. It reduces the natural frequency. The main objective of this research is to find suitable techniques for a reliable, cost-effective design that is able to fulfill the desired requirements. That is why the important feature of this research is to apply numerical techniques for solving these problems. Three different approximation techniques such as homotopy perturbation technique, power series method, and Maclaurin series method are used for solving these problems. These techniques are useful for solving linear and non-linear differential equations. However, these techniques are rare to analyze the nano-material. These techniques are applied effectively to scrutinize the model of nanobeams. Obtained results are verified with the results of other researchers in the existing literature. This analysis can be used to design nano-electromechanical devices effectively.https://www.ester.ee/record=b550871

Influence of geometric and material parameters on the damping properties of multilayer structures

In this paper, we investigate the influence of deviations in the design and implementation parameters on the damping properties of multilayer viscoelastic structures. This work is based on a numerical approach, which uses recently developed solid–shell elements that have been specifically designed for the modeling of multilayer structures. The originality in the current study lies in the analysis of variation in the design parameters, which could be of geometric or material type. Indeed, although several models have been proposed to study variability, they remain mostly complex to implement. Our approach is rather simple, and is based on the uncertainty on the actual values of several parameters in some well-defined intervals. The developed method is applied to the vibration modeling of multilayer structures, with elastic faces and viscoelastic core material. The resulting problem is discretized by using quadratic solid–shell finite elements. To solve the associated nonlinear equations, we adopt the method that couples the homotopy technique to the Asymptotic Numerical Method (ANM) as well as the Automatic Differentiation (AD) and path continuation. The obtained results provide useful information on the error tolerance margin that could be allowed without compromising structural integrity

LI-HE’S MODIFIED HOMOTOPY PERTURBATION METHOD FOR DOUBLY-CLAMPED ELECTRICALLY ACTUATED MICROBEAMS-BASED MICROELECTROMECHANICAL SYSTEM

This paper highlights Li-He’s approach in which the enhanced perturbation method is linked with the parameter expansion technology in order to obtain frequency amplitude formulation of electrically actuated microbeams-based microelectromechanical system (MEMS). The governing equation is a second-order nonlinear ordinary differential equation. The obtained results are compared with the solution achieved numerically by the Runge-Kutta (RK) method that shows the effectiveness of this variation in the homotopy perturbation method (HPM)