-
Faculty of Arts and HumanitiesDean's Office, Faculty of Arts and HumanitiesJakobi 2, r 116-121 51005 Tartu linn, Tartu linn, Tartumaa EST0Institute of History and ArchaeologyJakobi 2 51005 Tartu linn, Tartu linn, Tartumaa EST0Institute of Estonian and General LinguisticsJakobi 2, IV korrus 51005 Tartu linn, Tartu linn, Tartumaa EST0Institute of Philosophy and SemioticsJakobi 2, III korrus, ruumid 302-337 51005 Tartu linn, Tartu linn, Tartumaa EST0Institute of Cultural ResearchÜlikooli 16 51003 Tartu linn, Tartu linn, Tartumaa EST0Institute of Foreign Languages and CulturesLossi 3 51003 Tartu linn, Tartu linn, Tartumaa EST0School of Theology and Religious StudiesÜlikooli 18 50090 Tartu linn, Tartu linn, Tartumaa EST0Viljandi Culture AcademyPosti 1 71004 Viljandi linn, Viljandimaa EST0Professors emeriti, Faculty of Arts and Humanities0Associate Professors emeriti, Faculty of Arts and Humanities0Faculty of Social SciencesDean's Office, Faculty of Social SciencesLossi 36 51003 Tartu linn, Tartu linn, Tartumaa EST0Institute of EducationJakobi 5 51005 Tartu linn, Tartu linn, Tartumaa EST0Johan Skytte Institute of Political StudiesLossi 36, ruum 301 51003 Tartu linn, Tartu linn, Tartumaa EST0School of Economics and Business AdministrationNarva mnt 18 51009 Tartu linn, Tartu linn, Tartumaa EST0Institute of PsychologyNäituse 2 50409 Tartu linn, Tartu linn, Tartumaa EST0School of LawNäituse 20 - 324 50409 Tartu linn, Tartu linn, Tartumaa EST0Institute of Social StudiesLossi 36 51003 Tartu linn, Tartu linn, Tartumaa EST0Narva CollegeRaekoja plats 2 20307 Narva linn, Ida-Virumaa EST0Pärnu CollegeRingi 35 80012 Pärnu linn, Pärnu linn, Pärnumaa EST0Professors emeriti, Faculty of Social Sciences0Associate Professors emeriti, Faculty of Social Sciences0Faculty of MedicineDean's Office, Faculty of MedicineRavila 19 50411 Tartu linn, Tartu linn, Tartumaa ESTInstitute of Biomedicine and Translational MedicineBiomeedikum, Ravila 19 50411 Tartu linn, Tartu linn, Tartumaa ESTInstitute of PharmacyNooruse 1 50411 Tartu linn, Tartu linn, Tartumaa ESTInstitute of DentistryL. Puusepa 1a 50406 Tartu linn, Tartu linn, Tartumaa ESTInstitute of Clinical MedicineL. Puusepa 8 50406 Tartu linn, Tartu linn, Tartumaa ESTInstitute of Family Medicine and Public HealthRavila 19 50411 Tartu linn, Tartu linn, Tartumaa ESTInstitute of Sport Sciences and PhysiotherapyUjula 4 51008 Tartu linn, Tartu linn, Tartumaa ESTProfessors emeriti, Faculty of Medicine0Associate Professors emeriti, Faculty of Medicine0Faculty of Science and TechnologyDean's Office, Faculty of Science and TechnologyVanemuise 46 - 208 51003 Tartu linn, Tartu linn, Tartumaa ESTInstitute of Computer ScienceNarva mnt 18 51009 Tartu linn, Tartu linn, Tartumaa ESTInstitute of GenomicsRiia 23b/2 51010 Tartu linn, Tartu linn, Tartumaa ESTEstonian Marine Institute0Institute of PhysicsInstitute of ChemistryRavila 14a 50411 Tartu linn, Tartu linn, Tartumaa EST0Institute of Mathematics and StatisticsNarva mnt 18 51009 Tartu linn, Tartu linn, Tartumaa EST0Institute of Molecular and Cell BiologyRiia 23, 23b - 134 51010 Tartu linn, Tartu linn, Tartumaa ESTTartu ObservatoryObservatooriumi 1 61602 Tõravere alevik, Nõo vald, Tartumaa EST0Institute of TechnologyNooruse 1 50411 Tartu linn, Tartu linn, Tartumaa ESTInstitute of Ecology and Earth SciencesJ. Liivi tn 2 50409 Tartu linn, Tartu linn, Tartumaa ESTProfessors emeriti, Faculty of Science and Technology0Associate Professors emeriti, Faculty of Science and Technology0Institute of BioengineeringArea of Academic SecretaryHuman Resources OfficeUppsala 6, Lossi 36 51003 Tartu linn, Tartu linn, Tartumaa EST0Area of Head of FinanceFinance Office0Area of Director of AdministrationInformation Technology Office0Administrative OfficeÜlikooli 17 (III korrus) 51005 Tartu linn, Tartu linn, Tartumaa EST0Estates Office0Marketing and Communication OfficeÜlikooli 18, ruumid 102, 104, 209, 210 50090 Tartu linn, Tartu linn, Tartumaa EST0Area of Vice Rector for Academic AffairsOffice of Academic AffairsUniversity of Tartu Youth AcademyUppsala 10 51003 Tartu linn, Tartu linn, Tartumaa EST0Student Union OfficeÜlikooli 18b 51005 Tartu linn, Tartu linn, Tartumaa EST0Centre for Learning and TeachingArea of Vice Rector for ResearchUniversity of Tartu LibraryW. Struve 1 50091 Tartu linn, Tartu linn, Tartumaa EST0Grant OfficeArea of Vice Rector for DevelopmentCentre for Entrepreneurship and InnovationNarva mnt 18 51009 Tartu linn, Tartu linn, Tartumaa EST0University of Tartu Natural History Museum and Botanical GardenVanemuise 46 51003 Tartu linn, Tartu linn, Tartumaa EST0International Cooperation and Protocol Office0University of Tartu MuseumLossi 25 51003 Tartu linn, Tartu linn, Tartumaa EST0Area of RectorRector's Strategy OfficeInternal Audit Office
Doctoral defence: Mohammed Mainul Hossain “Numerical analysis of vibrations of nanobeams”
On 30 August at 11:15 Mohammed M. Hossain will defend his doctoral thesis “Numerical analysis of vibrations of nanobeams” for obtaining the degree of Doctor of Philosophy (in Mathematics).
Supervisor:
Professor Emeritus Jaan Lellep, University of Tartu
Opponents:
Professor Zdeněk Kala, Brno University of Technology (Czech Republic)
Professor Evgeny Barkanov, Riga Technical University (Latvia)
Summary
In this dissertation, an analysis of the dynamic behaviour 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 modelled 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 modelled 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 fulfil 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.