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.

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