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Application of Bessel functions
Lorenczyk, Jiří ; Lomtatidze, Aleksandre (referee) ; Dosoudilová, Monika (advisor)
The purpose of this work is the introduction to the theory of Bessel differential equation and Bessel functions and its application to the problem of the vibration of a circular plate. In order to tackle this problem succesfully, it is needed to find a solution to the Bessel differential equation in the form of the eponymous Bessel functions and it will be shown how to do so. After that, some characteristics of the obtained Bessel functions of the first kind will be thoroughly demonstrated. Then the other solutions to the Bessel differential equation will be introduced, namely Bessel functions of the second kind, Hankel functions and modified Bessel functions which are obtained as a solution to the modified Bessel equation. In the second chapter, the area of interest will be the application of Bessel functions to the problem of the vibration of a circular plate. However, this problem will be severely restricted since the board will be considered to be perfectly fixed around its circumference, there will be no holes in it and there will be no external force acting on its surface. To solve this problem, it will be needed to make a use of each of the aformentioned Bessel functions.
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Application of Bessel functions
Lorenczyk, Jiří ; Lomtatidze, Aleksandre (referee) ; Dosoudilová, Monika (advisor)
The purpose of this work is the introduction to the theory of Bessel differential equation and Bessel functions and its application to the problem of the vibration of a circular plate. In order to tackle this problem succesfully, it is needed to find a solution to the Bessel differential equation in the form of the eponymous Bessel functions and it will be shown how to do so. After that, some characteristics of the obtained Bessel functions of the first kind will be thoroughly demonstrated. Then the other solutions to the Bessel differential equation will be introduced, namely Bessel functions of the second kind, Hankel functions and modified Bessel functions which are obtained as a solution to the modified Bessel equation. In the second chapter, the area of interest will be the application of Bessel functions to the problem of the vibration of a circular plate. However, this problem will be severely restricted since the board will be considered to be perfectly fixed around its circumference, there will be no holes in it and there will be no external force acting on its surface. To solve this problem, it will be needed to make a use of each of the aformentioned Bessel functions.
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