Name: LUAN HENRIQUE SIRTOLI
Publication date: 10/03/2021
Advisor:
Name |
Role |
|---|---|
| CARLOS FRIEDRICH LOEFFLER NETO | Advisor * |
Examining board:
| Name |
Role |
|---|---|
| CARLOS FRIEDRICH LOEFFLER NETO | Advisor * |
| HERCULES DE MELO BARCELOS | External Examiner * |
| LUCIANO DE OLIVEIRA CASTRO LARA | Internal Examiner * |
Summary: The present work aims to solve an eigenvalue problem obtained after the development of the Helmholtz Equation in its integral form and its later discretization following the methodology associated with the Direct Interpolation Boundary Elements Method. In order to eliminate the singularities eliminating mathematical procedure based on the Hadammard Regularization, a new integral equation was generated based on the use of a more elaborate fundamental solution.
However, the discrete form of this formulation, called self-regulated, generated matrices in addition to those usually obtained by the most common numerical methods. Unlike the scanning and obtaining and response problems, in which the mentioned formulation presented good results and easy operation, the calculation of natural frequencies becomes quite complex and unorthodox, as the associated eigenvalue problem is of the fourth order.
Thus, solving this type of problem requires a different approach, WHERE laborious mathematical manipulation and some approximations will be necessary. In this context, the generalization of the Przeminiecky Proposition stands out, because it is well known in the treatment of damped vibration problems, aiming to write the matrix equation in an accessible form for its computational resolution.
