UT
U. Tabak
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In this thesis, we present numerical techniques for analyzing vibro-acoustic problems that emerge from the coupling of elastic structures with fluid domains. The main analysis tool used for numerical modelling is the Finite Element Technique (FEM). By using FEM, the goal of our research was to either improve the already available techniques or propose new ones for problems involving this type of coupling. The thesis is divided into two main topics/parts which can be followed independently.
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In this thesis, we present numerical techniques for analyzing vibro-acoustic problems that emerge from the coupling of elastic structures with fluid domains. The main analysis tool used for numerical modelling is the Finite Element Technique (FEM). By using FEM, the goal of our research was to either improve the already available techniques or propose new ones for problems involving this type of coupling. The thesis is divided into two main topics/parts which can be followed independently.
An efficient symmetric Lanczos method for the solution of vibro-acoustic eigenvalue problems is presented in this paper. Although finite element discretization results in real but nonsymmetric system matrices, we show that an efficient iteration scheme on a symmetric representation can be built up by using a transformation matrix. In order to decrease the numerical costs of the orthogonalizations performed, we propose to use a partial orthogonalization scheme for the symmetric case. The proposed method is tested on two large problems in order to demonstrate its efficiency and accuracy.
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An efficient symmetric Lanczos method for the solution of vibro-acoustic eigenvalue problems is presented in this paper. Although finite element discretization results in real but nonsymmetric system matrices, we show that an efficient iteration scheme on a symmetric representation can be built up by using a transformation matrix. In order to decrease the numerical costs of the orthogonalizations performed, we propose to use a partial orthogonalization scheme for the symmetric case. The proposed method is tested on two large problems in order to demonstrate its efficiency and accuracy.