Frequencies evaluation in three-dimensional piecewise homogeneous Helmholtz problems. (December 2020)

• Record Type: Journal Article
• Authors: Barbosa, J.P.; Loeffler, C.F.; Lara, L.O.C.
• Is Part Of: Engineering analysis with boundary elements. Volume 121(2020)
• Page Start: 104
• Page End: 115
• Publication Date: 2020-12
• Subjects: Boundary elements method -- Three-dimensional eigenvalue problems -- Sectorally homogeneous problems -- Natural frequencies; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2020.09.008
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this work, two new techniques of the Boundary Elements Method are coupled for solving eigenvalues in three-dimensional piecewise scalar problems. The Domain Superposition Technique (DST) is used to approach the sectorial homogeneities, modeling the domain as a sum of a homogeneous surrounding sector and other complementary ones with different constitutive properties. The Direct Interpolation Technique (DIBEM) with Radial Basis Functions transform domain integrals, in this case referring to the inertia, into boundary integrals. Thus, after discretization, a classical boundary element matrix system is formed in which the natural frequencies are achieved solving an eigenvalue problem. Considering the absence of analytical solutions for three-dimensional dynamic problems, benchmarks are taken by the Finite Element Results, using finer meshes.