Building spectral element dynamic matrices using finite element models of waveguide slices and elastodynamic equations

Autor(es)

Silva, P. B. ^[1] ; Goldstein, A. L. ^[1] ; Arruda, J. R. F. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, FEM, Dept Mecan Computac, BR-13083960 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: SHOCK AND VIBRATION; v. 20, n. 3, p. 439-458, 2013.
• Citações Web of Science: 3

Resumo

Structural spectral elements are formulated using the analytical solution of the applicable elastodynamic equations and, therefore, mesh refinement is not needed to analyze high frequency behavior provided the elastodynamic equations used remain valid. However, for modeling complex structures, standard spectral elements require long and cumbersome analytical formulation. In this work, a method to build spectral finite elements from a finite element model of a slice of a structural waveguide (a structure with one dimension much larger than the other two) is proposed. First, the transfer matrix of the structural waveguide is obtained from the finite element model of a thin slice. Then, the wavenumbers and wave propagation modes are obtained from the transfer matrix and used to build the spectral element matrix. These spectral elements can be used to model homogeneous waveguides with constant cross section over long spans without the need of refining the finite element mesh along the waveguide. As an illustrating example, spectral elements are derived for straight uniform rods and beams and used to calculate the forced response in the longitudinal and transverse directions. Results obtained with the spectral element formulation are shown to agree well with results obtained with a finite element model of the whole beam. The proposed approach can be used to generate spectral elements of waveguides of arbitrary cross section and, potentially, of arbitrary order. (AU)

• Processo FAPESP: 09/10715-1 - Modelagem Teórica e Ensaios Experimentais do Controle Ativo de Transmissão Sonora Através de Painéis Duplos
• Beneficiário: Andre Lucchino Goldstein
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 10/17317-9 - Estudo da propagação de ondas elásticas em estruturas periódicas
• Beneficiário: Priscilla Brandão Silva
• Modalidade de apoio: Bolsas no Brasil - Doutorado Direto