Affiliations: Departamento de Mecânica Computacional, FEM,
Universidade Estadual de Campinas. R. Mendeleyev, Campinas – SP,
Brazil
Note: [] Corresponding author: P.B. Silva, Departamento de Mecânica
Computacional, FEM, Universidade Estadual de Campinas. R. Mendeleyev, 200,
13083-960, Campinas – SP, Brazil. Tel.: +55 19 3521 3395; Fax: +55 19
3289 3722; E-mail: pbrandaos@fem.unicamp.br
Abstract: 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.
