Título: | EFFICIENCY ASSESSMENT OF ADVANCED MODAL ANALYSIS AS COMPARED TO TECHNIQUES BASED ON NUMERICAL INVERSE TRANSFORMS | ||||||||||||||||||||||||||||||||||||||||
Autor: |
CARLOS ANDRES AGUILAR MARON |
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Colaborador(es): |
NEY AUGUSTO DUMONT - Orientador |
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Catalogação: | 13/FEV/2009 | Língua(s): | PORTUGUESE - BRAZIL |
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Tipo: | TEXT | Subtipo: | THESIS | ||||||||||||||||||||||||||||||||||||||
Notas: |
[pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio. [en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio. |
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Referência(s): |
[pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=13046&idi=1 [en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=13046&idi=2 |
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DOI: | https://doi.org/10.17771/PUCRio.acad.13046 | ||||||||||||||||||||||||||||||||||||||||
Resumo: | |||||||||||||||||||||||||||||||||||||||||
An established technique to solve time-dependent problems is
the formulation
of a complete frequency-domain analysis via Laplace or
Fourier transforms,
with subsequent ad hoc expression of results by numerical
inversion.
Although usually easy to implement, such a transform
inversion is computationally
intensive, if accurate results are desired, and liable to
numerical
instabilities. For diffusion-type problems, the
Gaver-Stehfest algorithm
seems well suited. General dynamics problems demand more
robust algorithms
usually based on Fourier series expansions, as firstly
proposed by
Dubner and Abate. Algorithms of either kind are already
implemented in
mathematical languages such as Matlab and Mathematica. The
Fortran library
has a Fourier-series algorithm proposed by Crump and improved by
de Hoog et al. More recently, it has been proposed to solve
transient problems
of potential and elasticity by using an advanced mode
superposition
technique that applies to equilibrium-based finite element
and boundary element
models. One starts with a frequency-domain formulation that
leads to
a complex-symmetric (if viscous damping is included),
effective stiffness matrix
expressed as a frequency power series with generalized
stiffness, dumping
and mass matrices. After solution of the associated
complex-symmetric,
non-linear eigenvalue problem, one arrives at an advanced
modal solution of
the problem, which leads to the straightforward solution in
the time domain
and the immediate expression of any results of interest. Aim
of the present
research work is to compare the computational efficiency of
the proposed
advanced modal analysis with the techniques based on
numerical inverse
transforms, as applied to general, large scale problems. The
relevant literature
is reviewed and the main conceptual differences of the
investigated
methods are briefly outlined. All algorithms are implemented
in Fortran so
as to assure a common basis of comparison. Some initial
results are displayed,
as more definitive conclusions can only be expected after a
large
series of numerical simulations.
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