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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 75
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and Z. Bittnar
Paper 33
Convergence and Causality of the Implicit Fourier Transform S.J. Rodrigues Júnior+ and F. Venâncio-Filho*
+Department of Civil Construction, Federal University of Pará, Belém, Brazil
Full Bibliographic Reference for this paper
, "Convergence and Causality of the Implicit Fourier Transform", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Sixth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 33, 2002. doi:10.4203/ccp.75.33
Keywords: fourier transforms, dynamic analysis, frequency domain, convergence, causality, frequency-dependent damping.
Summary
The Implicit Fourier Transform (ImFT) concept, introduced in 1992,
Reference [1], has proven to be very efficient for frequency-domain dynamic analysis of
structural systems. This concept has been employed with success in the linear and
nonlinear analysis of structural systems with nonproportional, hysteretic and
frequency-dependent damping, Reference [2]. In a previous paper, Reference [3],
the convergence and causality of the response of SDOF systems obtained through a
frequency-domain analysis with the ImFT was proven. In this paper the convergence
and causality of the ImFT matrix
![]() A brief survey of the ImFT concept is firstly presented then important properties of the ImFT matrices are analysed.
The first property is related to matrices
The second property refers to the generation of the product
The most important property of matrix
Moreover it is proven that the entries of
The proof of the convergence property stems from the fact that the last terms of
each element of
The numerical validation shows that convergence is fairly fast for The causality property is proven and numerically verified. The influence of the variation of the extended period upon the causality is considered. References
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