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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 is proven and very important properties of this matrix are discussed.

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 and . These matrices have a great number of identical elements. Therefore very few elements only must be generated.

The second property refers to the generation of the product . As a consequence of this property the matrix is obtained by the product of two matrices.

The most important property of matrix is that the knowledge of its first column defines the entire matrix. It is proven that the vector corresponding to this column can be efficiently generated by computational resources that permit the separation of the real part of complex numbers.

Moreover it is proven that the entries of are real as it must be physically the case.

The proof of the convergence property stems from the fact that the last terms of each element of tend to zero when the number of discrete terms tends to infinity.

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

1: Venâncio-Filho F. and Claret A.M., "Matrix formulation of the Dynamic Analysis of SDOF System in the Frequency Domain", Computers and Structures, Vol. 42, pp. 853-855, 1992. doi:10.1016/0045-7949(92)90196-7
2: Mansur W.J., Ferreira W.G., Claret A.M., Venâncio-Filho F., Carrer J.M. "Time Segmented Frequency-Domain Analysis for non-linear mult-degree-of-freedom Structural Systems", Journal of Sound and Vibration, Vol 237, pp. 457-475, 2000. doi:10.1006/jsvi.2000.3066
3: Venâncio-Filho F., Claret A.M. and Barbosa F.S., "Frequency and Time Domain Dynamic Strutural Analysis: Convergence and Causality", Computers and Structures, 2002 (in press). doi:10.1016/S0045-7949(02)00103-7

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	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 Department of Civil Engineering, Pontifical Catholic University of Rio de Janeiro, Brazil doi:10.4203/ccp.75.33 purchase the full-text of this paper 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 is proven and very important properties of this matrix are discussed. 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 and . These matrices have a great number of identical elements. Therefore very few elements only must be generated. The second property refers to the generation of the product . As a consequence of this property the matrix is obtained by the product of two matrices. The most important property of matrix is that the knowledge of its first column defines the entire matrix. It is proven that the vector corresponding to this column can be efficiently generated by computational resources that permit the separation of the real part of complex numbers. Moreover it is proven that the entries of are real as it must be physically the case. The proof of the convergence property stems from the fact that the last terms of each element of tend to zero when the number of discrete terms tends to infinity. 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 1 Venâncio-Filho F. and Claret A.M., "Matrix formulation of the Dynamic Analysis of SDOF System in the Frequency Domain", Computers and Structures, Vol. 42, pp. 853-855, 1992. doi:10.1016/0045-7949(92)90196-7 2 Mansur W.J., Ferreira W.G., Claret A.M., Venâncio-Filho F., Carrer J.M. "Time Segmented Frequency-Domain Analysis for non-linear mult-degree-of-freedom Structural Systems", Journal of Sound and Vibration, Vol 237, pp. 457-475, 2000. doi:10.1006/jsvi.2000.3066 3 Venâncio-Filho F., Claret A.M. and Barbosa F.S., "Frequency and Time Domain Dynamic Strutural Analysis: Convergence and Causality", Computers and Structures, 2002 (in press). doi:10.1016/S0045-7949(02)00103-7 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £125 +P&P)
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