DYNAMICS ANALYSIS OF 1D STRUCTURE INCLUDING RANDOM PARAMETER VIA FREQUENCY-DOMAIN STATE-VECTOR EQUATIONS

Autores

  • Marcela Rodrigues Machado University of Brasília
  • Vilson Souza Pereira Federal University of Maranhão
  • Dalmo I. G. Costa
  • Elson C. Moraes Federal University of Maranhão
  • José Maria Campos dos Santos State University of Campinas

DOI:

https://doi.org/10.26512/ripe.v2i16.21623

Palavras-chave:

Uncertainty quantification. Transfer matrix. State-Vector. Monte Carlo simulation. Spectral element method.

Resumo

The consideration of uncertainties in numerical models to obtain the probabilistic descriptions of dynamic response is becoming more desirable in the way to quantify the parametric and non-parametric uncertainties associated with the model. In this work, an alternative approach to the spectral element formulation, in which the exact wave solutions are not required, the spectral element matrix including random parameters is derived from the transfer matrix formulated directly from the frequency-domain state-vector equation of motion. The analyses were made to quantify the effect of uncertainty in the dynamic responses at high frequency bands and the Monte Carlo simulation is used to propagate the variation in dimensional properties of the structural parameters. Some interesting results are presented, showing the effects of uncertainty parameters in the dynamic response of the structure.

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Referências

Cho, P. and Bernhard, R. . Energy flow analysis of coupled beams. Journal of Sound and Vibration, 211:593–605, 1998.

Doyle, J. F. . Wave propagation in structures : spectral analysis using fast discrete Fourier transforms. Mechanical engineering. Springer-Verlag New York, Inc., New York, second edition, 1997.

Ghanem, R. and Spanos, P. . Stochastic Finite Elements - A Spectral Approach. Sprin, 1991.

J.C. Wohlever, R. B. . Mechanical energy flow models of rods and beams. Journal of Sound and Vibration, 153:1–19, 1992.

Kinsler, L. E. , Frey, A. R. , Coppens, A. B. , and Sanders, J. V. . Fundamentals of Acoustics. John Wiley & Sons, 1982.

Kleiber, M. and Hien, T. . The Stochastic Finite Element Method. John Wiley, 1992.

Lee, U. . Vibration analysis of one-dimensional structures using the spectral transfer matrix method. Engineering Structures, 22(6):681–690, 2000. doi: 10.1016/S0141-0296(99)00002-4.

Lee, U. . Spectral Element Method in Structural Dynamics. BInha University Press, 2004.

Lyon, R. H. and DeJong, R. G. . Theory and Application of Dynamics Systems, Second edition. Butterworth-Heinemann, Boston, 1975.

Maˆıtre, O. L. and Knio, O. . Spectral methods for uncertainty quantification. Springer, 2010.

Rubinstein, R. Y. . Simulation and the Monte Carlo Method, 2nd Edition. Wiley, 2008.

Sampaio, R. and Lima, R. . Modelagem Estoc´astica e Gerac¸ ˜ao de Amostras de Vari´aveis e Vetores Aleat´orios. SBMAC (Notas em Matem´atica Aplicada; v. 70), 2012.

Santos, E. , Arruda, J. , and Santos, J. D. . Modeling of coupled structural systems by an energy spectral element method. Journal of Sound and Vibration, 36:1 – 24, 2008.

Sobol’, I. M. . A primer for the Monte Carlo method. CRC Press, 1994.

Xiu, D. . Numerical Methods for Computations-A Spectral method approcah. Princeton University Press, 2010.

Yamazaki, F. , Shinozuka, M. , and Dasgupta, G. . Neumann expansion for stochastic finite element analysis. Journal Engineering Mechanics-ASCE, 114 (8):1335–1354, 1988.

Zhu,W. , Ren, Y. , andWu,W. . Stochastic fem based on local averages of random vector fields. Journal Engineering Mechanics-ASCE, 118 (3):496–511, 1992.

Publicado

2019-01-07

Como Citar

Machado, M. R., Pereira, V. S., I. G. Costa, D., C. Moraes, E., & Santos, J. M. C. dos. (2019). DYNAMICS ANALYSIS OF 1D STRUCTURE INCLUDING RANDOM PARAMETER VIA FREQUENCY-DOMAIN STATE-VECTOR EQUATIONS. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(16), 130-143. https://doi.org/10.26512/ripe.v2i16.21623