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Artificial Neural Network Based Solution of Fractional Vibration Model

  • Susmita MallEmail author
  • S. Chakraverty
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

The purpose of the investigation is to handle the fractional vibration problem using the multilayer artificial neural network (ANN) method. Fractional calculus has found several applications in different fields of physical systems, viz., viscoelasticity, dynamics, and anomalous diffusion transport. Fractional derivatives are practically described viscoelasticity features in structural dynamics. In general, damping models involve ordinary integer differential operators that are relatively easy to handle. On the other hand, fractional derivatives give better models with respect to the vibration systems in comparison to classical integer-order models. Here, the fractional order in the damping coefficient has been considered. We have employed the multilayer feed-forward neural architecture and error back-propagation algorithm with unsupervised learning for minimizing the error function and modification of the parameters (weights and biases). The results obtained by the present method are compared with the analytical results and are found to be in good agreement.

Keywords

Fractional differential equation Vibration problem Bagley–Torvik problem Artificial neural network model Feed-forward structure Back-propagation algorithm 

Notes

Acknowledgements

The first author is thankful to the Department of Science and Technology (DST), Government of India for financial support under Women Scientist Scheme-A.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of Technology Rourkela‎RourkelaIndia

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