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Mathematical Problems in Engineering
Volume 2018, Article ID 2394124, 14 pages
Research Article

Higher-Order Spectral Analysis to Identify Quadratic Nonlinearities in Fluid-Structure Interaction

1Department of Mechanical Engineering, College of Electrical & Mechanical Engineering, National University of Sciences & Technology (NUST), Islamabad 44000, Pakistan
2ANSYS, Inc., Houston, TX 7745, USA

Correspondence should be addressed to Imran Akhtar;

Received 21 June 2017; Revised 8 October 2017; Accepted 1 November 2017; Published 9 January 2018

Academic Editor: Efstratios Tzirtzilakis

Copyright © 2018 Imran Akhtar and Mohammad Elyyan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Hydrodynamic forces on a structure are the manifestation of fluid-structure interaction. Since this interaction is nonlinear, these forces consist of various frequencies: fundamental, harmonics, excitation, sum, and difference of these frequencies. To analyze this phenomenon, we perform numerical simulations of the flow past stationary and oscillating cylinders at low Reynolds numbers. We compute the pressure, integrate it over the surface, and obtain the lift and drag coefficients for the two configurations: stationary and transversely oscillating cylinders. Higher-order spectral analysis is performed to investigate the nonlinear interaction between the forces. We confirmed and investigated the quadratic coupling between the lift and drag coefficients and their phase relationship. We identify additional frequencies and their corresponding energy present in the flow field that appear as the manifestation of quadratic nonlinear interaction.