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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 6707092, 13 pages
Research Article

New Look at Nonlinear Aerodynamics in Analysis of Hypersonic Panel Flutter

College of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China

Correspondence should be addressed to Honghua Dai

Received 25 November 2016; Revised 13 February 2017; Accepted 28 February 2017; Published 23 March 2017

Academic Editor: Xiao-Qiao He

Copyright © 2017 Dan Xie et al. 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.


A simply supported plate fluttering in hypersonic flow is investigated considering both the airflow and structural nonlinearities. Third-order piston theory is used for nonlinear aerodynamic loading, and von Karman plate theory is used for modeling the nonlinear strain-displacement relation. The Galerkin method is applied to project the partial differential governing equations (PDEs) into a set of ordinary differential equations (ODEs) in time, which is then solved by numerical integration method. In observation of limit cycle oscillations (LCO) and evolution of dynamic behaviors, nonlinear aerodynamic loading produces a smaller positive deflection peak and more complex bifurcation diagrams compared with linear aerodynamics. Moreover, a LCO obtained with the linear aerodynamics is mostly a nonsimple harmonic motion but when the aerodynamic nonlinearity is considered more complex motions are obtained, which is important in the evaluation of fatigue life. The parameters of Mach number, dynamic pressure, and in-plane thermal stresses all affect the aerodynamic nonlinearity. For a specific Mach number, there is a critical dynamic pressure beyond which the aerodynamic nonlinearity has to be considered. For a higher temperature, a lower critical dynamic pressure is required. Each nonlinear aerodynamic term in the full third-order piston theory is evaluated, based on which the nonlinear aerodynamic formulation has been simplified.