Nonlinear Aeroelastic Analysis of Heated Curved Panels in Supersonic Air Flow
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ORIGINAL PAPER
Nonlinear Aeroelastic Analysis of Heated Curved Panels in Supersonic Air Flow Jian Zhou1 · Minglong Xu1 · Zhichun Yang2 Received: 2 March 2019 / Revised: 22 August 2019 / Accepted: 29 October 2019 © The Korean Society for Aeronautical & Space Sciences 2020
Abstract A nonlinear aeroelastic model for a two-dimensional heated curved panel in supersonic air flow is established by using Galerkin method. The von Karman large deflection theory and the third-order piston theory appended with the static aerodynamic loading are used in the governing equations. The static aero-thermal deflection of the curved panel is firstly obtained by using Newton iterative approach. Then the stability boundary under different temperature elevations is achieved by using Lyapunov’s indirect method. Lastly, the motion equations of a heated curved panel in supersonic air flow are solved by a fourth-order Runge–Kutta numerical scheme. Time history responses, phase plots, Poincare maps and bifurcation diagrams are used for better understanding of the pre/post-flutter responses of a curved panel by varying parameters, including curvatures, dynamic pressures and temperature elevations. The results demonstrate that the flutter boundary drops significantly with increasing temperature elevation for panels with small curvatures. However, the flutter boundary almost keeps the same for panels with large curvatures. The nonlinear flutter characteristics of the curved panel differs from those of flat panels significantly, the nonlinear flutter response of heated curved panels changes from static equilibrium point or LCO to chaos with the increase of temperature elevation or dynamic pressure and the static, LCO motions also exist in the chaotic area. For panels with large curvatures, the chaotic motions cannot occur, and the amplitude of LCO is limited in a certain range. Keywords Curved panels · Supersonic flow · Bifurcation · Chaos · Temperature elevation
1 Introduction Since aircrafts reached supersonic speeds in the early 1950s, supersonic panel flutter is a well-known phenomenon and many researchers have done intensive theoretical and experimental investigations [1–4]. The panel flutter is a kind of dynamic aeroelastic instability resulting from the interaction of aerodynamic force, inertial force and elastic force. For supersonic or hypersonic aircraft, thermal stress induced by aerodynamic heating plays an important role and leads to more complex dynamic behaviors. In the published literatures on panel flutter problem, a large number of efforts were dedicated to investigate flat * Jian Zhou [email protected] 1
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, China
School of Aeronautics, Northwestern Polytechnical University, Xi’an, China
2
panel flutter in the supersonic or hypersonic flow regime [5–11], while the curvature of aircraft skin panel exists in the engineering practice of supersonic aircraft structure design. Owing to the inherent curvature,
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