Nonlinear single-mode and multi-mode panel flutter oscillations at low supersonic speeds

Abstract In this study we numerically analyse nonlinear flutter oscillations of elastic plate in a gas flow. In contrast to many other studies, we use inviscid flow model instead of piston theory or other simplified aerodynamic theories. This study aims to investigate the region of low supersonic Mach numbers, 1 M 2 , where several plate eigenmodes can be simultaneously unstable, and resulting oscillations are governed by nonlinear interaction of growing modes. Three types of unstable plate behaviour have been obtained. First, at 0.76 M 1 , the plate diverges. Second, at 1 M ≤ 1.67 , single-mode flutter occurs in three distinct forms: limit cycle in the first mode ( 1 M 1.33 and 1.5 M ≤ 1.67 ) or higher modes; limit cycle in the first and second modes being in internal 1:2 resonance ( 1.12 M 1.33 and 1.42 M 1.5 ); and non-periodic oscillations with several dominating frequencies being in more complex ratio ( 1.33 M 1.42 ). Third, at M=1.82 and increased dynamic pressure, coupled-mode flutter appears. Amplitudes and spectra of each limit cycle type are analysed. The role of aerodynamic nonlinearity in the formation of limit cycle oscillations is discussed.

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