Analysis on location of maximum vibration amplitude in panel flutter

Abstract

When the panel is under limit cycle oscillation, the location of maximum vibration amplitude always locates at 0.75 of panel length under different dynamic pressure. However, this conclusion is drawn from engineer practice without further investigations on its theoretical basis. Thus, the current study focuses on the theoretical and mathematical basis of this problem. The pattern of the location of maximum amplitude is verified at first by using three numerical methods. Then, based on the law of energy conservation, the displacement function of linear panel oscillation is derived for theoretical investigation. The linear panel consists of two structural modes. Theoretical analysis shows that, under critical dynamic pressure, the generalized displacement responses of two structural modes have opposite phase, the same vibration amplitude and the same vibration frequency. As a result, the superposition of displacement function of two structural modes, which is the displacement function of panel, leads to the occurrence of maximum vibration amplitude at 0.7 of panel length. With more structural modes considered, the location of maximum moves to 0.75 of panel length.

Mechanism of characteristic change of panel flutter caused by oblique shock impingement

“…1 Two types of structural models are usually considered: linear and nonlinear models. 4 The linear structure model assumes a linear relationship between the load and the deflection, which can only determine the flutter boundary and does not provide information about the flutter oscillation itself. 9 The nonlinear structure model, established by Dowell, 37,38 incorporates nonlinear forces into the analysis of the panel structure through von Kármán's large deflection equations.…”

“…The oscillation is generally a bounded limit-cycle oscillation (LCO) due to the geometric nonlinearity of the panel. 4 Although not catastrophic at an early stage, panel flutter remains a structural concern because of the potential for fatigue failure. 5 Panel flutter will also significantly disturb the downstream flow field, which could compromise the engine performance 6,7 and increase noise generation.…”