Influence of vibration characteristics on the nonlinearity of piston theory

Piston theory is widely used in modeling unsteady aerodynamic loads. The piston theory exhibits different nonlinear characteristics under variant conditions. However, the theoretical study regarding the influence of these conditions only receives limited attention, impeding the accurate applications of piston theory in engineering practice. Based on previous researches, the current study theoretically investigates the influence of structural mode shape and vibration frequency on the nonlinear characteristics of piston theory. Corresponding to different engineering problems, three different structural mode shapes are proposed. For a wedge-like mode shape under one-side flow, the flow nonlinearity is significant and consists of 40% of aerodynamic loads, while the flow only exhibits linear features for a sharpened sine-wave-like mode shape under one-side flow and control surface under two-side flow. The analysis shows that the mode shapes can significantly influence the nonlinearity of piston theory through the interaction between linear and nonlinear aerodynamic components in different regions of the structure. Moreover, the vibration frequency has a major influence on the nonlinearity and validity of piston theory. Due to the interaction between high-order terms in piston theory, the flow nonlinearity is insignificant at intermediate frequency (200–300Hz), while the nonlinearity at lower and higher frequencies becomes significant. The piston theory becomes invalid with decreasing frequency, but applicable when the frequency reaches 0.