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.

活塞理论广泛用于模拟非定常气动载荷。活塞理论在不同条件下表现出不同的非线性特性。然而，关于这些条件影响的理论研究受到的关注有限，阻碍了活塞理论在工程实践中的准确应用。本研究在前人研究的基础上，从理论上探讨结构振型和振动频率对活塞理论非线性特性的影响。针对不同的工程问题，提出了三种不同的结构振型。对于单侧流下的楔形模态，流动非线性非常显着，占气动载荷的 40%，而流动仅表现出线性特征，即一侧流动下的尖锐正弦波状模式形状和两侧流动下的控制面。分析表明，模态振型可以通过结构不同区域中线性和非线性气动部件之间的相互作用显着影响活塞理论的非线性。此外，振动频率对活塞理论的非线性和有效性有重大影响。由于活塞理论中高阶项之间的相互作用，在中频（200–300Hz）处的流动非线性无关紧要，而在较低和较高频率下的非线性变得很明显。活塞理论随着频率的降低而失效，但在频率达到 0 时适用。分析表明，模态振型可以通过结构不同区域中线性和非线性气动部件之间的相互作用显着影响活塞理论的非线性。此外，振动频率对活塞理论的非线性和有效性有重大影响。由于活塞理论中高阶项之间的相互作用，流动非线性在中频（200-300Hz）处不显着，而在低频和高频处非线性变得显着。活塞理论随着频率的降低而失效，但在频率达到 0 时适用。分析表明，模态振型可以通过结构不同区域中线性和非线性气动部件之间的相互作用显着影响活塞理论的非线性。此外，振动频率对活塞理论的非线性和有效性有重大影响。由于活塞理论中高阶项之间的相互作用，流动非线性在中频（200-300Hz）处不显着，而在低频和高频处非线性变得显着。活塞理论随着频率的降低而失效，但在频率达到 0 时适用。此外，振动频率对活塞理论的非线性和有效性有重大影响。由于活塞理论中高阶项之间的相互作用，在中频（200–300Hz）处的流动非线性无关紧要，而在较低和较高频率下的非线性变得很明显。活塞理论随着频率的降低而失效，但在频率达到 0 时适用。此外，振动频率对活塞理论的非线性和有效性有重大影响。由于活塞理论中高阶项之间的相互作用，流动非线性在中频（200-300Hz）处不显着，而在低频和高频处非线性变得显着。活塞理论随着频率的降低而失效，但在频率达到 0 时适用。