活塞理论非线性项对壁板颤振特性的影响研究

Currently, there is no systematic summary of the influence of the nonlinear terms in piston theory on the panel flutter. The two⁃dimensional nonlinear panel flutter equations under supersonic airflow based on the first, sec⁃ ond, and third⁃order piston theories is established. The stability of the heated panel is analyzed by using the Lya⁃ punov′s indirect method, and the panel flutter equations are numerically solved based on the numerical analysis method to investigate the influence of the nonlinear terms in piston theory on the panel flutter. The results show that: ①Under a small temperature rise ratio, the panel response under the first⁃order piston theory only exhibits the convergent motion and single⁃period limit cycle flutter. While under higher⁃order piston theories, the panel response is more complex, exhibiting more complex nonlinear dynamic phenomena such as multi⁃period limit cycle flutter and chaotic motion in addition to the aforementioned characteristics. ②As the Mach number increases, the required dynamic pressure and temperature rise ratio decrease gradually when the dynamic response of the panel under the first⁃order piston theory and higher⁃order piston theories exhibit significant differences. ③The significant differences in the computational results of the second⁃order and third⁃order piston theory appear under the high Mach numbers and relatively high dynamic pressures, and the same phenomenon occurs underthe high temperature rise ratios. ④ When the dynamic response characteristics of the panel are basically consistent, the displacement response peak calculated by using the higher⁃order piston theory is usually smaller than the result calculated by using the first⁃or⁃ der piston theory, and the maximum error can reach about 16.66%. The present results have certain reference value for selecting the appropriate analysis method for the panel flutter under different conditions in practical applications.