In this study, the stability and nonlinear vibrations of a thin plate in narrow aero-thermal channel are studied. According to the classic nonlinear plate theory and linear potential flow theory, the governing equation of the thin plate in narrow aero-thermal channel is obtained by employing the Hamilton’s principle and discretized into nonlinear ordinary differential equations by using the assumed mode method. The effects of the temperature variation, airflow velocity and slit height on the stability and nonlinear vibrations of the plate are considered. The stability of the thin plate in flow field is obtained by generalized eigenvalue method. For the nonlinear system, the nonlinear vibrations of the plate subjected to harmonic excitation are studied by using incremental harmonic balance method. From the results, with the temperature change, the airflow velocity, and the slit height decreasing, the stability of the plate becomes worse. The effects of the temperature change, airflow velocity and slit height on the nonlinear amplitude-frequency response of the first four generalized coordinates of the plate are discussed. It is found that with the temperature change, the airflow velocity, and the slit height decreasing, the resonance frequency of the plate decreases and resonance amplitude of the plate increases. In the simulation, some novel nonlinear dynamic behaviors of the plate in narrow aero-thermal channel are also observed such as the resonance trough and the resonance peak of the unstable solution.

在本研究中，研究了狭窄气热通道中薄板的稳定性和非线性振动。根据经典的非线性板理论和线性势流理论，利用哈密顿原理得到了狭窄气热通道中薄板的控制方程，并采用假设模态法将其离散化为非线性常微分方程。考虑了温度变化、气流速度和狭缝高度对板的稳定性和非线性振动的影响。采用广义特征值法求得薄板在流场中的稳定性。对于非线性系统，采用增量谐波平衡法研究谐波激励下板的非线性振动。结果表明，随着温度变化、气流速度和狭缝高度的减小，板材的稳定性变差。讨论了温度变化、气流速度和狭缝高度对板前四个广义坐标非线性幅频响应的影响。研究发现，随着温度的变化、气流速度和狭缝高度的减小，板的共振频率降低，板的共振幅度增大。在模拟中，还观察到板在狭窄气热通道中的一些新颖的非线性动力学行为，例如不稳定解的共振谷和共振峰。