功能梯度二维壁板的非线性颤振特性分析

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (11) : 203-214.

振动理论与交叉研究

功能梯度二维壁板的非线性颤振特性分析

汪卫东,韩明君*,冯瑞龙

作者信息 +

Nonlinear flutter characteristics analysis of functionally graded two-dimensional panel

WANG Weidong, HAN Mingjun*, FENG Ruilong

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文章历史 +

摘要

基于Von Kármán非线性应变-位移关系和一阶活塞气动理论研究功能梯度壁板的非线性颤振特性分析。考虑不同梯度指数和孔隙率下功能梯度壁板，采用Galerkin法将功能梯度壁板的控制方程在整个气动弦长上进行积分变换得到非线性方程，再利用Routh-Hurwitz系统稳定性判据，将Hopf分岔化为非线性方程求根问题，求解出无量纲临界频率和无量纲临界流速。通过算例，分析了各参数变量对壁板气动弹性的稳定性影响，最后通过Runge-Kutta法对系统的气动弹性稳定性进行理论验证，其研究结果将为功能梯度壁板的设计优化提供理论依据。

Abstract

Nonlinear vibration characterization of functionally graded panels is investigated based on von Kármán nonlinear strain-displacement relationship and first-order piston aerodynamic theory. Considering the functionally graded panels under different gradient indices and porosities, the Galerkin method is used to obtain the nonlinear equations by integrally transforming the control equations of the functionally graded panels over the whole aerodynamic chord length, Then, the Routh-Hurwitz system stability criterion is used to transform the Hopf bifurcation into the root problem of the nonlinear equation, and the dimensionless critical frequency and dimensionless critical velocity are solved. Through the arithmetic example, the influence of each parameter variable on the aeroelastic stability of the panel is analyzed. Finally, the aeroelastic stability of the system is theoretically verified by the Runge-Kutta method. The research results will provide a theoretical basis for the design optimization of the functionally graded panels.

导出引用

汪卫东, 韩明君, 冯瑞龙. 功能梯度二维壁板的非线性颤振特性分析[J]. 振动与冲击, 2025, 44(11): 203-214

WANG Weidong, HAN Mingjun, FENG Ruilong. Nonlinear flutter characteristics analysis of functionally graded two-dimensional panel[J]. Journal of Vibration and Shock, 2025, 44(11): 203-214

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