摘要
为系统揭示热退化与阻尼效应对壁板颤振边界与响应的作用机制,构建含热退化与阻尼项的壁板气动弹性模型,并基于稳定性判据开展了关键参数的灵敏度分析。首先,基于Von Kármán板大变形理论、Kelvin阻尼模型及一阶活塞理论建立考虑热退化和阻尼效应的二维超声速壁板动力学方程,并通过Galerkin法进行空间离散。然后,基于李雅普诺夫间接法和Routh-Hurwitz准则,得到不同热退化程度下的稳定性区域图,并确定各区域内平衡点的数量及其稳定性。最后,使用四阶Runge-Kutta方法求解非线性常微分方程组,得到壁板非线性气动弹性响应,并通过时间历程图、相轨迹图和分岔图等非线性动力学描述工具进行分析。研究结果表明,热退化和材料阻尼的存在会显著缩小壁板的稳定区域范围且使得壁板厚度成为影响稳定性区域的因素之一。热退化系数的增大不仅会导致壁板振动幅值的增大,还会使得分岔点提前出现,并加速分岔演化过程。并且,热退化效应还会显著提高壁板响应类型的多样性和对系统参数的敏感性。此外,材料阻尼效应能够有效抑制壁板的类周期振动与混沌振动响应。
To systematically investigate the mechanisms of thermal degradation and damping effects on panel flutter boundaries and responses,an aeroelastic model incorporating thermal degradation and damping terms was developed,followed by a sensitivity analysis of key parameters based on stability criteria.Firstly,based on the von Kármán plate large deformation theory,the Kelvin damping model,and the first-order piston theory,a two-dimensional supersonic panel dynamic equation was established.This equation considered thermal degradation and damping effects.Spatial discretization was achieved using the Galerkin method.Next,the Lyapunov indirect method and the Routh-Hurwitz criterion were used to obtain stability region diagrams for various degrees of thermal degradation.This identified the number and stability of equilibrium points in each region.Finally,the nonlinear ordinary differential equations were solved using the fourth-order Runge-Kutta method to determine the panel’s nonlinear aeroelastic response.This response was analyzed using nonlinear dynamic tools,such as time history plots,phase trajectory diagrams,and bifurcation diagrams.The results indicate that both thermal degradation and material damping significantly reduce the stability region of the panel.Panel thickness also influences the stability region.An increase in the thermal degradation coefficient not only amplifies the panel’s vibration amplitude but also causes the bifurcation points to appear earlier,accelerating the bifurcation evolution process.Furthermore,thermal degradation significantly increases the diversity of panel response types and their sensitivity to system parameters.In addition,material damping effectively suppresses the panel’s quasi-periodic and chaotic vibrations responses.
作者
祁武超
张梓浩
李亚冬
田素梅
QI Wuchao;ZHANG Zihao;LI Yadong;TIAN Sumei(Key Laboratory of Liaoning Province for Aircraft Composite Structural Analysis and Simulation,Shenyang Aerospace University,Shenyang 110136,China)
出处
《沈阳航空航天大学学报》
2025年第6期20-27,共8页
Journal of Shenyang Aerospace University
基金
辽宁省教育厅基本科研面上项目(项目编号:JYTMS20230253,JYTMS20230224)
辽宁省科技厅联合计划面上项目(项目编号:2025-MSLH-565)。
关键词
热退化
材料阻尼
壁板
稳定性边界
气动弹性响应
颤振
thermal degradation
material damping
panel
stability boundary
aeroelastic response
flutter
