热过屈曲功能梯度壁板的气动弹性颤振

功能梯度材料的宏观物理性能随空间位置连续变化,能充分减少不同组份材料结合部位界面性能的不匹配因素.功能梯度壁板用作高速飞行器的热防护结构,能有效消除气动加热带来的壁板内部热应力集中.本文考虑热过屈曲变形引入的结构几何非线性,分析功能梯度壁板的气动弹性颤振边界.基于幂函数材料分布假设,采用混合定律计算功能梯度材料的等效力学性能.根据一阶剪切变形板理论、冯·卡门应变-位移关系和一阶活塞理论,基于虚功原理建立超声速气流中受热功能梯度壁板的非线性气动弹性有限元方程.采用牛顿-拉弗森迭代法数值求解壁板的热屈曲变形,分析超声速气流对热屈曲变形的影响机理.在壁板热过屈曲的静力平衡位置分析动态稳定性,确定了壁板的颤振边界.研究表明,当陶瓷-金属功能梯度壁板的组份材料沿厚度方向梯度分布时,会破坏结构的对称性导致壁板在面内热应力作用下发生指向金属侧的热屈曲变形.超声速气流中壁板热屈曲变形最大的位置随气流速压增大向下游推移,并伴随屈曲变形量的减小.热过屈曲壁板的几何非线性效应会提高壁板的颤振边界,这种影响在高温、低无量纲速压且壁板发生大挠度热屈曲变形时表现显著.较高无量纲气流速压下由于壁板的热屈曲变形被气动力限定在小挠度范围,几何非线性效应不明显.

AEROELASTIC FLUTTER OF POST-BUCKLED FUNCTIONALLY GRADED PANELS

Functionally graded materials (FGMs) with continuously varied composition effectively reduce the mismatch at bonding surface between different constituents. As thermal protection structures, functionally graded panels (FGPs) eliminate the internal thermal stress concentration which arises from aerodynamic heating. The aeroelastic flutter bound-ary of an FGP is analyzed considering the structural geometric nonlinearity due to thermal post-buckling deflection. The effective FGM properties are calculated using the rule of mixture homogenization with the power law distribution assump-tion. The first-order shear deformable plate theory, von Karman strain-displacement relations and the first-order piston theory are adopted to formulate the nonlinear aeroelastic finite element equations of FGPs in supersonic flow according to the principle of virtual work. The numerical simulation results of thermal post-buckling response are obtained using the Newton-Raphson iterative method, and the mechanism of post-buckling deflection affected by the airflow is discussed. The panel flutter boundary is determined by analyzing the stability of post-buckling equilibriums. It is concluded that the symmetry of a ceramic-metal FGP is destroyed by through-the-thickness material distribution, and the panel tends to buckle to the metal side under in-plane thermal stresses. The position of maximum post-buckling deflection moves to the down-stream in the supersonic airflow, and the post-buckling deflection decreases with the increase of flow dy-namic pressure. The geometric nonlinearity increases the flutter critical dynamic pressure of post-buckled FGPs when the large post-buckling deflection is occurred at relative high temperature and low non-dimensional dynamic pressure flow. However, the geometric nonlinearity is not so important at high non-dimensional dynamic pressure flow because the post-buckling deflection is restrained to a small one by the supersonic airflow.