功能梯度圆柱曲板在超音速流中的非线性动力学分析

Nonlinear dynamics of FGM cylindrical panel in supersonic flow

研究了在外部激励作用下,功能梯度圆柱面曲板在超音速流中的非线性动力学行为。假设材料属性与温度有关,功能梯度曲板的组分材料沿厚度方向呈梯度变化,并按照体积分数的幂律分布,运用一阶活塞理论得到了超音速空气动力载荷;以von-Karman型的非线性应变位移几何关系为基础,通过Hamilton原理推出了曲板的非线性运动控制方程;运用伽辽金法离散化控制方程,得到一个包含二次非线性项和三次非线性项的二自由度非线性系统;利用数值计算,分析了面外内载荷对系统非线性动力学的影响。

An analysis on the nonlinear dynamics of a FGM cylindrical panel in hypersonic flow subjected to an external excitation and uniform temperature change is presented in this paper. Material properties of the constituents are assumed to be temperature-dependent and the effective properties of FGM panel are graded in thickness direction according to a simple power law function in terms of the volume fractions. Based on von Karman type nonlinear strain-displacement relationship, the nonlinear governing equations of motion are derived by using Hamilton＇ s principle. Galerkin＇ s method is then utilized to discretize the governing partial equations to a two- degree- of-freedom nonlinear system including the quadratic and cubic nonlinear terms. A first- order piston theory is applied for the supersonic aerodynamic load. Numerical results are presented for FGM plate to show the influences of external load parameter on the nonlinear dynamics.