摘要
本文基于经典梁理论(CBT),研究了在高超音速作用下,活塞气动力理论的非线性效应对纤维增强功能梯度材料(FGM)的颤振特性的影响。首先通过混合率模型来表征纤维增强FGM梁的材料属性,然后通过Hamilton原理推导出只考虑横向振动的纤维增强FGM梁的非线性气动弹性偏微分方程,利用Galerkin方法,把该方程转化为非线性常微分方程,再利用Hurwitz行列式,把该方程的求根问题用以判定Hopf分叉,得到不同温度应力下梁的无量纲临界流速和无量纲临界频率。最后通过Runge-Kutta法得到纤维体积分数和无量纲温升对无量纲临界动压的影响。
Based on the classical beam theory (CBT), the influence of the nonlinear effects of piston aerodynamic theory on the flutter characteristics of fiber-reinforced functionally graded materials (FGM) at hypersonic speeds is studied in this paper. First, the material properties of fiber-reinforced FGM beams are characterized by the mixing rate model. Then, the nonlinear aeroelastic partial differen-tial equation of fiber-reinforced FGM beams that only consider the transverse vibration is derived from Hamilton’s principle. The Galerkin method is used to convert the equation into a nonlinear ordinary differential equation, and the Hurwitz determinant is used to determine the Hopf bifurcation, the dimensionless critical velocity and the dimensionless critical frequency of the beam under different temperature stresses are obtained. Finally, fiber volume fraction and dimensionless tem-perature rise on dimensionless critical dynamic pressure are obtained by the Runge-Kutta method.
出处
《力学研究》
2023年第2期79-90,共12页
International Journal of Mechanics Research
