【摘要】 根据作者由Hamilton变分原理导出的一个孔隙热弹性梁的非线性数学模型和气弹性原理中的一阶修正线性活塞理论,本文首先给出了位于高速或者超高速流动中两端固定的平面孔隙热弹性梁的控制微分方程和定解条件,其中基本未知量是梁的轴向和横向位移以及孔隙百分比和温度变化引起的"力矩".为了考察孔隙热弹性梁在横向载荷和气弹性载荷联合作用下的非线性力学特性,采用微分求积方法对问题进行空间离散,得到一组关于时间的非线性常微分方程,然后在给定初始条件下采用变步长Runge-Kutta方法对方程组进行数值求解,由此研究了孔隙热弹性梁的气弹性特性,考察了参数的影响,得到了一些有益的结论.更多还原

【Abstract】 In this study,based on the complete nonlinear mathematical model obtained from the generalized Hamilton principle of isotropic thermoelastic beams with voids and the aerodynamic pressure loading presented by the first order modified piston theory,the governing differential equations and the deterministic conditions of solutions for a ther- moelastic beam with fixed ends and located in a high-speed or an ultra-high speed flow are presented,which are ex- pressed by the axial and lateral displacements and the two "moments"defined by changes of the volume fraction of voids and the temperature field. In order to consider the nonlinear aeroelastic characteristic of the thermoelastic beam with voids subjected to the transverse loading and aerodynamic pressure loading,the differential quadrature method is applied to discretize the governing differential equations on the spatial domains,and a system of ordinary differential e- quations with respect to time is yielded and solved through the fourth-order Runge-Kutta method. From this,the aero- elastic characteristic of the beam is studied and the effect of parameters is considered as well.更多还原