旋转中心刚体-FGM梁刚柔热耦合动力学特性研究

对旋转中心刚体-功能梯度材料(functionally graded material,FGM)梁刚柔热耦合动力学特性进行研究.FGM梁为物理性能参数沿厚度方向呈幂律分布的欧拉伯努利梁.考虑柔性梁的横向弯曲变形和轴向拉伸变形, 并计入横向弯曲变形引起的纵向缩短,即非线性耦合变形量.考虑变截面空心梁在外部高温、内冷通道冷却情况下的热力耦合对系统动力学特性的影响,求解得到FGM梁沿厚度方向分布的温度场, 进而在本构关系中计入热应变.采用假设模态法对柔性梁变形场进行离散,运用第二类拉格朗日方程推导得到系统的刚柔热耦合动力学方程,并编制动力学仿真软件, 然后通过仿真算例对系统的动力学问题进行研究.结果表明:不同截面梁动力学响应差异较大, 因此需对实际系统合理建模;大范围运动已知时, 考虑热冲击载荷的FGM梁将有效抑制横向弯曲变形,而大范围运动恒定时随热冲击的叠加会出现高频振荡; 大范围运动未知时,外力矩和热冲击载荷相互作用产生热力耦合效应, 导致系统呈现高频振荡,同时与中心刚体大范围旋转运动产生刚柔热耦合效应. 

RESEARCH ON DYNAMICS OF A RIGID-FLEXIBLE-THERMAL COUPLING ROTATING HUB-FGM BEAM 1)

The rigid-flexible-thermal coupling dynamics of the hub-FGM beam system under large overall rotating motion is studied. The FGM beam is an Euler-Bernoulli beam, and its physical properties follow certain kinds of power law gradient distribution and vary in the thickness direction. The longitudinal deformation and the transverse deformation of the flexible beam are considered and the coupling term of the deformation which is caused by transverse deformation of the flexible beam is included in the expression of longitudinal deformation. Considering the influence of the thermal coupling of the tapered hollow beam which is under the condition of external high temperature and internal cooling passage cooling on the dynamic characteristics of the system, the temperature field distributed along the thickness direction of the FGM beam is obtained, and the thermal strain is included in the constitutive relationship of the beam. By using the assumed mode method to describe the deformation of the beam, the rigid-flexible-thermal coupling dynamic equations of the system are derived via employing Lagrange's equations of the second kind, as well as to compile the dynamics simulation software. Then the dynamics of the system are studied through simulation examples. The results show that the dynamic response of beams with different sections is quite different, so it is necessary to model the actual system reasonably. When the large overall rotating motion is known, the FGM beam considering the thermal shock load will effectively suppress the transverse bending deformation, and the high-frequency oscillation will occur with the superposition of the thermal shock when the large overall rotating motion is constant; When the large overall rotating motion is unknown, the external torque and the thermal shock load interact to produce a thermal coupling effect, which causes the system to exhibit high-frequency oscillation, at the same time , the rigid-flexible thermal coupling effect of the hub-FGM beam system is appeared.