变温度场中刚柔耦合功能梯度梁系统的动力学特性研究

摘要

Based on the high order approximate rigid-flexible coupling and thermodynamic theories,dynamics of the rotating hub-FGM-beam system in the variable temperature field environment is studied.The FGM beam is made of ceramic and metal materials and its typical material properties (i.e.Young's modulus or density or thermal conductivity or thermal expansion coefficient,etc) are assumed to follow certain kinds of power law gradient distribution and vary in the thickness direction.Two different gradient distributions are designed and a lumped mass at any position of the FGM beam is considered.The nonlinear coupling deformation variable,also called the longitudinal shrinking caused by transversal deformation,is included in the dynamic modeling process.The temperature fields along the thickness direction of the FGM beam are solved by considering the influence of the temperature gradients.Meanwhile,the thermal strain is included in the constitutive relationship of the beam.By using the method of assumed modes to describe the deformation of the FGM beam,the rigid-flexible coupling dynamical equations of the system are derived via Lagrange's equations of the second kind.Numerical simulation results show that the design of the lumped mass position and material distributions have great influence on the dynamic characteristics of the system.The thermal load impact resistance of FGM beams following the second gradient distribution considered in this article is superior to those following the first one.%基于刚柔耦合动力学和热力学建模理论,研究变温度场环境下的旋转柔性功能梯度梁系统的动力学问题.功能梯度梁由陶瓷和金属两种材料组成,假设梁的典型物性参数为梁厚度方向坐标的幂函数.设计两种材料梯度分布规律,考虑功能梯度梁上任意位置附着集中质量,在梁纵向位移中计及由于横向变形而引起的纵向缩短项,即非线性耦合变形量.考虑温度梯度变化对系统动力学特性的影响,求解得到功能梯度梁沿厚度方向分布的温度场,在功能梯度梁本构关系式中计及热应变.采用假设模态法描述变形,运用第二类Lagrange方程推导得到系统的刚柔耦合动力学方程.仿真结果表明,集中质量位置和材料梯度分布规律的选取都将对系统动力学特性产生重大影响,第二种梯度分布规律下的功能梯度梁抗热载荷冲击性能优于第一种梯度分布规律下的功能梯度梁.