旋转输流功能梯度管道刚柔流耦合非线性动力学研究

????.The main aim of this project is to investigate nonlinear dynamics of rigid- flexible-liquid coupling for rotating pipes conveying fluid made of functionally graded materials. Firstly, the linear and nonlinear differential equation of motion or variational expression for the pipes conveying fluid are derived, which are subjected to thermal load and follower damping, pulsating variation of rotating angular velocity and flow speed, nonlinear elastic constraint at any location of the pipe, and considering a second-order coupling item of the pipe deformation which is caused by transverse and lateral bending deformation in the expression of longitudinal deformation. Secondly, the generalized wavelet-differential quadrature method, element-free Galerkin method, wavelet Galerkin method combined with PNF method (Poincaré-Newton-Floquet) and homotopy method are employed respectively in the numerical calculation. Finally, the modal characteristics and stability, parametrically excited vibration, amplitude-frequency characteristics curve in the parameter resonance，more complicated motion and bifurcate phenomenon resulted from coupling flutter instability and divergence instability，and the rigid-flexible- liquid coupling motion bifurcation，periodic, double-periodic, quasi-periodic and chaotic motion of the pipes conveying fluid and nonlinear dynamic behavior and so on are deeply analyzed, and the effect of gradient index of functionally graded materials, environmental temperature variation, rotating angular velocity, flow speed on dynamical characteristics of the pipes conveying fluid are systematically explored. We are sure that research achievements in this project will provide a solid theory basis for dynamic design and safety work of the fluid-conveying pipes with excellent performance, such as designability and high temperature resistant. Therefore, this project has very important theoretical significance and engineering application prospect.

本项目拟对旋转输流功能梯度管道的刚柔流耦合动力学问题，建立受热载荷和随从阻尼作用、旋转角速度和流速脉动变化、非线性弹性约束、以及在轴向位移中计及横向和侧向弯曲变形产生的二次耦合项时的线性和非线性运动微分方程或变分表达式，采用广义小波-微分求积法、无网格Galerkin法、小波-Galerkin法结合PNF法（Poincaré-Newton- Floquet）和同伦算法，分析系统的模态特性和稳定性，参数激励振动，参数共振时的幅频特性曲线，颤振失稳和发散失稳相互耦合而产生的多种复杂的运动和分叉现象，以及刚柔流耦合运动时的分岔，周期、倍周期、概周期运动, 甚至混沌运动等非线性动力学行为，探讨功能梯度材料的梯度指标、环境温度变化、旋转角速度及流速等参数对输流管道动力特性的影响。其研究将为具有可设计和耐高温等优良性能的输流管道的动态设计和安全使用提供理论依据，具有重要的理论意义和工程应用背景。

本项目的研究内容主要有五个方面：(1) 伸展/缩回竖直输流管道的动力学特性；(2)旋转FGM输流管道和旋转变截面输流管道的动态特性（功能梯度材料制成的环形截面梁的自由振动，功能梯度输流管道横向振动的辛方法，热环境中FGM输流管道振动问题的辛方法），旋转FGM等截面和旋转变截面输流管道的振动特性；(3) 旋转输流管道的横向振动主动控制（弹性地基上输流管道主参数共振的主动振动控制，旋转输流管道的横向振动控制，面内平动功能梯度斜板的主动振动控制）；(4) 旋转FGM圆环形截面柔性梁、旋转变截面悬臂梁的动态特性和旋转Timoshenko变截面（双线性变化）悬臂梁的双横向弯曲非线性动力学特性；(5) 轴向运动功能梯度系统和旋转圆板的横向振动（运动功能梯度斜板的横向振动，旋转圆板的横向自由振动，随从力作用下矩形薄板的稳定性，形状记忆合金杆的拉-弯非线性变形分析，轴向运动功能梯度Timoshenko梁的稳定性，连铸板坯的粘弹性鼓肚变形的辛几何法分析，计及不同剪切变形的功能梯度材料梁的弯曲分析）。在上述研究范围内，得到了旋转FGM输流管道失稳临界转速、复频率实部和虚部分别随梯度指标和轮毂转速的变化规律以及自由端挠度响应等，其对旋转输流管道系统的工程设计有一定的参考价值。.本项目取得的主要成果有：标注NSFC的论文12篇，其中SCI收录论文5篇（中科院JCR期刊SCI一区1篇，二区2篇，四区2篇），EI收录论文10篇，均为期刊论文；未标注论文4篇，其中SCI收录论文2篇（JCR期刊SCI二区1篇，四区1篇），EI收录论文4篇，均为期刊论文；获2014年度陕西高等学校科学技术二等奖1项；在人才培养方面，项目负责人共指导与本项目研究内容相关的硕士研究生9人，均获硕士学位；指导博士研究生1人，已于2016年12月通过博士学位论文预答辩。