引用本文: 杜超凡, 郑燕龙, 周晓婷, 章定国. 作旋转运动功能梯度材料矩形Mindlin板的刚柔耦合动力学建模1)[J]. 力学与实践, 2021, 43(6): 849-860.
DU Chaofan, ZHENG Yanlong, ZHOU Xiaoting, ZHANG Dingguo. RIGID-FLEXIBLE COUPLING DYNAMIC MODELING OF A ROTATING FUNCTIONALLY GRADED MATERIAL RECTANGULAR MINDLIN PLATE$^{1)}$[J]. MECHANICS IN ENGINEERING, 2021, 43(6): 849-860.
 Citation: DU Chaofan, ZHENG Yanlong, ZHOU Xiaoting, ZHANG Dingguo. RIGID-FLEXIBLE COUPLING DYNAMIC MODELING OF A ROTATING FUNCTIONALLY GRADED MATERIAL RECTANGULAR MINDLIN PLATE$^{1)}$[J]. MECHANICS IN ENGINEERING, 2021, 43(6): 849-860.

## RIGID-FLEXIBLE COUPLING DYNAMIC MODELING OF A ROTATING FUNCTIONALLY GRADED MATERIAL RECTANGULAR MINDLIN PLATE^1)

• 摘要: 研究了作大范围运动功能梯度材料矩形板的刚柔耦合动力学问题。从连续介质力学理论出发,基于Mindlin板理论,采用无网格径向基点插值法(radial point interpolation method,RPIM)对矩形板变形场进行离散,考虑柔性板变形位移中二阶非线性耦合变形量,即横向弯曲引起的纵向缩短量,运用第二类拉格朗日方程推导了大范围运动功能梯度材料板的刚柔耦合动力学方程。分别采用一次近似耦合模型和传统零次近似耦合模型对不同转速下的功能梯度悬臂板进行了仿真,结果说明随着转速的提高,传统零次模型将发散,而一次近似模型依然收敛。将仿真结果与假设模态法和有限元法对比,验证了本文基于RPIM建立的动力学模型的正确性及在同等计算条件下的优越性。研究了功能梯度指数对作旋转运动的功能梯度矩形板动力学特性的影响。结果表明,随着功能梯度指数的增大,板的横向变形增大,且固有频率随之减小,说明功能梯度指数的增大会使系统柔性增加。同时,对中心刚体-功能梯度悬臂板的自由振动频率转向现象进行了讨论。

Abstract: The rigid-flexible coupling dynamics of a functionally graded material rectangular plate with large overall motion is studied. Starting from the theory of continuum mechanics and based on the Mindlin plate theory, the meshless radial point interpolation method (RPIM) is used to discretize the deformation field of the rectangular plate. Considering the second-order nonlinear coupling deformation which is the longitudinal shortening caused by the transverse bending, the Lagrange equation of the second kind is used to derive the rigid-flexible coupling dynamics equation of the functionally graded material plate with large overall motion. The first-order approximate coupling model and the traditional zero-order approximate coupling model were used to simulate FGM cantilever plates at different speeds. The results show that the traditional zero-order model diverges and the first-order approximation model converges as the speed increases. The simulation results are compared with the assumed modal method and the finite element method to verify the correctness of the method in this paper and its superiority under the same calculation conditions. The effect of functional gradient index on the dynamic characteristics of a rotating functionally graded rectangular plate is studied. The results show that the lateral deformation of the plate increases and the natural frequency decreases as the functional gradient index increases, indicating that the increasing of the functional gradient index will increase the flexibility of the system. At the same time, the frequency loci veering phenomenon of the hub-FGM cantilever plate is discussed.

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈