### Discretization Methods of a Rotating Flexible Rectangular Thin Plate

FAN Jihua1;2 (范纪华), ZHANG Dingguo3¤ (章定国), SHEN Hong2 (谌宏)

1. (1. School of Mechanical-Electronic and Power Engineering, Jiangsu University of Science and Technology, Zhangjiagang 215600, Jiangsu, China; 2. Suzhou Institute of Technology, Jiangsu University of Science and Technology, Zhangjiagang 215600, Jiangsu, China; 3. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China)
2. (1. School of Mechanical-Electronic and Power Engineering, Jiangsu University of Science and Technology, Zhangjiagang 215600, Jiangsu, China; 2. Suzhou Institute of Technology, Jiangsu University of Science and Technology, Zhangjiagang 215600, Jiangsu, China; 3. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China)
• Online:2020-01-15 Published:2020-01-12
• Contact: ZHANG Dingguo (章定国) E-mail: zhangdg419@mail.njust.edu.cn

Abstract: The rigid-flexible coupling dynamic modeling theory and the discretization methods of a rotating flexible rectangular thin plate are investigated in this paper. Based on the continuum mechanics, the rigid-flexible coupling dynamic model is established for the flexible rectangular thin plate undergoing large overall rotation, and the coupling term of the deformation which is caused by transverse deformation is considered. Assumed mode method (AMM), spline finite point method (SFPM) and Beizer ˉnite point method (BFPM) are used to describe the deformation of the flexible rectangular plate, and then the dynamic equations of a rotating flexible rectangular thin plate undergoing overall motion are derived by Lagrange's equation of the second kind. The dynamics of a cantilever plate undergoing large overall rotation is simulated via using different dynamic models, and the simulation results of the first order approximation model are compared with those of the traditional zero-order approximation model. It is shown that the first order approximation model with the dynamic stiffening terms can correctly describe the dynamic behavior of the system undergoing large overall rotation, while the zero-order approximation model cannot get the correct results. And AMM, SFPM, BFPM can well describe the deformation of a rotating flexible rectangular plate.

Key words: rectangular plate| assumed mode method (AMM)| spline finite point method (SFPM)| Beizer finite point method (BFPM)| natural frequencies

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