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.
FAN Jihua (范纪华), ZHANG Dingguo (章定国), SHEN Hong (谌宏)
. Discretization Methods of a Rotating Flexible Rectangular Thin Plate[J]. Journal of Shanghai Jiaotong University(Science), 2020
, 25(1)
: 118
-126
.
DOI: 10.1007/s12204-019-2129-8
[1] KANE T R, RYAN R, BANERJEE A K. Dynamics of a cantilever beam attached to a moving base [J].Journal of Guidance, Control, and Dynamics, 1987,10(2): 139-151.
[2] BANERJEE A K, KANE T R. Dynamics of a plate in large overall motion [J]. Journal of Applied Mechanics,1989, 56(4): 887-892.
[3] JIANG L Z, HONG J Z. Dynamics of thin elastic plates in large overall motions considering geometric non-linearity and coupling deformation [J]. Acta Mechanica Sinica, 1999, 31(2): 243-249 (in Chinese).
[4] ZHANG D J, HUSTON R L. On dynamic stiffening of flexible bodies having high angular velocity [J]. Mechanics of Structures and Machines, 1996, 24(3): 313-329.
[5] YOO H H, CHUNG J. Dynamics of rectangular plates undergoing prescribed overall motion [J]. Journal of Sound and Vibration, 2001, 239(1): 123-137.
[6] LI L, ZHANG D G. Free vibration analysis of rotating functionally graded rectangular plates [J]. Composite Structures, 2016, 136: 493-504.
[7] LIU Y W, WANG J M, ZHANG D J, et al. Dynamic analysis of rectangular plates undergoing large overall motion [J]. Journal of Vibration and Shock, 1998,17(1): 38-43 (in Chinese).
[8] ZHAO F Y, HONG J Z, LIU J Y, et al. Dynamic modeling and modal truncation approach for a high-speed rotating thin elastic rectangular plate [J]. Journal of Vibration Engineering, 2006, 19(3): 416-421 (in Chinese).
[9] LIU J Y, PAN K Q. Rigid-flexible-thermal coupling dynamic formulation for satellite and plate multibody system [J]. Aerospace Science and Technology, 2016,52: 102-114.
[10] LIU J Y, HONG J Z. Dynamic modeling theory and finite element method for a rectangular plate undergoing large overall motion [J]. Journal of Vibration Engineering, 2003, 16(2): 175-179 (in Chinese).
[11] QIN R. Spline finite point method for analysis of laminated composite plates and shells [J]. Engineering Mechanics, 2001, 18(1): 14-23 (in Chinese).
[12] LI S B, HUANG L X, JIANG L J, et al. A bidirectional B-spline ˉnite point method for the analysis of piezoelectric laminated composite plates and its application in material parameter identiˉcation [J]. Composite Structures, 2014, 107: 346-362.
