Dynamic modeling of a three-dimensional braided compositethin plate considering braiding directions

doi:10.1007/s10483-025-3205-8

摘要/Abstract

Abstract:

Currently, there are a limited number of dynamic models available for braided composite plates with large overall motions, despite the incorporation of three-dimensional (3D) braided composites into rotating blade components. In this paper, a dynamic model of 3D 4-directional braided composite thin plates considering braiding directions is established. Based on Kirchhoff's plate assumptions, the displacement variables of the plate are expressed. By incorporating the braiding directions into the constitutive equation of the braided composites, the dynamic model of the plate considering braiding directions is obtained. The effects of the speeds, braiding directions, and braided angles on the responses of the plate with fixed-axis rotation and translational motion, respectively, are investigated. This paper presents a dynamic theory for calculating the deformation of 3D braided composite structures undergoing both translational and rotational motions. It also provides a simulation method for investigating the dynamic behavior of non-isotropic material plates in various applications.

Key words: three-dimensional (3D) braided composite, braiding direction, composite thin plate, large overall motion, dynamic model

中图分类号:

O313.7

. [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(1): 123-138.

Chentong GAO, Huiyu SUN, Jianping GU, W. M. HUANG. Dynamic modeling of a three-dimensional braided compositethin plate considering braiding directions[J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(1): 123-138.

图/表 17

Property	Matrix	Carbon fiber
$E 11$ /GPa	2.74	231
$E 22$ /GPa	–	15
$G 12$ /GPa	–	24
$G 23$ /GPa	–	5.03
$μ 12$	0.35	0.28

Method	$E x$ /GPa	$E y$ /GPa	$G x y$ /GPa	$G y z$ /GPa	$μ x y$	$μ y z$
Homogenization method	84.21	9.11	13.55	3.98	0.29	0.47
Fabric geometry model^[34]	98.50	12.12	16.46	4.23	0.34	0.48

Braided angle/(°)	$E x$ /GPa	$E y$ /GPa	$G x y$ /GPa	$G y z$ /GPa	$μ x y$	$μ y z$
12	102.041	8.871	16.472	4.756	0.264	0.548
20	98.039	11.881	17.042	5.066	0.294	0.391
30	71.945	16.647	19.723	7.346	0.401	0.360
40	37.886	20.124	21.053	13.555	0.422	0.251

Braided angle/(°)	$E x$ /GPa	$E y$ /GPa	$G x y$ /GPa	$G y z$ /GPa	$μ x y$	$μ y z$
12	80.002	9.893	12.672	3.545	0.326	0.408
20	71.947	10.406	12.932	3.991	0.280	0.330
30	61.733	13.818	13.554	4.675	0.264	0.260
40	43.676	20.162	21.651	6.257	0.213	0.181

参考文献 36

[1]	SUN, H. Y. and QIAO, X. Prediction of the mechanical properties of three-dimensionally braided composites. Composites Science and Technology, 57(6), 623–629 (1997)
[2]	MÜLLER, P. C. Kurt Magnus: a pioneer of multibody system dynamics. Multibody System Dynamics, 30, 199–207 (2013)
[3]	WINFREY, R. C. Dynamic analysis of elastic link mechanisms by reduction of coordinates. Journal of Engineering for Industry, 94(2), 577–581 (1972)
[4]	WINFREY, R. C. Elastic link mechanism dynamics. Journal of Engineering for Industry, 93(1), 268–272 (1971)
[5]	ERDMAN, A. G., SANDOR, G. N., and OAKBERG, R. G. A general method for kineto-elastodynamic analysis and synthesis of mechanisms. Journal of Engineering for Industry, 94(4), 1193–1205 (1972)
[6]	LIKINS, P. W. Finite element appendage equations for hybrid coordinate dynamic analysis. International Journal of Solids and Structures, 8(5), 709–731 (1972)
[7]	MEIROVITCH, L. Hybrid state equations of motion for flexible bodies in terms of quasi-coordinates. Journal of Guidance, Control, and Dynamics, 14(5), 1374–1383 (1990)
[8]	KANE, T. R., RYAN, R., and BANERJEE, A. K. Dynamics of a cantilever beam attached to a moving base. Journal of Guidance, Control, and Dynamics, 10(2), 139–151 (1987)
[9]	BANERJEE, A. K. and KANE, T. R. Dynamics of a plate in large overall motion. Journal of Applied Mechanics, 56(4), 887–892 (1989)
[10]	ZHANG, D. J. and HUSTON, R. L. On dynamic stiffening of flexible bodies having high angular velocity. Mechanics of Structures and Machines, 24(3), 313–329 (1996)
[11]	SHABANA, A. A., HUSSIEN, H. A., and ESCALONA, J. L. Application of the absolute nodal coordinate formulation to large rotation and large deformation problems. ASME Journal of Mechanical Design, 120(2), 188–195 (1998)
[12]	LIU, J. Y. and HONG, J. Z. Dynamic modeling and modal truncation approach for a high-speed rotating elastic beam. Archive of Applied Mechanics, 8(72), 554–563 (2002)
[13]	CHEN, Y. Z., ZHANG, D. G., and LI, L. Dynamic analysis of rotating curved beams by using absolute nodal coordinate formulation based on radial point interpolation method. Journal of Sound and Vibration, 441, 63–83 (2019)
[14]	CHEN, Y. Z., ZHANG, D. G., and LI, L. Dynamics analysis of a rotating plate with a setting angle by using the absolute nodal coordinate formulation. European Journal of Mechanics/A Solids, 74, 257–271 (2019)
[15]	LI, L., ZHU, W. D., ZHANG, D. G., and DU, C. F. A new dynamic model of a planar rotating hub-beam system based on a description using the slope angle and stretch strain of the beam. Journal of Sound and Vibration, 345, 214–232 (2015)
[16]	GUO, Y. B., LI, L., and ZHANG, D. G. Dynamic modeling and vibration analysis of rotating beams with active constrained layer damping treatment in temperature field. Composite Structures, 226, 111217 (2019)
[17]	GAO, C. T., KHATIBI, A. A., GU, J. P., XIE, Z. M., and SUN, H. Y. Dynamic modeling of a 3-D 4-directional braided composite beam with a central rigid body. Mechanics of Advanced Materials and Structures, 30(15), 3215–3224 (2022)
[18]	PIOVAN, M. T. and SAMPAIO, R. A study on the dynamics of rotating beams with functionally graded properties. Journal of Sound and Vibration, 327(1-2), 134–143 (2009)
[19]	YUAN, J., PAO, Y. H., and CHEN, W. Exact solutions for free vibrations of axially inhomogeneous Timoshenko beams with variable cross section. Acta Mechanica, 227(9), 2625–2643 (2016)
[20]	ZARRINZADEH, H., ATTARNEJAD, R., and SHAHBA, A. Free vibration of rotating axially functionally graded tapered beams. Proceedings of the Institution of Mechanical Engineers Part G: Journal of Aerospace Engineering, 226(G4), 363–379 (2012)
[21]	YANG, J. M., MA, C. L., and CHOU, T. W. Fibre inclination model of three-dimensional textile structural composites. Journal of Composite Materials, 20(5), 472–484 (1986)
[22]	KALIDINDI, S. R. and FRANCO, E. Numerical evaluation of isostrain and weighted-average models for elastic moduli of three-dimensional composites. Composites Science and Technology, 57(3), 293–305 (1997)
[23]	WU, D. L. Three-cell model and 5D braided structural composites. Composites Science and Technology, 56(3), 225–233 (1996)
[24]	CHEN, L., TAO, X. M., and CHOY, C. L. On the microstructure of three-dimensional braided preforms. Composites Science and Technology, 59(3), 391–404 (1999)
[25]	FENG, M. L., WU, C. C., and SUN, H. Y. Three-dimensional homogenization method in constitutive simulation of braided composite materials. Materials Science and Engineering, 19(3), 34–37 (2001)
[26]	ZHANG, D., SUN, Y., WANG, X., and CHEN, L. Prediction of macro-mechanical properties of 3D braided composites based on fiber embedded matrix method. Composite Structures, 134(12), 393–408 (2015)
[27]	XU, K. and QIAN, X. M. An FEM analysis with consideration of random void defects for predicting the mechanical properties of 3D braided composites. Advances in Materials Science and Engineering, 2014(1), 439819 (2014)
[28]	DONG, J. and HUO, N. A. Two-scale method for predicting the mechanical properties of 3D braided composites with internal defects. Composite Structures, 152(9), 1–10 (2016)
[29]	TOLOSANA, N., CARRERA, M., DE VILLORIA, R. G., CASTEJON, L., and MIRAVETE, A. Numerical analysis of three-dimensional braided composite by means of geometrical modeling based on machine emulation. Mechanics of Advanced Materials and Structures, 19(1-3), 207–215 (2012)
[30]	QAMHIA, I. I., SHAMS, S. S., and EL-HAJJAR, R. F. Quasi-isotropic triaxially braided cellulose-reinforced composites. Mechanics of Advanced Materials and Structures, 22(12), 988–995 (2015)
[31]	DONG, J. W. and HUO, N. F. Progressive tensile damage simulation and strength analysis of three-dimensional braided composites based on three unit-cells models. Journal of Composite Materials, 52(15), 2017–2031 (2018)
[32]	GU, Q. J., QUAN, Z. Z., YU, J. Y., YAN, J. H., SUN, B. Z., and XU, G. B. Structural modeling and mechanical characterizing of three-dimensional four-step braided composites: a review. Composite Structures, 207, 119–128 (2019)
[33]	DONG, J. W. and FENG, M. L. Asymptotic expansion homogenization for simulating progressive damage of 3D braided composites. Composite Structures, 92(4), 873–882 (2010)
[34]	LIANG, S. Q., ZHOU, Q. H., CHEN, G., and FRANK, K. Open hole tension and compression behavior of 3D braided composites. Polymer Composites, 41(6), 2455–2465 (2020)
[35]	YOO, H. H. and PIERRE, C. Modal characteristic of a rotating rectangular cantilever plate. Journal of Sound and Vibration, 259(1), 81–96 (2003)
[36]	WANG, L. J., LI, L., ZHANG, D. G., and QIAN, Z. Z. Rigid-flexible coupling dynamic characteristics of a FGM thin plate undergoing large overall motions in thermal environment (in Chinese). Journal of Vibration and Shock, 38(18), 79–88 (2019)