Modeling and nonlinear vibration response of antisymmetric cross-ply bistable shallow shell in humid and hot environment

PDF(1959 KB)

Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (19) : 80-89.

ZHANG Boyu, ZHANG Wei

Author information +

History +

Abstract

Firstly, the nonlinear dynamic modeling of antisymmetric cross-ply bistable shallow shell in hot and humid environment is carried out. Based on the classical shell theory and considering the effects of temperature and humidity, the thermal expansion coefficient and wet expansion coefficient are added to the constitutive equation. Secondly, the compatible equation and the dynamic equilibrium equation are combined to establish a nonlinear dynamic model for the antisymmetric cross-ply laminated bistable shell. Finally, Galerkin discretization is conducted on the vibration partial differential equation to obtain the three-degree-of-freedom nonlinear ordinary differential equation. The averaged equation under the polar coordinate system and the averaged equation under the rectangular coordinate system is used to study the non-linear dynamics in the antisymmetric bistable shallow shell. The influence law of the external excitation parameters on the system is explored and the system’s non-linear dynamic behavior characteristics are explored when the main resonance is close to and the internal resonance is 1: 2: 2.
Keywords: Antisymmetric cross-ply; Bistable shell; Galerkin discretization; Nonlinear dynamics

Key words

Antisymmetric cross-ply / Bistable shell / Galerkin discretization / Nonlinear dynamics

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

ZHANG Boyu, ZHANG Wei. Modeling and nonlinear vibration response of antisymmetric cross-ply bistable shallow shell in humid and hot environment[J]. Journal of Vibration and Shock, 2022, 41(19): 80-89

References

[1] M. W. Hyer, Some observations on the cured shape of thin unsymmetric laminates, Journal of composite materials 15, p175-194, 1981.
[2] A. Daton-Lovett, An extendible member, Patent cooperation treaty application, PCT/GB97/00839, 1996.
[3] 沈观林, 胡更开. 复合材料力学 [M]. 北京: 清华大学出版社, 2006.
[4] 刘伟, 刘新东. 复合材料力学基础 [M]. 西安: 西北工业大学出版社, 2010.
[5] Harras B, Benamar R. Geometrically non-linear free vibration of fully clamped composite laminated rectangular composite plates [J]. Journal of Sound and Vibration, 2002, 251: 579-619.
[6] 段纪成. 层合板弯曲与振动的近似计算 [J]. 武汉理工大学学报, 2002, 12: 58-60.
DUAN Jicheng.Approximate analysis for bending and vibration of laminates[J].Journal of Wuhan University of Technology, 2002, 12: 58-60.
[7] 胡浩, 傅衣铭. 粘弹性正交各向异性对称层合板的非线性动力响应 [J]. 湖南大学学报(自然科学版), 2003(5): 79-83.
HU Hao,FU Yiming.Nonlinear dynamic responses of viscoelastic orthotropy symmetric laminated plates[J].Journal of Hunan University(Natural Sciences) , 2003(5): 79-83.
[8] Leung Y T, Leung Y T, Niu J, et al. A new unconstrained third-order plate theory for navier solutions of symmetrically laminated plates [J]. Computers and Structures, 2003, 81: 2539-2548.
[9] Ye M, Lu J, Ding Q, et al. Nonlinear dynamics of a parametrically excited rectangular symmetric cross-ply laminated composite plate [J]. Acta Mechanica Sinica, 2004, 37: 64-71.
[10] Guo X Y, Zhang W, Yao M W. Mulit-pulse orbits and chaotic motion of composite laminated plates [A]. International Mechanical Engineering Conferences and Exposition [C]. 2008.
[11] Zhang J H, Zhang W, Yao M H, et al. Multi-pulse shilnikov chaotic dynamics for a non-autonomous buckled thin plate under parametric excitation [J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2008, 9: 381-394.
[12] Zhang W, Guo X Y. Periodic and chaotic oscillations of composite laminated thin plate with third-order shear deformation [A]. International Design Engineering Technical Conferences [C]. 2009.
[13] Zhang W, Guo X Y, Lai S K. Research on periodic and chaotic oscillations of composite laminated plates with one-to-one internal resonance [J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2009, 10: 1567-1583.
[14] 郭翔鹰, 张伟. 复合材料层合板的混沌运动 [J]. 振动与冲击, 2009, 28(6): 139-144.
GUO Xiangying,ZHANG Wei.Nonlinear dynamics and chaotic oscillations of composite laminated thin plate[J].Journal of Vibration and Shock, 2009, 28(6): 139-144.
[15] Zhang W, Guo X Y, Wang Q, et al. A new kind of energy transfer from the high-frequency to low-frequency mode in a composite laminated plate [A]. International Design Engineering Technical Conferences & Computers and Information in Engineering Conference [C]. 2010.
[16] Zhang W, Guo X Y, Wang Q, et al. Nonlinear oscillation of an angle-ply composite laminated thin plate with 1:2 resonance [A]. The 8th International Conference on Computing, Communications and Control Technologies [C]. 2010.
[17] Swaminathan K, Ragounadin D. Analytical solutions using a higher order refined theory for the static analysis of antisymmetric angle-ply composite and sandwich plates [J]. Composite Structure, 2004, 64: 405-417.
[18] Huang X L, Shen H S, Zheng J J. Nonlinear vibration and dynamic response of shear deformable laminated plates in hygrothermal environments [J]. Composites Science and Technology, 2004, 64: 1419-1435.
[19] Nath Y, Prithviraju M, Mufti A A. Nonlinear statics and dynamics of antisymmetric composite laminated square plates supported on nonlinear elastic subgrade [J]. Communications in Nonlinear Science and Numerical Simulation, 2006, 11: 340-354.
[20] Soula M, Nasri R, Ghazel A, et al. The effects of kinematic model approximations on natural frequencies and modal damping of laminated composite plates [J]. Journal of Sound and Vibration, 2006, 297: 315-328.
[21] Aagah M R, Mahinfalah M, Jazar G N. Natural frequencies of laminated composite plates using third order shear deformation theory [J]. Composite Structures, 2006, 72: 273-279.
[22] Swaminathan K, Patil S S, Nataraja M S, et al. Bending of sandwich plates with antisymmetric angle-ply face sheets-analytical evaluation of higher order refined computational models [J]. Composite Structure, 2006, 75: 114-120.
[23] Swaminathan K, Patil S S. Higher order refined computational model with 12 degrees of freedom for the stress analysis of antisymmetric angle ply plates- analytical solutions [J]. Composite Structure, 2007, 4: 595-608.
[24] Swaminathan K, Patil S S. Analytical solutions using a higher order refined computational model with 12 degrees of freedom for the free vibration analysis of antisymmetric angle-ply plates [J]. Composite Structure, 2008, 82: 209-216.
[25] Matsunaga H. Thermal buckling of angle-ply laminated composite and sandwich plates according to a global higher-order deformation theory [J]. Composite Structure, 2006, 72: 177-192.
[26] Matsunaga H. Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading [J]. Composite Structure, 2007, 77: 249-262.
[27] Weaver P. Seman A. Potter K. Phenomena in the bifurcation of unsymmetric composite plates [J]. Composites, Part A, 2007, 38: 100-106.
[28] Guo X Y, Zhang W, Yao M H. Nonlinear dynamics of angle-ply composite laminated thin plate with third-order shear deformation [J]. Science in China Series E, Technological Sciences, 2010, 53: 612-622.
[29] Zhang W, Guo X Y, Wang Q, et al. Nonlinear responses of an angle-ply composite laminated plate with two different internal resonances [A]. The Canadian Society for Mechanical Engineering Forum [C]. 2010.
[30] Honda S, Narita Y. Vibration design of laminated fibrous composite plates with local anisotropy induced by short fibers and curvilinear fibers [J]. Composite Structures, 2011, 93: 902-910.