Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell: an experimental and numerical study

doi:10.1007/s10483-024-3111-7

摘要/Abstract

Abstract:

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches. An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition, which is composed of an asymmetric region and a symmetric region. The symmetric region of the experimental specimen is entirely clamped, which is rigidly connected to an electromagnetic shaker, while the asymmetric region remains free of constraint. Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker, and the displacement responses of the shell are collected by the laser displacement sensors. The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell, and an off-axis three-dimensional dynamic snap-through domain is obtained. The numerical solutions are in good agreement with the experimental results. The nonlinear stiffness characteristics, dynamic snap-through domain, and chaos and bifurcation behaviors of the shell are quantitatively analyzed. Due to the asymmetry of the boundary condition and the shell, the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic, and the lower stable-state shows a linear stiffness characteristic of the shell.

Key words: bistable composite laminated cantilever shell, snap-through behavior, nonlinear vibration, nonlinear stiffness characteristic, chaos and bifurcation

中图分类号:

74H45

. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(5): 779-794.

Lele REN, Wei ZHANG, Ting DONG, Yufei ZHANG. Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell: an experimental and numerical study[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(5): 779-794.

图/表 19

参考文献 45

1	ZHANG,Z.,LI,Y.,YU,X. C.,LI,X. H.,WU,H. L.,WU,H. P.,JIANG,S. F., andCHAI,G. Z.Bistable morphing composite structures: a review.Thin-Walled Structures,142,74-97(2019)
2	EMAM,S. A., andINMAN,D. J.A review on bistable composite laminates for morphing and energy harvesting.Applied Mechanics Reviews,67(6),060803(2015)
3	NAKHLA,S., andELRUBY,A. Y.Applied finite element procedure for morphing wing design.Applied Composite Materials,28(4),1193-1220(2021)
4	DONG,T.,ZHANG,W., andDONG,M. M.The novel morphing airfoil based on the bistable composite laminated shell.Nonlinear Dynamics,111(19),17667-17685(2023)
5	NICASSIO,F.,SCARSELLI,G.,PINTO,F.,CIAMPA,F.,IERVOLINO,O., andMEO,M.Low energy actuation technique of bistable composites for aircraft morphing.Aerospace Science and Technology,75,35-46(2018)
6	BOWEN,C. R.,BETTS,D. N.,GIDDINGS,P. F.,SALO,A. I. T., andKIM,H. A.A study of bistable laminates of generic lay-up for adaptive structures.Strain,48(3),235-240(2012)
7	DAYNES,S., andWEAVER,P. M.Analysis of unsymmetric CFRP-metal hybrid laminates for use in adaptive structures.Composites Part A: Applied Science and Manufactures,41(11),1712-1718(2010)
8	DING,S. Y.,SUN,M.,LI,Y.,MA,W. L., andZHANG,Z.Novel deployable panel structure integrated with thick origami and morphing bistable composite structures.Materials,15(5),1942(2022)
9	LEI,Y. M., andYAO,X. F.Experimental study of bistable behaviors of deployable composite structure.Journal of Reinforced Plastics and Composites,29(6),865-873(2010)
10	HYER,M. W.Some observations on the cured shape of thin unsymmetric laminates.Journal of Composite Materials,15,175-194(1981)
11	HYER,M. W.The room-temperature shapes of four-layer unsymmetric cross-ply laminates.Journal of Composite Materials,16,318-340(1982)
12	BETTS,D. N.,SALO,A. I. T.,BOWEN,C. R., andKIM,H. A.Characterisation and modelling of the cured shapes of arbitrary layup bistable composite laminates.Composite Structures,92(7),1694-1700(2010)
13	NICASSIO,F.Shape prediction of bistable plates based on Timoshenko and Ashwell theories.Composite Structures,265,113645(2021)
14	ANILKUMAR,P. M.,RAO,B. N.,SCHEFFLER,S.,WOLNIAK,M.,ROLFES,R.,HALDAR,A., andJANSEN,E. L.Refined semi-analytical framework to predict the natural vibration characteristics of bistable laminates.AIAA Journal,61,062289(2023)
15	SABERI,S.,HOSSEINI,A. S.,YAZDANIFAR,F., andCASTRO,S. G. P.Developing equations for free vibration parameters of bistable composite plates using multi-objective genetic programming.Polymers,14(8),1559(2022)
16	SABERI,S.,GHAYOUR,M.,MIRDAMADI,H. R., andGHAMAMI,M.Free vibration analysis and mode management of bistable composite laminates using deep learning.Archive of Applied Mechanics,91(6),2795-2816(2021)
17	EMAM,S. A.Snapthrough and free vibration of bistable composite laminates using a simplified Rayleigh-Ritz model.Composite Structures,206,403-414(2018)
18	POTTER,K.,WEAVER,P.,SEMAN,A. A., andSHAH,S.Phenomena in the bifurcation of unsymmetric composite plates.Composites Part A: Applied Science and Manufacturing,38(1),100-106(2007)
19	EMAM,S. A.,PHERWANI,T.,ANIL,A., andMUHAMMED,A.Parametric study on the influence of material properties and geometry on the thermally induced bistability of composite laminates.Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science,236(8),4194-4218(2022)
20	CHILLARA,V. S. C., andDAPINO,M. J.Review of morphing laminated composites.Applied Mechanics Reviews,72(1),010801(2020)
21	ZHANG,Z.,ZHOU,Y. S.,SHEN,H. C.,SUN,M.,CHAI,H.,WU,H. P., andJIANG,S. F.Experimental study of orthogonal bistable laminated composite shell driven by magnetorheological elastomer.Composite Structures,271,114119(2021)
22	LIU,T. W.,BAI,J. B., andFANTUZZI,N.Analytical model for predicting folding stable state of bistable deployable composite boom.Chinese Journal of Aeronautics,(2023) doi: 10.1016/j.cja.2023.05.021
23	HABIBZADEH,N.,TIKANI,R.,ZIAEI-RAD,S., andTAKI,M. S.Static and dynamic analysis of a bistable plate under nonlinear magnetic force.Journal of Vibration and Control,28(7-8),745-757(2020)
24	HAO,Y. X.,BAI,C. P.,ZHANG,W.,LIU,L. T., andYANG,S. W.Intrawell and interwell oscillations for bi-stable cross-ply laminates actuated by MFC under oscillating impulse voltages.International Journal of Non-Linear Mechanics,143,104025(2022)
25	HAO,Y. X.,ZHOU,W. B.,ZHANG,W.,YANG,S. W., andCAO,Y. T.Dynamic snap-through of bi-stable laminates with simply supported at four corners under impact loads.Mechanics Based Design of Structures and Machines,52,1584-1603(2022)
26	LIU,Y. T.,ZHANG,J. Y.,PAN,D. K.,WU,Z. M., andWANG,Q. Y.Resonant actuation based on dynamic characteristics of bistable laminates.Machines,11(3),318(2023)
27	LAMACCHIA,E.,PIRRERA,A.,CHENCHIAH,I. V., andWEAVER,P. M.Morphing shell structures: a generalised modelling approach.Composite Structures,131,1017-1027(2015)
28	VIDOLI,S., andMAURINI,C.Tristability of thin orthotropic shells with uniform initial curvature.Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences,464(2099)
29	ANILKUMAR,P. M.,SCHEFFLER,S.,HALDAR,A.,BROD,M.,RAO,B.,JANSEN,E. L., andROLFES,R.Nonlinear dynamic modeling of bistable variable stiffness composite laminates.Journal of Sound and Vibration,545,117417(2023)
30	EMAM,S. A.,HOBECK,J., andINMAN,D. J.Experimental investigation into the nonlinear dynamics of a bistable laminate.Nonlinear Dynamics,95(4),3019-3039(2019)
31	DAYNES,S.,WEAVER,P. M., andPOTTER,D.Aeroelastic study of bistable composite airfoils.Journal of Aircraft,46(6),2169-2174(2009)
32	BRUNETTI,M.,VINCENTI,A., andVIDOLI,S.A class of morphing shell structures satisfying clamped boundary conditions.International Journal of Solids and Structures,82,47-55(2016)
33	CAO,Y. T.,DERAKHSHANI,M.,FANG,Y. H.,HUANG,G. L., andCAO,C. Y.Bistable structures for advanced functional systems.Advanced Functional Materials,31(45),2106231(2021)
34	LEMOS,D. M.,MARQUES,F. D., andFERREIRA,A. J. M.A review on bistable composite laminates for aerospace applications.Composite Structures,329,117756(2024)
35	REN,L. L.,ZHANG,W., andZHANG,Y. F.Dynamic snap-through and nonlinear vibrations of bistable asymmetric cross-ply composite laminated cantilever shell under external excitation.Mechanical Systems and Signal Processing,195,110193(2023)
36	MITURA,A.,BRUNETTI,M.,KLODA,L.,ROMEO,F., andWARMINSKI,J.Experimental nonlinear dynamic regimes for energy harvesting from cantilever bistable shells.Mechanical Systems and Signal Processing,206,110890(2024)
37	MUKHERJEE,A.,FRISWELL,M. I.,ALI,S. F., andAROCKIARAJAN,A.Modeling and design of a class of hybrid bistable symmetric laminates with cantilever boundary configuration.Composite Structures,239,112019(2020)
38	MUKHERJEE,A.,ALI,S. F., andAROCKIARAJAN,A.Hybrid bistable composite laminates for structural assemblies: a numerical and experimental study.Composite Structures,260,113467(2021)
39	BRUNETTI,M.,FAVATA,A., andVIDOLI,S.Enhanced models for the nonlinear bending of planar rods: localization phenomena and multistability.Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences,476(2242)
40	BRUNETTI,M.,MITURA,A.,ROMEO,F., andWARMINSKI,J.Nonlinear dynamics of bistable composite cantilever shells: an experimental and modelling study.Journal of Sound and Vibration,526,116779(2022)
41	LIU,X. H.,LI,M., andDAI,F. H.Wind-induced vibration behavior of bistable hybrid symmetric laminate.Composite Structures,301,116126(2022)
42	HIJAZI,S., andEMAM,S.An investigation into the static configurations and snapthrough response of clamped hybrid bistable symmetric laminates.Composite Structures,312,116880(2023)
43	STOJANOVIC,V.,DENG,J., andMILIC,D.Moment Lyapunov exponents and stochastic nonstability of a circular cylindrical shells.International Journal of Solids and Structures,270,112222(2023)
44	STOJANOVIC,V.,PETKOVIC,M. D., andDENG,J.Stability and vibrations of an overcritical speed moving multiple discrete oscillators along an infinite continuous structure.European Journal of Mechanics-A/Solids,75,367-380(2019)
45	STOJANOVIC,V.,KOZIC,P., andRISTIC,M.Vibrations and stability analysis of multiple rectangular plates coupled with elastic layers based on different plate theories.International Journal of Mechanical Sciences,92,233-244(2015)

[1]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(12): 2075-2092.
[2]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(11): 1987-2010.
[3]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(11): 1949-1964.
[4]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(11): 1895-1912.
[5]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(10): 1807-1820.
[6]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(10): 1749-1772.
[7]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(9): 1595-1612.
[8]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(9): 1539-1556.
[9]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(8): 1403-1414.
[10]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(8): 1295-1314.
[11]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(7): 1261-1278.
[12]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(7): 1155-1170.
[13]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(7): 1107-1118.
[14]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(6): 1033-1050.
[15]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(5): 763-778.