Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

doi:10.1007/s10483-024-3105-6

摘要/Abstract

Abstract:

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors. The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified. The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated, and the four-dimensional (4D) nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method. The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed. The discussion focuses on investigating the effects of key parameters, e.g., excitation amplitude, damping coefficient, and detuning parameters, on the resonance responses. The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system. Furthermore, the significant motions under particular excitation conditions are visualized by bifurcation diagrams, time histories, phase portraits, three-dimensional (3D) phase portraits, and Poincare maps. Finally, the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell, yielding results that are qualitatively consistent with the theoretical results.

Key words: bistable laminated composite shell, dynamic snap-through mode, Hopf bifurcation, chaotic dynamics, vibration experiment

中图分类号:

74F10
74J20

. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(4): 581-602.

Meiqi WU, Peng LV, Hongyuan LI, Jiale YAN, Huiling DUAN, Wei ZHANG. Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(4): 581-602.

图/表 17

参考文献 48

1	HYER, M. W. Some observations on the cured shape of thin unsymmetric laminates. Journal of Composite Materials, 15 (2), 175- 194 (1981)
2	HYER, M. W. The room-temperature shapes of four-layer unsymmetric cross-ply laminates. Journal of Composite Materials, 16 (4), 318- 340 (1982)
3	JUN, W. J., and HONG, C. S. Effect of residual shear strain on the cured shape of unsymmetric cross-ply thin laminates. Composites Science & Technology, 38 (1), 55- 67 (1990)
4	BRAMPTON, C. J., BETTS, D. N., BOWEN, C. R., and KIM, H. A. Sensitivity of bistable laminates to uncertainties in material properties, 2013, geometry and environmental conditions. Composite Structures, 102, 276- 286 (2013)
5	DANO, M. L., and HYER, M. W. Snap-through of unsymmetric fiber-reinforced composite laminates. International Journal of Solids and Structures, 39 (1), 175- 198 (2002)
6	CANTERA, M., ROMERA, J., ADARRAGA, I., and MUJIKA, F. Modelling and testing of the snap-through process of bistable cross-ply composites. Composite Structures, 120, 41- 52 (2015)
7	DIACONU, C. G., WEAVER, P. M., and ARRIETA, A. F. Dynamic analysis of bi-stable composite plates. Journal of Sound and Vibration, 322 (4-5), 987- 1004 (2009)
8	DAYNES, S., WEAVER, P., and POTTER, K. Aeroelastic study of bistable composite airfoils. Journal of Aircraft, 46 (6), 2169- 2174 (2009)
9	GATTO, A., MATTIONI, F., and FRISWELL, M. Experimental investigation of bistable winglets to enhance aircraft wing lift takeoff capability. Journal of Aircraft, 46 (2), 647- 655 (2009)
10	BETTS, D. N., KIM, H. A., BOWEN, C. R., and INMAN, D. Optimal configurations of bistable piezo-composites for energy harvesting. Applied Physics Letters, 100 (11), 114104 (2012)
11	PAN, D., MA, B., and DAI, F. Experimental investigation of broadband energy harvesting of a bi-stable composite piezoelectric plate. Smart Materials and Structures, 26 (3), 035045 (2017)
12	HUANG, J., ZHANG, Q., SCARPA, F., LIU, Y., and LENG, J. Shape memory polymer-based hybrid honeycomb structures with zero Poisson's ratio and variable stiffness. Composite Structures, 179, 437- 443 (2017)
13	SHAN, S., KANG, S. H., RANEY, J. R., WANG, P., FANG, L., CANDIDO, F., LEWIS, J. A., and BERTOLDI, K. Multistable architected materials for trapping elastic strain energy. Advanced Materials, 27 (29), 4296- 4301 (2015)
14	SUN, J., TIGHE, B., and ZHAO, J. Tuning the energy landscape of soft robots for fast and strong motion. 2020 IEEE International Conference on Robotics and Automation (ICRA), 10082–10088 (2020)
15	ZHANG, Z., NI, X., WU, H., SUN, M., BAO, G., WU, H., and JIANG, S. Pneumatically actuated soft gripper with bistable structures. Soft Robotics, 9 (1), 57- 71 (2021)
16	ZHANG, Z., CHEN, D., WU, H., BAO, Y., and CHAI, G. Non-contact magnetic driving bioinspired venus flytrap robot based on bistable anti-symmetric CFRP structure. Composite Structure, 135, 17- 22 (2016)
17	WANG, D. A., CHEN, J. H., and PHAM, H. T. A constant-force bistable micromechanism. Sensors & Actuators A-Physical, 189, 481- 487 (2013)
18	PUTHANVEETIL, S., LIU, W. C., RILEY, K. S., ARRIETA, A. F., and LE FERRAND, H. Programmable multistability for 3D printed reinforced multifunctional composites with reversible shape change. Composites Science and Technology, 217, 109097 (2022)
19	ARRIETA, A. F., NEILD, S. A., and WAGG, D. J. Nonlinear dynamic response and modeling of a bistable composite plate for applications to adaptive structures. Nonlinear Dynamics, 58, 259- 272 (2009)
20	ARRIETA, A. F., NEILD, S. A., and WAGG, D. J. On the cross-well dynamics of a bi-stable composite plate. Journal of Sound and Vibration, 330 (14), 3424- 3441 (2011)
21	ARRIETA, A. F., SPELSBERG-KORSPETER, G., HAGEDORN, P., NEILD, S. A., and WAGG, D. J. Low order model for the dynamics of bi-stable composite plates. Journal of Intelligent Material Systems and Structures, 22 (17), 2025- 2043 (2011)
22	LI, H., DAI, F., and DU, S. Broadband energy harvesting by exploiting nonlinear oscillations around the second vibration mode of a rectangular piezoelectric bistable laminate. Smart Materials and Structures, 24 (4), 045024 (2015)
23	PAN, D., JIANG, W., and DAI, F. Dynamic analysis of bi-stable hybrid symmetric laminate. Composite Structures, 225, 111158 (2019)
24	WU, Z., LI, H., and FRISWELL, M. I. Advanced nonlinear dynamic modelling of bi-stable composite plates. Composite Structures, 201, 582- 596 (2018)
25	EMAM, S. A., HOBECK, J., and INMAN, D. J. Experimental investigation into the nonlinear dynamics of a bistable laminate. Nonlinear dynamics, 95, 3019- 3039 (2019)
26	MITURA, A., BRUNETTI, M., KLODA, L., ROMEO, F., and WARMINSKI, J. Experimental nonlinear dynamic regimes for energy harvesting from cantilever bistable shells. Mechanical Systems and Signal Processing, 206, 110890 (2024)
27	ZHANG, W., LIU, Y., and WU, M. Theory and experiment of nonlinear vibrations and dynamic snap-through phenomena for bi-stable asymmetric laminated composite square panels under foundation excitation. Composite Structure, 225, 111140 (2019)
28	WU, M. Q., ZHANG, W., and NIU, Y. Experimental and numerical studies on nonlinear vibrations and dynamic snap-through phenomena of bistable asymmetric composite laminated shallow shell under center foundation excitation. European Journal of Mechanics A-Solids, 89, 104303 (2021)
29	WU, M., ZHANG, W., and CHRONOPOULOS, D. Nonlinear vibrations and dynamic snap-through behaviors of four-corner simply supported bi-stable asymmetric laminated composite square shell. Mechanical Systems and Signal Processing, 173, 109023 (2022)
30	BRUNETTI, M., MITURA, A., ROMEO, F., and WARMINSKI, J. Nonlinear dynamics of bistable composite cantilever shells: an experimental and modelling study. Journal of Sound and Vibration, 526, 116779 (2022)
31	NAYFEH, A. H., and MOOK, D. T. Nonlinear Oscillations, Oxford University Press, Oxford (1981)
32	ABE, A., KOBAYASHI, Y., and YAMADA, G. Two-mode response of simply supported, rectangular laminated plates. International Journal of Non-Linear Mechanics, 33 (4),675- 690 (1998)
33	PELLICANO, F., and AVRAMOV, K. Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk. Communications in Nonlinear Science and Numerical Simulation, 12 (4), 496- 518 (2007)
34	LIU, Y., and CHU, F. Nonlinear vibrations of rotating thin circular cylindrical shell. Nonlinear Dynamics, 67, 1467- 1479 (2011)
35	CHEN, J., ZHANG, W., GUO, X., and SUN, M. Theoretical and experimental studies on nonlinear oscillations of symmetric cross-ply composite laminated plates. Nonlinear Dynamics, 73, 1697- 1714 (2013)
36	TENG, M. W., and WANG, Y. Q. Nonlinear forced vibration of simply supported functionally graded porous nanocomposite thin plates reinforced with graphene platelets. Thin-Walled Structures, 164, 107799 (2021)
37	AMABILI, M. Internal resonances in non-linear vibrations of a laminated circular cylindrical shell. Nonlinear Dynamics, 69, 755- 770 (2012)
38	NIU, Y., WU, M., YAO, M., and WU, Q. Dynamic instability and internal resonance of rotating pretwisted composite airfoil blades. Chaos Solitons & Fractals, 165, 112835 (2022)
39	NIU, Y., YAO, M., and WU, Q. Nonlinear vibrations of functionally graded graphene reinforced composite cylindrical panels. Applied Mathematical Modelling, 101, 1- 18 (2022)
40	ZHANG, W., MA, W., ZHANG, Y., and LIU, Y. Double excitation multi-stability and multi-pulse chaotic vibrations of a bistable asymmetric laminated composite square panels under foundation force. Chaos, 30 (8), 083105 (2020)
41	DING, H., JI, J., and CHEN, L. Q. Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics. Mechanical Systems and Signal Processing, 121, 675- 688 (2019)
42	DING, H., and CHEN, L. Q. Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dynamics, 95 (3), 2367- 2382 (2019)
43	YAO, M., LIU, P., MA, L., WANG, H., and ZHANG, W. Experimental study on broadband bistable energy harvester with L-shaped piezoelectric cantilever beam. Acta Mechanica Sinica, 36, 557- 577 (2020)
44	YAO, M., WANG, X., WU, Q., NIU, Y., and WANG, S. Dynamic analysis and design of power management circuit of the nonlinear electromagnetic energy harvesting device for the automobile suspension. Mechanical Systems and Signal Processing, 170, 108831 (2022)
45	AWREJCEWICZ, J., SYPNIEWSKA-KAMIŃSKA, G., and MAZUR, O. Analysing regular nonlinear vibrations of nano/micro plates based on the nonlocal theory and combination of reduced order modelling and multiple scale method. Mechanical Systems and Signal Processing, 163, 108132 (2022)
46	QATU, M. S. Vibration of Laminated Shells and Plates, Elsevier, Amsterdam (2004)
47	PARKER, T. S. and CHUA, L. Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, New York (2012)
48	WANG, Y. Q., WAN, Y. H., and ZHANG, Y. F. Vibrations of longitudinally traveling functionally graded material plates with porosities. European Journal of Mechanics A-Solids, 66, 55- 68 (2017)

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