Skip to main content

Advertisement

SpringerLink
Log in

Suppression of cross-well vibrations of a bistable square cross-ply laminate using an additional composite strip

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

The behavior of bistable structures having two local potential energy minima has been extensively explored in recent years. In bistable systems, both stable states are located at their potential energy wells, where the shape transition can be triggered by overcoming the energy barrier between them. Nature of the potential energy landscape plays a vital role in the snap-through behavior of such structures. For regular geometries like a perfect square-shaped bistable plate, minima of the potential energy landscape is perfectly symmetric and complementary to each other. Potential energy landscape with perfectly symmetric local minima may lead to continuous cross-well vibrations as the snap-through, and reversible snap-through requirements are identical. Such vibrations are often undesirable for morphing applications where stationary control of the structural configurations is required. In continuation to the previously reported novel strategy to generate a tunable potential energy landscape in a square bistable cross-ply laminate by attaching an additional composite strip, the present study reveals the dynamic design space of strip attached to square bistable cross-ply laminate. A Rayleigh–Ritz-based semi-analytical formulation and a fully nonlinear finite element model are employed to investigate the dynamic characteristics of unsymmetrical laminate with an additional composite strip. A parametric study is performed to explore the changes in the potential energy landscape and corresponding dynamic characteristics with changes in the width and thickness of the strip. In order to suppress undesirable cross-well vibrations from a periodic excitation, optimum design parameters of the strip (width and thickness) are reported in the study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Availability of data and material

The necessary data required to replicate the findings presented in the manuscript may be made available on request.

Code Availability

The necessary data required to replicate the findings presented in the manuscript may be made available on request.

Notes

  1. Reader can find the basic formulations in Ref. [37].

References

  1. Lachenal X, Daynes S, Weaver PM (2013) Review of morphing concepts and materials for wind turbine blade applications. Wind Energy 16(2):283–307

    Article  Google Scholar 

  2. Khaniki HB, Ghayesh MH, Chin R, Amabili M (2022) Hyperelastic structures: a review on the mechanics and biomechanics. Int J Non-Linear Mech 104275

  3. Emam SA, Inman DJ (2015) A review on bistable composite laminates for morphing and energy harvesting. Appl Mech Rev 67(6)

  4. Sun M, Xiong L, Zhang Z, Zhang H, Chai H, Zhang F, Wu H, Jiang S (2021) Systematic analysis of a new novel variable stiffness stable composite structures using theory, fem and experiment. Mech Adv Mater Struct 1–10

  5. Zhang Z, Li Y, Yu X, Li X, Wu H, Wu H, Jiang S, Chai G (2019) Bistable morphing composite structures: a review. Thin-walled Struct 142:74–97

    Article  Google Scholar 

  6. Chai H, Li Y, Zhang Z, Sun M, Wu H, Jiang S (2020) Systematic analysis of bistable anti-symmetric composite cylindrical shells and variable stiffness composite structures in hygrothermal environment. Int J Adv Manuf Technol 108(4):1091–1107

    Article  Google Scholar 

  7. Zhang Z, Pei K, Sun M, Wu H, Yu X, Wu H, Jiang S, Zhang F (2020) A novel solar tracking model integrated with bistable composite structures and bimetallic strips. Compos Struct 248:112–506

    Article  Google Scholar 

  8. Li Y, Li M, Dai F (2022) Twisting control strategy of bistable composite shell with initial curvature. Thin-Walled Struct 181:110–121

    Article  Google Scholar 

  9. Hyer MW (1981) Some observations on the cured shape of thin unsymmetric laminates. J Compos Mater 15:175–194

    Article  Google Scholar 

  10. Fazli M, Sadr M, Ghashochi-Bargh H (2021) Analysis of the bi-stable hybrid laminate under thermal load. Int J Struct Stab Dyn 21(05):2150–069

    Article  MathSciNet  Google Scholar 

  11. Srikanth GS, Scheffler S, Anilkumar PM, Rao BN, Rolfes R (2022) In: Recent advances in applied mechanics: proceedings of virtual seminar on applied mechanics (VSAM 2021). Springer, pp 321–335

  12. Pirrera A, Avitabile D, Weaver P (2010) Bistable plates for morphing structures: a refined analytical approach with high-order polynomials. Int J Solids Struct 47(25–26):3412–3425

    Article  MATH  Google Scholar 

  13. Haldar A, Groh R, Jansen E, Weaver PM, Rolfes R (2020) An efficient semi-analytical framework to tailor snap-through loads in bistable variable stiffness laminates. Int J Solids Struct 195:91–107

    Article  Google Scholar 

  14. Mukherjee A, Ali SF, Arockiarajan A (2021) Hybrid bistable composite laminates for structural assemblies: A numerical and experimental study. Compos Struct 260:113–467

    Article  Google Scholar 

  15. Varelis D (2021) Small-amplitude free vibration analysis of active multistable shells under static multifield loading. J Vib Control 27(1–2):18–30

    Article  MathSciNet  Google Scholar 

  16. Cao J, Hao Y, Zhang W, Liu L, Yang S, Cao Y (2022) Bi-stability and vibration of asymmetric and antisymmetric laminates with four points simply supported at arbitrary location. J Vib Eng Technol 1–17

  17. Habibzadeh N, Tikani R, Ziaei-Rad S, Taki MS (2022) Static and dynamic analysis of a bistable plate under nonlinear magnetic force. J Vib Control 28(7–8):745–757

    Article  MathSciNet  Google Scholar 

  18. Liu X, Karami B, Shahsavari D, Civalek Ö (2021) Elastic wave characteristics in damped laminated composite nano-scaled shells with different panel shapes. Compos Struct 267:113–924

    Article  Google Scholar 

  19. Khaniki HB, Ghayesh MH, Chin R, Hussain S (2022) Internal resonance and bending analysis of thick visco-hyper-elastic arches. Contin Mech Thermodyn 1–44

  20. Amabili M, Ferrari G, Ghayesh MH, Hameury C, Zamal HH (2022) Nonlinear vibrations and viscoelasticity of a self-healing composite cantilever beam: theory and experiments. Compos Struct 294:115–741

    Article  Google Scholar 

  21. Vogl GA, Hyer MW (2011) Natural vibration of unsymmetric cross-ply laminates. J Sound Vib 330(20):4764–4779

    Article  Google Scholar 

  22. Akhil KS, Anilkumar PM, Haldar A, Rao BN (2022) Vibration analysis of bistable unsymmetric laminates with curvilinear fiber paths. Int J Struct Stab Dyn 2350089

  23. Arrieta AFD (2009) Nonlinear dynamics and control of bi-stable composites for morphing applications. Ph.D. thesis, University of Bristol

  24. Nejad AF, Ziaei-Rad S, Moore M (2017) Vibration analysis of bi-stable composite cross-ply laminates using refined shape functions. J Compos Mater 51(8):1135–1148

    Article  Google Scholar 

  25. Yang S, Wang Z, Zhang W (2022) Dynamic jump analysis of bi-stable square plate under foundation excitation. Int J Dyn Control 1–10

  26. Liu T, Zhang W, Zheng Y, Zhang Y, Zhao W (2022) Potential well evolution and metastable dynamics of bistable asymmetric laminated composite square shallow shell under external and parametric excitations. Compos Struct 280:114–936

    Article  Google Scholar 

  27. Arrieta A, Hagedorn P (2012) In: 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA, p 1742

  28. Wu M, Zhang W, Niu Y (2021) Experimental and numerical studies on nonlinear vibrations and dynamic snap-through phenomena of bistable asymmetric composite laminated shallow shell under center foundation excitation. Eur J Mech-A/Solids 89:104–303

    Article  MathSciNet  MATH  Google Scholar 

  29. Harne RL, Wang K (2013) A review of the recent research on vibration energy harvesting via bistable systems. Smart Mater Struct 22(2):023–001

    Article  Google Scholar 

  30. Lee AJ, Xie A, Inman DJ (2020) Suppression of cross-well oscillations for bistable composites through potential well elimination. J Vib Acous 142(3)

  31. Johnson DR, Thota M, Semperlotti F, Wang K (2013) On achieving high and adaptable damping via a bistable oscillator. Smart Mater Struct 22(11):115–027

    Article  Google Scholar 

  32. Lakes R (2001) Extreme damping in composite materials with a negative stiffness phase. Phys Rev Lett 86(13):2897

    Article  Google Scholar 

  33. Cui Y, Santer MJ (2014) In: Spacecraft structures conference, p 0671

  34. Cui Y, Santer M (2015) Highly multistable composite surfaces. J Compos Struct 124:44–54

    Article  Google Scholar 

  35. Kumar AP, Anilkumar PM, Haldar A, Scheffler S, Jansen EL, Rao BN, Rolfes R (2021) Tailoring bistability in unsymmetrical laminates using an additional composite strip. Thin-Walled Struct 168:108–212

    Article  Google Scholar 

  36. Wu Z, Li H, Friswell MI (2018) Advanced nonlinear dynamic modelling of bi-stable composite plates. Compos Struct 201:582–596

    Article  Google Scholar 

  37. Emam SA (2018) Snapthrough and free vibration of bistable composite laminates using a simplified rayleigh-ritz model. Compos Struct 206:403–414

    Article  Google Scholar 

  38. Haldar A, Reinoso J, Jansen E, Rolfes R (2018) Snap-through of bistable configurations generated from variable stiffness composites, multiscale modeling of heterogeneous structures. Springer International Publishing, Cham, pp 61–82

    Google Scholar 

  39. Anilkumar PM, Rao BN (2021) Impact of hygrothermal environment on the bistability of variable stiffness laminates with curvilinear fibre paths. Int J Adv Eng Sci Appl Math 13(1):33–48

    Article  MathSciNet  Google Scholar 

  40. Diaconu CG, Weaver PM, Arrieta AF (2009) Dynamic analysis of bi-stable composite plates. J Sound Vib 322(4–5):987–1004

    Article  Google Scholar 

  41. Khaniki HB, Ghayesh MH (2023) Highly nonlinear hyperelastic shells: Statics and dynamics. Int J Eng Sci 183:103–794

    Article  MathSciNet  MATH  Google Scholar 

  42. Berghouti H, Adda Bedia E, Benkhedda A, Tounsi A (2019) Vibration analysis of nonlocal porous nanobeams made of functionally graded material. Adv Nano Res 7(5):351–364

    Google Scholar 

  43. Liu G, Wu S, Shahsavari D, Karami B, Tounsi A (2022) Dynamics of imperfect inhomogeneous nanoplate with exponentially-varying properties resting on viscoelastic foundation. Eur J Mech-A/Solids 95:104–649

    Article  MathSciNet  MATH  Google Scholar 

  44. Cui Y, Santer M (2016) Characterisation of tessellated bistable composite laminates. J Compos Struct 137:93–104

    Article  Google Scholar 

  45. Lee A (2019) Piezoelectrically generated bistable composites for morphing, energy harvesting, and vibration control. Ph.D. thesis

  46. Casals-Terre J, Fargas-Marques A, Shkel AM (2008) Snap-action bistable micromechanisms actuated by nonlinear resonance. J Microelectromech Syst 17(5):1082–1093

  47. Diaconu CG, Weaver PM, Mattioni F (2008) Concepts for morphing airfoil sections using bi-stable laminated composite structures. Thin-Walled Struct 46(6):689–701

    Article  Google Scholar 

  48. Khaniki HB, Ghayesh MH, Chin R (2023) Theory and experiment for dynamics of hyperelastic plates with modal interactions. Int J Eng Sci 182:103–769

    Article  MathSciNet  MATH  Google Scholar 

  49. Hao Y, Bai C, Zhang W, Liu L (2022) Yang S Intrawell and interwell oscillations for bi-stable cross-ply laminates actuated by mfc under oscillating impulse voltages. Int J Non-Linear Mech 143:104–025

    Article  Google Scholar 

  50. Anilkumar PM, Scheffler S, Haldar A, Brod M, Rao BN, Jansen EL, Rolfes R (2023) Nonlinear dynamic modeling of bistable variable stiffness composite laminates. J Sound Vib 545:117–417

    Article  Google Scholar 

Download references

Acknowledgements

B. Danish would like to acknowledge Prime Minister’s Research Fellowship, Ministry of Education, India for the research grant on Doctoral Degrees during the course of research.

Author information

Authors and Affiliations

  1. Structural Engineering Division, Department of Civil Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu, 600036, India

    B. Danish, P. M. Anilkumar & B. N. Rao

Authors
  1. B. Danish
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. M. Anilkumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. N. Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. N. Rao.

Ethics declarations

Conflicts of interest

Authors declare no conflicts of interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Danish, B., Anilkumar, P.M. & Rao, B.N. Suppression of cross-well vibrations of a bistable square cross-ply laminate using an additional composite strip. Int. J. Dynam. Control 11, 2680–2690 (2023). https://doi.org/10.1007/s40435-023-01153-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-023-01153-1

Keywords

Search

Navigation