Recurrence Plot and Recurrence Quantification of the Dynamic Properties of Cross-Shaped Laminated Energy Harvester

Abstract:

The paper examines the dynamic properties of bistable cross-shaped laminate plates for broadband energy harvesting applications by converting mechanical vibration energy into the electrical power output. Bistable laminates plates coupled to piezoelectric transducers were excited by application of harmonic excitations and exhibited a range of vibration patterns. The vibration patterns included single-well oscillations and snap-through vibrations of both periodic and chaotic character; such vibration patterns led to a different power output. Classical spectral analysis of measured voltage, displacement and velocity time histories indicated the presence of a variety of nonlinear and chaotic phenomena. As a result, an analysis of the measured displacement and voltage time histories was carried out with the use of the Recurrence Plots and the Recurrence Quantification Analysis methods. The Recurrence Plots method was used for detection of qualitative changes in the dynamic behaviour of the non-linear harvesting system. In order to facilitate interpretation of piezoelectric voltage and laminate displacement, a detailed analysis using Recurrence Plots, Recurrence Quantification Analysis was employed.

• Periodical: Applied Mechanics and Materials (Volume 849)
• Pages: 95-105
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.849.95
• Online since: August 2016
• Authors: Peter Harris, Grzegorz Litak*, Joanna Iwaniec, Chris R. Bowen
• Keywords: Bistable Laminated Plate, Cross-Shaped Laminated Plate, Energy Harvesting, Recurrence Plots, RQA Analysis

References

[1] H.A. Sodano, D.J. Inman, G. Park, Shock. Vib. Dig. 36, 197 (2004).

[2] S.R. Anton, H.A. Sodano, Smart Mat. Struct. 16, R1 (2007).

[3] R.L. Harne, K. W. Wang, Smart Mat. Struct., 22, 023001 (2013).

[4] M.F. Daqaq, R. Masana, A. Erturk, D.D. Quinn, Appl. Mech. Rev. 66, 040801 (2014).

DOI: 10.1115/1.4027259

[5] S.P. Pellegrini, N. Tolou, M. Schenk, J.L. Herder, J. Intell. Mater. Syst. Struct. 24, 1303 (2013).

[6] Y. Wang, L. Peng, Z. Huang, Theor. Appl. Mech. Lett. 5, 151 (2015).

[7] Y. Wang, D.J. Inman, J. Intell. Mater. Syst. Struc. 23, 2021 (2012).

[8] C.A.K. Kwuimy, G. Litak, M. Borowiec, C. Nataraj, Appl. Phys. Lett. 100, 024103 (2012).

DOI: 10.1063/1.3676272

[9] M.I. Friswell, O. Bilgen, S.F. Ali, G. Litak, S. Adhikari, Z. Angew. Math. Mech. 95, 433 (2015).

[10] M.D. McDonnell, N.G. Stocks, C.E.M. Pearce, D. Abbott, Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization, Cambridge University Press, New York (2008).

DOI: 10.1017/cbo9780511535239

[11] J. Naprstek, Stochastic Resonance – Challenges to Engineering Dynamics, in B.H.V. Topping, J. Kurths (Eds. ), Computation Technology Reviews, vol. 12, Civil-Comp Ltd. (Scotland) 2015, pp.53-101.

[12] A.F. Arrieta, P. Hagedorn, A. Erturk, D.J. Inman, Appl. Phys. Lett. 97, 104102 (2010).

[13] A.F. Arrieta, T. Delpero, A. Bergamini, P. Ermanni, Appl. Phys. Lett. 102, 173904 (2013).

[14] D.N. Betts, C.R. Bowen, H.A. Kim, N. Gathercole, C.T. Clarke, D.J. Inman, Euro. Phys. J. ST 222, 1553 (2013).

[15] D.N. Betts, H.A. Kim, C.R. Bowen, D.J. Inman, Appl Phys Lett., 100, 114104 (2012).

[16] D.N. Betts, H.A. Kim, C.R. Bowen, in Proc. of 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA 2012-1492 (2012).

DOI: 10.2514/6.2012-1492

[17] D.N. Betts, H.A. Kim, C.R. Bowen, Smart Mat. Res., 621364 (2012).

[18] M. Borowiec, A. Rysak, D.N. Betts, C.R. Bowen, H.A. Kim, G. Litak, Euro. Phys. J. Plus 129, 211 (2014).

[19] A. Syta, C.R. Bowen, H.A. Kim, A. Rysak, G. Litak, Meccanica 50, 1961 (2015).

[20] H. Poincaré, Acta Mathematica 13, 1 (1890).

[21] N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007).

[22] J.P. Eckmann, K.S. Oliffson, D. Ruelle, Europhys. Lett. 5, 973 (1987).

[23] J.P. Zbilut., A. Giuliani, C.L. Weber, Phys. Lett. A 237, 131 (1998).

[24] J.P. Zbilut, C.L. Weber, Phys. Lett. A 171, 199 (1992).

[25] G. Litak, M. Wiercigroch, B.W. Horton, X. Xu, Z. Angew. Math. Mech. 90, 33 (2010).

[26] M. Thiel, M.C. Romano, J. Kurths, Physics Letters A 330, 343 (2004).

[27] N. Marwan, J. Kurths, Line structures in recurrence plots, Phys. Lett. A 336, 349 (2005).

[28] E.J. Ngamga, A. Nandi, R. Ramaswamy, M.C. Romano, M. Thiel, J. Kurths PRAMANA J. Phys. 70, 1039 (2008).

DOI: 10.1007/s12043-008-0108-y

[29] A.S. Elwakil, A.M. Soliman, Chaos Solit. Fract. 10, 1399 (1999).

[30] J.M. Nichols, S.T. Trickey, M. Seaver, Mech. Syst. Signal Process. 20, 421 (2006).

[31] G. Litak, J.T. Sawicki, R. Kasperek, Nondestr. Testing Evaluat. 24, 347 (2009).

[32] J. Kurths, U. Schwarz, C.P. Sonett, U. Parlitz, Nonlin. Processes Geophys. 1, 72 (1994).

DOI: 10.5194/npg-1-72-1994

[33] N.V. Zolotova, D.I. Ponyavin, Astron. Astrophys. 449, L1 (2006).

[34] C. Manetti, A. Giuliani, M.A. Ceruso, C.L. Webber, J.P. Zbilut, Phys. Lett. A 281, 317 (2001).

[35] A. Giuliani, C. Manetti, Phys. Rev. E 53, 6336 (1996).

[36] N. Marwan, M. Thiel, N.R. Nowaczyk, Nonlin. Process Geophys. 9, 325 (2002).

[37] J.P. Zbilut, M. Koebbe, H. Loeb, G. Mayer-Kress, in Proceedings of the IEEE Conference on Computers in Cardiology 1990, IEEE Computer Society Press, 1991, Chicago, pp.263-266.

[38] N. Thomasson, T.J. Hoeppner, C.L. Webber, J.P. Zbilut, Phys. Lett. A 279, 94 (2001).

[39] J.A. Hołyst, M. Zebrowska, K. Urbanowicz, Eur. Phys. J. B 20, 531 (2001).

[40] F. Takens, Detecting Strange Attractors in Turbulence, in D. A. Rand and L. -S. Young (Eds. ), Dynamical Systems and Turbulence, Lecture Notes in Mathematics, vol. 898, Springer 1981, p.366–381.

DOI: 10.1007/bfb0091924

[41] A.M. Fraser, H.L. Swinney, Phys. Rev. A 33, 1133 (1986).

[42] M.B. Kennel, R. Btrown, H.D.A. Abardanel, Phys. Rev. A 45, 3403 (1992).

[43] H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, Cambridge University Press, Cambridge, (1997).

[44] N. Marwan, Cross Recurrence Plot Toolbox for Matlab, Reference Reference Manual, Version 5. 15, Release 28. 6, 2010, http: /tocsy. pik-potsdam. de.