Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap

doi:10.1007/s10483-017-2171-7

Abstract

Abstract:

A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method (FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369 Hz to 1 687 Hz and 2 127 Hz to 4 000 Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap. Thus, a low-frequency and broad band gap of 369 Hz to 4 000 Hz is obtained.

Key words: Accretive mapping, probabilistic normed space, pseudo-contractive mapping, phononic crystal, band gap, folding beam-type structure, wave propagation, piezoelectric

2010 MSC Number:

Shan JIANG, Longxiang DAI, Hao CHEN, Hongping HU, Wei JIANG, Xuedong CHEN. Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 411-422.

TrendMD

References

[1] Wei, C. Q., Yan, Z. Z., Zheng, H., and Zhang, C. Z. RBF collocation method and stability analysis for phononic crystals. Applied Mathematics and Mechanics (English Edition), 37(5), 627-638(2016) DOI 10.1007/s10483-016-2076-8
[2] Shi, Z. J., Wang, Y. S., and Zhang, C. Z. Band structure calculations of in-plane waves in twodimensional phononic crystals based on generalized multipole technique. Applied Mathematics and Mechanics (English Edition), 36(5), 557-580(2015) DOI 10.1007/s10483-015-1938-7
[3] Liu, T. W., Tsai, Y. C., Lin, Y. C., Ono, T., Tanaka, S., and Wu, T. T. Design and fabrication of a phononic-crystal-based Love wave resonator in GHz range. AIP Advances, 4, 124201(2014)
[4] Lee, I. K., Kim, Y. J., Oh, J. H., and Kim, Y. Y. One-dimensional broadband phononic crystal filter with unit cells made of two non-uniform impedance-mirrored elements. AIP Advances, 3, 022105(2013)
[5] Dai, L. X., Jiang, S., Lian, Z. Y., Hu, H. P., and Chen, X. D. Locally resonant band gaps achieved by equal frequency shunting circuits of piezoelectric rings in a periodic circular plate. Journal of Sound and Vibration, 337, 150-160(2015)
[6] Yantchev, V. A transversely coupled phononic surface acoustic wave transducer. Applied Physics Letters, 104, 103503-103503-3(2014)
[7] Chen, X. D., Chen, H., Luo, X., Ye, Y. X., Hu, Y. T., and Xu, J. Q. Air vortices and nano-vibration of aerostatic bearings. Tribology Letters, 42, 179-183(2011)
[8] Yan, T., Pu, H., Chen, X., Li, Q., and Xu, C. Integrated hybrid vibration isolator with feedforward compensation for fast high-precision positioning X/Y tables. Measurement Science and Technology, 21, 065901(2010)
[9] Aggogeri, F., Al-Bender, F., Brunner, B., Elsaid, M., Mazzola, M., Merlo, A., Ricciardi, D., de la O Rodriguez, M., and Salvi, E. Design of piezo-based AVC system for machine tool applications. Mechanical Systems and Signal Processing, 36, 53-65(2013)
[10] Liu, Z., Zhang, X., Mao, Y., Zhu, Y., Yang, Z., Chan, C., and Sheng, P. Locally resonant sonic materials. Science, 289, 1734-1736(2000)
[11] Goffaux, C., Sánchez-Dehesa, J., Yeyati, A. L., Lambin, P., Khelif, A., Vasseur, J., and DjafariRouhani, B. Evidence of Fano-like interference phenomena in locally resonant materials. Physical Review Letters, 88, 225502(2002)
[12] Goffaux, C., and Sánchez-Dehesa, J. Two-dimensional phononic crystals studied using a variational method:application to lattices of locally resonant materials. Physical Review B, 67, 144301(2003)
[13] Spadoni, A., Ruzzene, M., and Cunefare, K. Vibration and wave propagation control of plates with periodic arrays of shunted piezoelectric patches. Journal of Intelligent Material Systems and Structures, 20, 979-990(2009)
[14] Casadei, F., Ruzzene, M., Dozio, L., and Cunefare, K. Broadband vibration control through periodic arrays of resonant shunts:experimental investigation on plates. Smart Materials & Structures, 19, 015002(2010)
[15] Wang, G., Chen, S. B., and Wen, J. H. Low-frequency locally resonant band gaps induced by arrays of resonant shunts with Antoniou's circuit:experimental investigation on beams. Smart Materials & Structures, 20, 015026(2011)
[16] Thorp, O., Ruzzene, M., and Baz, A. Attenuation of wave propagation in fluid-loaded shells with periodic shunted piezoelectric rings. Smart Materials & Structures, 14, 594-604(2005)
[17] Chen, S. B., Wang, G., Wen, J. H., and Wen, X. S. Wave propagation and attenuation in plates with periodic arrays of shunted piezo-patches. Journal of Sound and Vibration, 332, 1520-1532(2013)
[18] Shu, H., Zhao, L., Shi, X., Liu, W., Shi, D., and Kong, F. Torsional wave propagation in a circular plate of piezoelectric radial phononic crystals. Journal of Applied Physics, 118, 184904(2015)
[19] Airoldi, L., and Ruzzene, M. Wave propagation control in beams through periodic multi-branch shunts. Journal of Intelligent Material Systems and Structures, 22, 1567-1579(2011)
[20] Jiang, S., Lian, Z. Y., Dai, L. X., Hu, H. P., and Xue, H. Band gap frequencies of piezoelectric phononic crystals tuned by aixal force. 2014 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications, Beijing (2014)
[21] Wang, G., Wang, J. W., Chen, S. B., and Wen, J. H. Vibration attenuations induced by periodic arrays of piezoelectric patches connected by enhanced resonant shunting circuits. Smart Materials & Structures, 20, 125019(2011)
[22] Kamesh, D., Pandiyan, R., and Ghosal, A. Passive vibration isolation of reaction wheel disturbances using a low frequency flexible space platform. Journal of Sound and Vibration, 331, 1310-1330(2012)
[23] Kawakubo, T., Nagano, T., Nishigaki, M., and Abe, K. RF-MEMS tunable capacitor with 3 V operation using folded beam piezoelectric bimorph actuator. Journal of Microelectromechanical Systems, 15, 1759-1765(2006)
[24] Wang, Y. J., Lian, Z. Y., Wang, J., and Hu, H. P. Analysis of a piezoelectric power harvester with adjustable frequency by precise electric field method. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 60, 2154-2161(2013)