Band-gap model improvement of tunable locally resonant beams
CHEN Sheng-bing 1, WANG Gang 2
1.China Aerodynamics Research and Development Center, Mianyang 621000；
2. College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082
Abstract：Locally resonant crystals possess elastic wave band-gaps, which can be used for vibration and noise control of structures. By introducing piezoelectric shunting arrays in host structures, band gaps can also be generated. Particularly, locally resonant gaps can be induced by resonant shunting circuits. Moreover, the properties of locally resonant gaps are conveniently tuned by modifying the circuit parameters. The modeling method of beams with piezoelectric shunting arrays is investigated in this paper, where deficiency of conventional model is pointed out and an improved model is proposed. By transfer matrix method, propagation constants of conventional and improved models are predicted and compared. The results demonstrate that conventional model presents great errors. Hence, improved model effectively boosts accuracy of locally resonant gap prediction.
陈圣兵 1,王刚 2. 可调谐局域共振梁带隙模型改进[J]. 振动与冲击, 2017, 36(14): 121-125.
CHEN Sheng-bing 1, WANG Gang 2. Band-gap model improvement of tunable locally resonant beams. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(14): 121-125.
[1] Mead D J. Free wave propagation in periodic-supported,infinite beams [J]. Journal of Sound and Vibration, 1970, 11(2): 181-197.
[2] Mead D J, Markus S. Coupled flexural-longitudinal wave motion in a periodic beam [J]. Journal of Sound Vibration, 1983, 90(1): 1-24.
[3] Mead D J. A new method of analyzing wave propagation in periodic structures: applications to periodic Timoshenko beams and stiffened plates [J]. Journal of Sound Vibration, 1986, 104(1): 9-27.
[4] Sigalas M M, Economou E N. Elastic and acoustic wave band structure [J]. Journal of Sound Vibration, 1992, 158(2): 377-382.
[5] Kushwaha M S, Halevi P, Dobrzynski L, et al. Acoustic band structure of periodic elastic composites [J]. Physics Review Letter. 1993,71(13): 2022-2025.
[6] Martinez-Salar R, Sancho J, Sanchez J V, et al. Sound attenuation by sculpture [J]. Nature, 1995,378: 241
[7] Liu Z Y, Zhang X, Mao Y, et al. Locally resonant sonic materials [J]. Science, 2000,289: 1734-1736.
[8] Li J, Chan C T. Double-negative acoustic metamaterial. Physics Review E, 2004, 70(5): 055602
[9] Fang N, Xi D, Xu J, et al. Ultrasonic metamaterials with negative modulus. Nature Materials, 2006, 5(6): 452-456.
[10] Milton G W. New metamaterials with macroscopic behavior outside that of continuum elastodynamics. New Journal of Physcis, 2007, 9: 359
[11] Thorp O, Ruzzene M, Baz A. Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches [J]. Smart Materials and Structures, 2001, 10(5): 979-989.
[12] Thorp O, Ruzzene M, Baz A. Attenuation of wave propagation in fluid-loaded shells with periodic shunted piezoelectric rings [J]. Smart Materials and Structures, 2005, 14: 594-604.
[13] Spadoni A, Ruzzene M, Cunefare K. Vibration and wave propagation control of plates with periodic arrays of shunted piezoelectric patches [J]. Journal of Intelligent Material System and Structures, 2009, 20: 979-990.
[14] Casadei F, Ruzzene M, Dozio L, et al. Broadband vibration control through periodic arrays of resonant shunts: experimental investigation on plates [J]. Smart Materials and Structures, 2010,19:015002
[15] Casadei F, Beck B S, Cunefare K A, et al. Vibration control of plates through hybrid configurations of periodic piezoelectric shunts [J]. Journal of Intelligent Material System and Structures, 2012, 23(10):1169-1177.
[16] Collet M, Ouisse M, Ichchou M N, et al. Semi-active optimization of 2D wave dispersion into shunted piezo-composite systems for controlling acoustic interation [J]. Smart Materials and Structures, 2012, 21: 094002
[17] Chen S B, Wen J H, Yu D L, et al. Band gap control of phononic beam with negative capacitance piezoelectric shunt. Chinese Physics B, 2011, 20(1): 014301
[18] Chen S B, Wen J H, Wang G, et al. Locally resonant gaps of phononic beams induced by periodic arrays of resonant shunts. Chinese Physics Letter, 2011, 28(9): 094301.
[19] Chen S, Wen J, Wang G, et al. Improved modeling of rods with periodic arrays of shunted piezoelectric patches [J]. Journal of Intelligent Material System and Structures, 2012, 23: 1613-1621.
[20] Chen S, Wang G, Wen J, et al. Wave propagation and attenuation in plates with periodic arrays of shunted piezo-patches [J]. Journal of Sound and Vibration, 2013,332: 1520-1532.
[21] Airoldi L, Ruzzene M. Wave propagation control in beams through periodic multi-branch shunts [J]. Journal of Intelligent Material System and Structures, 2011, 10: 1567-1578.
[22] Airoldi L, Ruzzene M. Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos [J]. New Journal of Physics, 2011, 13: 113010
