可调谐局域共振梁带隙模型改进

PDF(836 KB)

振动与冲击 ›› 2017, Vol. 36 ›› Issue (14) : 121-125.

论文

可调谐局域共振梁带隙模型改进

陈圣兵 1 ，王刚 2

作者信息 +

Band-gap model improvement of tunable locally resonant beams

CHEN Sheng-bing 1, WANG Gang 2

Author information +

文章历史 +

摘要

局域共振声子晶体具有弹性波带隙特性，可用于结构振动与噪声控制。通过引入压电分流阵列也可以在基体结构形成弹性波带隙，尤其是谐振分流电路可以产生局域共振带隙。而且，通过调节分流电路参数可以方便地改变其局域共振带隙特性。本文研究了含压电分流阵列的局域共振梁带隙计算建模方法，指出了传统带隙模型的不足，并提出了改进模型。利用传递矩阵法计算了传统模型和改进模型弯曲波传播常数，比较了两种模型对带隙预测的差异，发现传统模型在局域共振带隙内形成了较大误差，利用改进模型可以大大提高局域共振带隙的预测精度。

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.

导出引用

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[J]. Journal of Vibration and Shock, 2017, 36(14): 121-125

参考文献

[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