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LCR分流电路下压电声子晶体智能材料的带隙

唐一璠 林书玉

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LCR分流电路下压电声子晶体智能材料的带隙

唐一璠, 林书玉

Band gaps of the phononic piezoelectric smart materials with LCR shunting circuits

Tang Yi-Fan, Lin Shu-Yu
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  • 将带有LCR分流电路的压电陶瓷片对贴在铝和环氧树脂组成的声子晶体结构中. 使智能材料的机械振动与压电陶瓷的压电效应耦合起来,推导出机械振动在压电陶瓷片上的等效附加应力;使LCR分流电路中的电磁振荡效应和声子晶体的能带特性有机结合,计算了在分流电路作用下智能材料扭转和弯曲振动的带隙特性,研究了电阻、电感、电容元件的改变对压电声子晶体智能材料带隙的影响. 研究结果表明:在合理尺寸下,随着分流电路中电阻值的增大,带隙的频率范围变宽,但衰减幅值有所降低;电感和电容值的增大都可以使带隙向低频移动,带隙的衰减幅值随着电感值的增大而升高,但随着电容值的增大而降低. 从而给压电声子晶体智能材料减震降噪的控制提供了一种新思路.
    Environmental forces can produce undesired vibrations in mechanical structures that can limit the precision of mechanical equipment and cause mechanical failure. Piezoelectric-shunt damping is an attractive technique for controlling the vibrating structures, which is reliable, economical and light-weight. Phononic crystal is an internal component whose elastic constant, density and sound velocity change periodically. When the elastic wave passes through a phononic crystal, special dispersion curve is formed due to the interaction of periodic arrangement materials. In order to study the electromagnetic oscillation band gap of the piezoelectric phononic crystal with LCR shunt network at torsional and flexural vibration, we propose a new phononic piezoelectric beam, which is composed of aluminum and epoxy resin. When the piezoelectric patch is strained, the electrical energy is dissipated as current flows through an external LCR shunting circuit. By combining the piezoelectric effect with the mechanical vibration of the smart material, the equivalent additional stress of piezoelectric patches is deduced. Moreover, coupling the energy band theory of phononic crystal with the effect of electromagnetic oscillation, we calculate the band gap characteristics of torsional and flexural vibration of intelligent material. Using the transfer matrix method and Bloch theorem for periodic boundary conditions, the band gap of the phononic beam can be calculated. With the increase of resistance, the amplitude attenuation of the band gap decreases. However, it can expand the frequency range. The inherent frequency of the electromagnetic oscillation is 1/[2π√L(C + CP)]. The sum of capacitance and inherent capacitance is the total capacitance of the shunting circuit. Therefore, the frequency of the electromagnetic oscillation decreases with the increases of the capacitance and inductance. The amplitude attenuation of the band gap increases with the increase of the inductance and decreases greatly with the rise of the capacitance. Three main differences between the LCR shunt networks and traditional circuits are found. First, the band gaps of the phononic piezoelectric smart material are composed of Bragg band gaps and local resonant band gaps. The former one is due to the mismatch between aluminum and epoxy resin, which makes the elastic waves have no corresponding vibration modes at certain frequencies. The latter one is from the effect of electromagnetic oscillation in LCR shunt networks, which consume the energy by resistor. Second, by tuning the resistance, capacitance and inductance, we can change the singularity position and stress magnitude of equivalent additional force curve. The amplitude attenuations of locally resonant band gaps and electromechanical coupling coefficient will be changed. Third, both locations and widths of the band gaps can be tuned by simply varying the value of negative capacitance of the shunting networks without needing to modify the configuration of the structure. Therefore, it provides a new idea for controlling the vibration and reducing the noise of the phononic piezoelectric smart material.
      通信作者: 林书玉, sylin@snnu.edu.cn
    • 基金项目: 国家自然科学基金(批准号:11374200,11474192)资助的课题.
      Corresponding author: Lin Shu-Yu, sylin@snnu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11374200, 11474192).
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    Wang Y Z, Li F M, Huang W H, Wang Y S 2008 J. Mech. Phys. Solids 56 1578

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    Tang J, Wang K W 2003 J. Vib. Acoust. 125 95

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    Airoldi L, Ruzzene M 2011 J. Intel. Mat. Syst. Struct. 22 1567

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  • [1]

    Zhang S W, Wu J H 2013 Acta Phys. Sin. 62 134302 (in Chinese) [张思文, 吴九汇 2013 物理学报 62 134302]

    [2]

    Wang G, Chen S B, Wen J H 2011 Smart Mater. Struct. 20 015026

    [3]

    Spadoni A, Ruzzene M, Cunefare K 2009 J. Intel. Mat. Syst. Struct. 20 979

    [4]

    Gripp J A B, L Góes C S, Heuss O, Scinocca F 2015 Smart Mater. Struct. 24 125017

    [5]

    Behrens S, Moheimani S O R, Fleming A J 2003 J. Sound Vib. 266 929

    [6]

    Yang M Y, Wu L C, Tseng J Y 2008 Phys. Lett. A 372 4730

    [7]

    Wang Y Z, Li F M, Huang W H, Jiang X A, Wang Y S, Kishimoto K 2008 Int. J. Solids Struct. 45 4203

    [8]

    Park J S, Lim S C, Choi S B, Kim J H, Park Y P 2004 J. Sound Vib. 269 1111

    [9]

    Degraeve S, Granger C, Dubus B, Vasseur J O, Pham T M, Hladky-Hennion A C 2014 J. Appl. Phys. 115 194508

    [10]

    Wang Y Z, Li F M, Huang W H, Wang Y S 2008 J. Mech. Phys. Solids 56 1578

    [11]

    Joo Hwan Oh, I I Kyu Lee, Pyung Sik Ma, Yoon Young Kim 2011 Appl. Phys. Lett. 99 083505

    [12]

    Chen S B, Wen J H, Yu D L, Wang G, Wen X S 2011 Chin. Phys. B 20 014301

    [13]

    Li J Q, Li F M, Wang Y S, Kishimoto K 2008 Acta Mech. Solida. Sin. 21 507

    [14]

    Forward R L 1979 Appl. Opt. 18 690

    [15]

    Yang L F, Wang Y F, Zhou Y 2012 Acta Phys. Sin. 61 107702 (in Chinese) [杨立峰, 王亚非, 周鹰 2012 物理学报 61 107702]

    [16]

    Tang J, Wang K W 1999 J. Vib. Acoust. 121 379

    [17]

    Tang J, Wang K W 2003 J. Vib. Acoust. 125 95

    [18]

    Airoldi L, Ruzzene M 2011 J. Intel. Mat. Syst. Struct. 22 1567

    [19]

    Yu D L, Liu Y Z, Wang G, Wen J H, Qiu J 2006 Journal of Vibration and Shock 25 104 (in Chinese) [郁殿龙,刘耀宗,王刚,温激鸿,邱静 2006 振动与冲击 25 104]

    [20]

    Chen S B, Han X Y, Yu D L, Wen J H 2010 Acta Phys. Sin. 59 0387 ( in Chinese) [陈圣兵, 韩小云, 郁殿龙, 温激鸿 2010 物理学报 59 0387]

    [21]

    Chen S B, Wen J H, Wang G, Yu D L, Wen X S 2012 J. Intel. Mat. Syst. Struct. 23 1613

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出版历程
  • 收稿日期:  2016-02-29
  • 修回日期:  2016-06-02
  • 刊出日期:  2016-08-05

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