具有压电分流电路的声子晶体杆振动带隙研究

Vibration bandgaps of a phononic rod with piezoelectric shunting circuits

压电分流电路的电磁振荡可以使声子晶体杆产生局域共振带隙。分析了杆局域共振带隙的形成机理,运用传递矩阵法计算了杆的带隙结构,并对分流电路中电感、电容和电阻对局域共振带隙的影响进行了研究。压电分流电路的电磁振荡可以使压电片的等效弹性模量变为负值,从而使贴有压电片梁的弹性模量减小,当弹性模量实部等于零时,振动无法在杆中传播,形成局域共振带隙。通过改变分流电路中电感和电容参数可以方便的调节局域共振带隙的位置,为声子晶体带隙的主动控制提供一种新的方法。

The electromagnetic oscillations of piezoelectric shunting circuits can lead to local resonant gap in a phononic rod.Here,the formation mechanisms of the local resonant gap were analyzed.The band gaps of the rod were calculated with the transfer matrix method.Furthermore,the influences of the inductance,capacitance and resistance of the shunting circuits on the local resonant gap were studied.The electromagnetic oscillations of piezoelectric shunting circuits could make the equivalent elastic modulus of a piezoelectric patch become negative and reduce the elastic modulus of a beam with the piezoelectric patch.When the real part of the elastic modulus was equal to zero,vibration could not propagate in the rod,so the local resonant gap formed.The location of the local resonant gap could be adjusted through changing the inductance and capacitance of the shunting circuits.The results provided a new way to actively control band gaps of phononic crystals.