含压电分流阻尼的声学黑洞梁振动特性研究

Vibration characteristics of acoustic black hole beam with piezoelectric shunt damping

针对声学黑洞梁结构,引入压电分流阻尼形成声学黑洞压电复合结构,采用半解析法对其振动特性进行分析。首先基于哈密顿原理,采用墨西哥帽状小波作为型函数,利用能量法对声学黑洞悬臂梁的自由振动和受迫振动进行求解,与有限元法结果吻合良好,验证了半解析法的可靠性。然后引入分流阻尼,通过等效介质法将分流阻尼等效为附加材料,利用其局域共振机制,分析了含分流阻尼的声学黑洞梁振动特性,从理论上分析了确定局域共振频率近似方法。压电分流阻尼可以通过调整电感值来使局域共振与结构共振产生耦合,从而使振动响应峰值产生衰减;另一方面适当的阻尼可以使振荡效应消失。针对第一阶共振峰值,设计出的含分流阻尼的声学黑洞梁比传统阻尼层声学黑洞梁的振动有明显衰减,为声学黑洞结构的低频振动控制提供了新的思路。

Here,for acoustic black hole beam structure,piezoelectric shunt damping was introduced to form the acoustic black hole piezoelectric composite structure,and its vibration characteristics were analyzed using the semi-analytical method.Firstly,based on Hamilton principle,Mexican Hat wavelet was taken as the type function,and the energy method was used to solve free vibration and forced vibration of acoustic black hole cantilever beam.The results agreed well with those obtained using the finite element method to verify the reliability of the semi-analytical method.Then,the shunt damping was introduced,and the shunt damping was equivalent to an additional material by using the equivalent medium method.Using its local resonance mechanism,vibration characteristics of acoustic black hole beam with shunt damping were analyzed,and the approximate method to determine the local resonance frequency was analyzed theoretically.It was shown that piezoelectric shunt damping can adjust inductance value to make local resonance be coupled with structural resonance,and attenuate the peak value of vibration response;on the other hand,proper damping can make the oscillation effect disappear;for the first order resonance peak value,the vibration of the designed acoustic black hole beam with shunt damping is obviously attenuated comparing with that of the traditional acoustic black hole beam with damping layer to provide a new idea for low-frequency vibration control of acoustic black hole structures.