力-压电混合弹性超材料梁的带隙调节特性

为实现宽带低频减振，本文将力振子和串联负电容的压电分流振子分别置于基体上下两侧，设计了混合弹性超材料梁。基于传递矩阵法建立了理论模型，用于计算混合弹性超材料梁的频散关系和动态有效参数，通过有限元法进行了验证。分别采用理论方法和数值方法研究了电路元件参数对混合弹性超材料梁的带隙和振动衰减特性的调节机理，通过与单振子超材料的带隙对比，分析了两种振子间的相互影响。结果表明：电路元件参数主要影响压电分流振子产生的带隙的位置、宽度及带隙内的振动衰减程度；两种振子的带隙重叠区域不一定为通带；两种振子会因为负动态有效刚度范围靠近而相互影响。本研究将为此类超材料的设计提供参考依据。

Tunning characteristic of bandgaps of a mechanical-piezoelectric hybrid elastic metamaterial beam

A hybrid elastic metamaterial beam is designed to achieve broadband low-frequency vibration attenuation, in which the mechanical resonator and the piezoelectric shunt resonator with negative capacitance in series are respectively placed on the upper and lower sides of the substrate. Based on the transfer matrix method, a theoretical model is established to calculate the dispersion relation and dynamic effective parameters of the hybrid metamaterial beam, which is verified by the finite element method. The tunning mechanism of the circuit parameters on bandgaps of the hybrid metamaterial beam was studied by theoretical model. The vibration attenuation of the hybrid meta-structure was studied by the finite element method. Furthermore, the interaction between the two resonators was analyzed through comparing with the bandgaps of metamterials only with a single resonator. The results show that the circuit parameters mainly affect the position, width and vibration attenuation coefficient of the bandgap produced by the piezoelectric shunt resonator. In addition, the overlapping region of the two bandgaps produced by two resonators is not always the passband. Moreover, the two resonators will influence each other due to the adjacent negative dynamic effective stiffness ranges. This investigation will provide reference for the design of such hybrid metamaterial.