中文摘要：

针对固体基局域共振型声子晶体中难以出现100Hz以下的完全弹性波禁带问题,提出了一种新型声子晶体板,其结构由锥形复合散射体周期性阵列于一个二维二组元声子晶体板两边构成。采用有限元方法对其禁带特性和禁带形成机理进行理论研究,获得了声子晶体板中低频完全禁带的形成机理以及禁带调节规律。研究发现,不同形式的板波模态与对应的局域共振模态依据模态叠加原理相互耦合生成面内、面外两种禁带,二者叠加形成完全禁带;散射体振子的等效弹簧质量系统耦合是难以产生低频完全禁带的主要原因。研究结果表明：新型声子晶体板中散射体振子的等效弹簧质量系统可被引入的橡胶填充体解耦,致使面内、面外禁带分离;引入的锥形复合散射体可使相互分离的面内、面外禁带被同时单独调节至低频发生重叠,最终生成了一条频率范围为59~103Hz的低频完全禁带。研究结果和结论可将声子晶体应用于工程结构低频减振中。

英文摘要：

A novel phononic crystal plate is proposed to obtain a complete band gap below 100 Hz for the application of localized resonance phononic crystals （LRPCs） to the reduction of low- frequency vibration control in engineering. The structure of the plate is composed of double-sided taper composite stubs which are deposited on a 2D locally resonant PC plate, and its theoretical properties are studied. The dispersion relationship, the power transmission spectrum and the displacement fields of the eigenmode are calculated using a finite element method. It is shown that the coupling between the local resonance mode and the Lamb wave mode follows the modal superposition principle and is responsible for the formation of the band gaps. Moreover, the spring-mass system of the resonator is decoupled by introducing the rubber filler, and then the out-of-plane band gap and the in-plane band gap are adjusted into the same lowest frequency range respectively. As a result, the frequency range of the generated complete band gap is between 59 Hz and 103 Hz due to the overlap between the in-plane and out-of-plane band gaps. This study provides an effective way for phononic crystals to obtain complete band gaps in low-frequency range （below 100 Hz）, and has potential application to the reduction of low frequency vibration.