一种多频局域共振型声子晶体板的低频带隙与减振特性

Low frequency band gaps and vibration reduction properties of a multi-frequency locally resonant phononic plate

设计了一种多频局域共振型声子晶体板结构,该结构由一薄板上附加周期性排列的多个双悬臂梁式子结构而构成.由于多个双悬臂梁式子结构的低频振动与薄板振动的相互耦合作用,这种局域共振型板结构可产生多个低频弯曲波带隙(禁带);带隙频率范围内的板弯曲波会被禁止传播,利用带隙可以实现对薄板的多个目标频率处低频减振.本文针对这种局域共振型板结构进行了简化,并基于平面波展开法建立了其弯曲波带隙计算理论模型;基于该模型,结合具体算例进行了带隙特性理论分析.设计、制备了一种存在两个低频弯曲波带隙的局域共振型板结构样件,通过激光扫描测振仪测试证实该结构存在两个低频带隙,在带隙频率范围的板弯曲振动被显著衰减.

A multi-frequency locally resonant（LR） phononic plate is proposed in this paper. The phononic plate consists of periodic arrays of multiple double-cantilevered thin beams attached to a thin homogeneous plate. This proposed phononic plate is simplified and modeled using a plane wave expansion method to enable the calculation of flexural wave band structures. The band gap behavior of the phononic plate is analyzed comprehensively. In addition, an experimental specimen is fabricated using a square aluminum plate with a thickness of 0.9 mm and an area of 840 mm × 840 mm, and attached to the specimens as periodic arrays of two types of double-cantilevered thin beams made of the same material as the host plate. And the specimen is measured by using a scanning laser Doppler vibrometer to verify the theoretical predictions of band gaps. Investigations of this paper yield the following findings and conclusions.1） Due to the interaction of low-frequency vibrational modes of attached multiple double-cantilevered beams and flexural vibration of the host plate, the proposed multi-frequency LR phononic plate can exhibit multiple low-frequency flexural wave band gaps（stop bands）. It is also found that the band gaps of a multi-frequency LR phononic plate,especially those appearing in a lower frequency range, are generally narrower than that of a single-frequency LR phononic plate with the same type of double-cantilevered beams.2） The frequency location of band gaps moves to higher frequency range when the thickness of the double-cantilevered beams is increased, or when the length of the double-cantilevered beams is decreased. It is also shown that a very small variation of the thickness（e.g., 0.1 mm） may lead to significant changes of frequency position of the band gaps.3） When the width of the double-cantilevered beams is enlarged or the number of the double-cantilevered beams is increased, the lower band gap edge will move to a lower frequency range, while the upper band gap edge will move to a higher frequency range. This implies that the bandwidth of the band gaps is broadened. However, at the same time, it is shown that the central frequencies of the band gaps remain almost unchanged.4） Experimental measurements of the fabricated specimen evidence the existence of two low frequency band gaps,and confirm that the flexural plate vibrations are significantly reduced in the predicted band gaps.