物理学报2016，Vol.65Issue(6)：205-215,11.DOI:10.7498/aps.65.064602
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 prop erties of a multi-frequency lo cally resonant phononic plate
摘要
Abstract
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.关键词
局域共振/声子晶体板/弯曲波带隙/低频减振Key words
local resonance/phononic plate/flexural wave band gap/low-frequency vibration reduction引用本文复制引用
吴健,白晓春,肖勇,耿明昕,郁殿龙,温激鸿..一种多频局域共振型声子晶体板的低频带隙与减振特性∗[J].物理学报,2016,65(6):205-215,11.基金项目
国家自然科学基金(批准号:51305448)、航空科学基金(批准号:2015ZA88003)和国家电网公司科学技术项目(批准号:5299001352UC)资助的课题.* Project supported by the National Natural Science Foundation of China (Grant No.51305448), the Aeronautical Science Fund, Chinia (Grant No.2015ZA88003), and the Science and Technology Project of State Grid Company of China (Grant No.5299001352UC) （批准号:51305448）
