相位失配弹性平板复合波导中的缺陷态*

为了在弹性波波导中实现缺陷态的调控,该文基于相位失配原理设计了一种周期性平板波导结构。以正弦边界弹性波导为例,通过连接具有不同相位的两段波导结构,形成了弹性板中不同程度的缺陷,并分析了其谱带特性和能量局域化特征。结果表明,禁带中存在两个不同模式的缺陷态,其以透射峰形式出现并随着相位的改变产生频移。与此同时,两个缺陷态在空间上对应的应力场和位移场分布也具有不同的模态特征。该文提出的复合弹性波导缺陷态调控方法,不仅为研究弹性波与结构之间的内在联系提供了关键的理论支持,也为实际弹性波探测器件的设计提供重要参考。     

周期变截面波导中的多缺陷态*

设计了一种具有对称结构的多缺陷周期变截面波导,并在其Bragg禁带中实现了多缺陷态的产生。研究表明,通过调整缺陷的个数和长度可实现对缺陷态数目的选择和缺陷态中心频率的调谐。另外,改变重复周期个数可对缺陷态的带宽进行调节。通过对各缺陷态的声场分布进一步分析,我们发现声压沿波导中心轴呈对称或反对称分布。对称缺陷态的最大声能量总是向长度较小的缺陷处偏移,而反对称缺陷态则相反,总是向长度较大的缺陷处偏移。利用这种偏移特性可实现对多缺陷态的声场调控。这不仅使我们对声缺陷态的认识更加深入,更有利于功能型声波导器件的发展与应用。     

Non-Bragg Resonance of Standing Acoustic Wave in a Cylindrical Waveguide with Sinusoidally Perturbed Walls

A novel type of acoustic resonance different from the well-known Bragg resonance is predicted theoretically in an acoustic cylindrical waveguide with sinusoidally perturbed hard walls. The resonance is caused by the interaction between the standing acoustic waves, i.e. transverse modes in the waveguide. It results in the frequency spectrum splitting and the appearance of forbidden bands. For small-perturbed wall corrugation, it is found that the shifts of resonant frequencies and the width of the forbidden gap can be as small as the wall amplitude. The appearance of the non-Bragg resonance depends highly on the wall period. When the period is greater than 2.319 times the average cylinder radius, all the non-Bragg resonances cut off. The smaller the wall period, the greater the transverse mode involvement.     

非Bragg禁带中的缺陷态

通过在周期柱状声波导中引入缺陷结构,研究了非Bragg禁带中的缺陷态.与传统Bragg禁带中的缺陷态相比,非Bragg禁带中的缺陷态具有完全不同的特性,所透射的缺陷模包含复杂的高阶横向模式,其形成与波导中的非Bragg共振密切相关.数值模拟表明缺陷态的频率与引入缺陷的几何尺寸有关,当缺陷长度变长时,非Bragg缺陷态与Bragg缺陷态一样向低频移动.而缺陷的半径变化时,非Bragg缺陷态却表现出完全不同的特性,随缺陷半径的变大而向高频移动.非Bragg缺陷态的这一反常变化与其模式结构密切相关,对非Bragg缺陷态的研究工作必将为声选频、滤波等器件的研制提供重要参考.     

Higher-Order Bragg Resonance in Gravity Surface Waves over Periodic Bottoms

A calculation method based on the Bloch theorem is developed for the gravity surface waves over the periodic bottoms of large undulations. The study shows the existence of comparable high-order bandgaps, which are demonstrated to result from the higher-order Bragg resonances, i.e. the resonant interactions between surface waves and the harmonic components of the fluctuating bottom. It is also shown that the band widths of the high-order gaps are quite sensitive to the amplitudes of high-order harmonics of the bottom.