负泊松比星型周期格栅结构的振动带隙特性

Bandgap Properties of Star-Shaped Periodic Grid Structure with Negative Poisson's Ratios

基于声子晶体的能带结构理论,结合弹性波动方程与Bloch定理建立结构单胞的动力学方程,研究负泊松比星型周期格栅结构的面内纵向振动与面外弯曲振动的带隙特性,发现其存在丰富的禁带特性,且在较低频率范围内存在稳定的宽大带隙。对比了2种振动模式的能带结构,研究了内凹夹角、长细比等几何参数对结构等效弹性参数与带隙特性的影响,并分析了带隙频率处单胞的振动模态。研究结果表明:星型格栅中存在2种振动都被抑制的完全带隙;内凹夹角和斜梁的几何参数是影响低阶带隙的关键;旋转共振模态的出现导致最低带隙处简并态的打开。星型周期格栅结构的这些带隙特性使其在工程减振降噪中具有潜在的价值。

Based on the band structure theory of phononic crystals,combined with the elastic wave equation and the Bloch theorem,the dynamic equation of the unit cell is established.The band gap of star-shaped periodic grid structure with negative Poisson's ratio is studied,including in-plane longitudinal vibration and out-of-plane bending vibration.It is found that the structure has rich band gap characteristics,and the lower frequency band gap is stable and wide.Band gaps of the two vibration modes are compared,and the influence of geometric parameters,such as the concave angle and slenderness ratio,on the equivalent elastic parameters and band gap is studied.It also analyses the vibration modes of the unit cell at the gap frequency.Results show that there is a complete band gap in which two vibrations are both suppressed.Concave angle and geometric parameters of the oblique beam are keys to the low-order band gap.The appearance of the rotating resonance mode leads to the lowest band gap.Band gap characteristics of the star-shaped periodic grid structure make it potentially valuable in engineering vibration and noise reduction.