含初应力周期性局域共振Mindlin板的衰减域特性研究

Attenuation zones of initially stressed periodic local resonant Mindlin plates

基于弱形式求积元法,提出了含初应力周期性局域共振Mindlin板衰减域的新型计算方法。与存在精确解的特例进行对比,验证了该方法的正确性;对初应力和几何参数对衰减域特性的影响进行了系统分析;结果表明压初应力作用下衰减域的频率降低,衰减域内波的衰减程度降低;而拉初应力作用下衰减域的频率升高,衰减域内波的衰减程度增强;研究了有限周期性局域共振Mindlin板的频域和时域动力响应,进一步了验证衰减域的理论计算结果。该研究成果为周期性局域共振板在隔振中的应用提供了有益的理论指导。

A novel numerical approach based on the weak form quadrature element method was developed to study the attenuation zones of initially stressed periodic local resonant Mindlin plates.The presented method was validated by comparison with available analytical solutions in special cases.A comprehensive parametric study was conducted to investigate the effects of initial stress and geometric parameters on the attenuation zones.The results show that the compressive initial stress shifts the attenuation zones to lower frequencies and weakens the attenuation of waves in the attenuation zones,while the tensile initial stress shifts the attenuation zones to higher frequencies and enhances the attenuation of waves in the attenuation zones.Furthermore,the frequency-domain and time-domain dynamic responses analyses of a periodic local resonant Mindlin plate with finite unit cells were carried out to verify the theoretical results.The present work provides some useful guidelines to the design and application of periodic local resonant plates in vibration isolation.