含初应力周期性局域共振Mindlin板的衰减域特性研究
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摘要
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.
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.
引文
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[13] NATEGHI A,BELLE L V,CLAEYS C,et al.Wave propagation in locally resonant cylindrically curved metamaterial panels[J].International Journal of Mechanical Sciences,2017,127:73-90.
[14] RAO G V.A simple formula to predict the fundamental frequency of initially stressed square plates[J].Journal of Sound and Vibration,2001,246(1):185-189.
[15] GOFFAUX C,SáNCHEZ-DEHESA J,YEYATI A L,et al.Evidence of Fano-like interference phenomena in locally resonant materials [J].Physical Review Letters,2002,88(22):225502.
[ 2 ] GUO Z W,SHENG M P,PAN J.Effect of boundary conditions on the band-gap properties of flexural waves in a periodic compound plate[J].Journal of Sound and Vibration,2017,395:102-126.
[ 3 ] WANG Y Z,LI F M,KISHIMOTO K,et al.Band gaps of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress [J].European Journal of Mechanics A-Solids,2010,29(2):182-189.
[ 4 ] LIU X N,SHI Z F,XIANG H J,et al.Attenuation zones of periodic pile barriers with initial stress[J].Soil Dynamics & Earthquake Engineering,2015,77:381-390.
[ 5 ] ANDERSON M S.Vibration of prestressed periodic lattice structures[J].AIAA Journal,1982,20(4):551-555.
[ 6 ] QIAN Z,JIN F,KISHIMOTO K,et al.Effect of initial stress on the propagation behavior of SH-waves in multilayered piezoelectric composite structures[J].Sensors and Actuators A,2004,112(2):368-375.
[ 7 ] 魏唯一,刘金喜,方岱宁.初应力对周期压电-压磁层状结构中SH波传播特性的影响[J].工程力学,2010,27(11):184-190.WEI Weiyi,LIU Jinxi,FANG Daining.Effect of initial stress on the propagation characteristics of SH-waves in periodic piezoelectric-piezomagnetic layered structures[J].Engineering Mechanics,2010,27(11):184-190.
[ 8 ] FENG R X,LIU K X.Tuning of band-gap of phononic crystals with initial confining pressure[J].Chinese Physics B,2012,21(12):366-371.
[ 9 ] FENG R X,LIU K X.Tuning the band-gap of phononic crystals with an initial stress[J].Physica B Physics of Condensed Matter,2012,407(12):2032-2036.
[10] LIU X N,SHI Z F,MO Y L.Attenuation zones of initially stressed periodic mindlin plates on an elastic foundation[J].International Journal of Mechanical Sciences,2016,115/116:12-23.
[11] 石志飞,程志宝,向宏军.周期结构:理论及其在隔震减振中的应用[M].北京:科学出版社,2017.
[12] ZHONG H Z,YU T.A weak form quadrature element method for plane elasticity problems[J].Applied Mathematical Modelling,2009,33(10):3801-3814.
[13] NATEGHI A,BELLE L V,CLAEYS C,et al.Wave propagation in locally resonant cylindrically curved metamaterial panels[J].International Journal of Mechanical Sciences,2017,127:73-90.
[14] RAO G V.A simple formula to predict the fundamental frequency of initially stressed square plates[J].Journal of Sound and Vibration,2001,246(1):185-189.
[15] GOFFAUX C,SáNCHEZ-DEHESA J,YEYATI A L,et al.Evidence of Fano-like interference phenomena in locally resonant materials [J].Physical Review Letters,2002,88(22):225502.