Abstract：For low frequency structural vibration reduction, a type of Inertial Amplification Locally Resonant Phononic Crystals (IALRPC) is designed in this paper. Finite Element Method (FEM) in conjunction with Bloch theory is used to study the band structure of IALRPC and the wave transmission in finite IALRPC is also analyzed using FEM. Based on this, the band gaps induced by inertial amplification and by locally resonant mechanism are analyzed and compared. Considering the vibration reduction of a beam frame structure, IALRPC is designed to embed into the frame and significant low frequency vibration reduction is found due to the band gaps of the IALRPC and the introduction of damping by the viscoelastic materials. Furthermore, the design of the IALRPC is optimized to achieve full suppression of the fundamental mode of the frame. Experimental specimen is manufactured and tested. The results show that the IALRPC proposed in this paper can provide an effective new measure for low frequency reduction.
[1] Liu Z Y, Zhang X, Mao Y, et al., Locally resonant sonic materials [J]. Science, 2000,289(5485): 1734-1736.
[2] Huang H, Sun C, Locally resonant acoustic metamaterials with 2D anisotropic effective mass density[J]. Philosophical Magazine, 2011,91(6) : 981-996.
[3] Huang G L, Sun C T, Band gaps in a multi-resonator acoustic metamaterial[J]. Journal of Vibration and Acoustics 2010,132(3) : 031003.
[4] Sheng P, Mei J, Liu Z, et al., Dynamic mass density and acoustic, metamaterials [J].Physics Review B, 2007, 394 (2):256-261
[5] 王刚, 声子晶体局域共振带隙机理及减振特性研究[D].长沙：国防科学技术大学，2005.
Wang G, Research on the Mechanism and the Vibration Attenuation Characteristic of Locally Resonant Band Gap in Phononic Crystals[D].Changsha: National University of Defense Technology (2005)
[6] 肖勇, 局域共振型结构的带隙调控与减振降噪特性研究[D].长沙：国防科学技术大学，2012.
Xiao Y, Locally Resonant Structures: Band Gap Manipulation and Properties of Vibration and Noise Reduction[D]. Changsha: National University of Defense Technology (2012)
[7] Liu X N, HU G K, Huang G L, et al., An elastic metamaterial with simultaneously negative mass density and bulk modulus[J]. Applied Physics Letters,2011,98(25):251907
[8] Yap H W, Lakes R S, Negative stiffness and enhanced damping of individual multi-walled carbon nanotubes[J]. Physics Review B, 2008(77):045423.
[9] Lakes R S, Extreme Damping in Composite Materials with a Negative Stiffness Phase[J]. Physics Review Letters, 2001,86(13):2897-2900.
[10] Lakes R S, Lee T., Extreme damping in composite materials with negative stiffness inclusions. Nature, 2001, 410 (3): 565-567.
[11] Wang Y C, Swadener J G, Lakes R S, Two-dimensional viscoelastic discrete triangular system with negative-stiffness components[J]. Philosophical Magazine Letters, 2006. 86(2):99-112.
[12] Wang Y, Lakes R S , Stable extremely-high-damping discrete viscoelastic systems due to negative stiffness elements[J]. Applied Physics Letters, 2004. 84(22):4451-4453.
[13] Baravelli E, Carrara M, Ruzzene M, High stiffness-high damping chiral metamaterial assemblies for low-frequency applications[R]. Health Monitoring of Structural and Biological Systems, 8695.California USA: 2013:86952
