Taking a dynamic anti-resonance vibration isolator (DAVI) as a resonator, a periodic structure was constructed by attaching periodic arrays of local resonators to a beam. This structure could exhibit lower local resonance bandgap initial frequency. Based on the transfer matrix method and the Bloch theory, the theoretical model for longitudinal vibration elastic wave energy band structure of an infinite periodic slender beam was derived. Using the finite element method, the numerical model for longitudinal vibration transmission characteristics of a finite periodic slender beam was built. The simulation results agreed well with those of theoretical calculation. By analyzing the correlation between local resonance bandgap and DAVI resonator’s equivalent mass & stiffness, the vibration isolation mechanism of a dynamic anti-resonance periodic structure against longitudinal vibration of a slender beam was presented. The variation law of the local resonance bandgap was deduced. The study showed that compared with the spring-mass local resonator, the dynamic anti-resonance structure can be used to realize lower bandgap initial frequency.
Key words
local resonance /
slender beam /
photonic crystal /
dynamic anti-resonance /
transfer matrix method
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References
[1] Kushwaha M S, Halevi P, Dobrzynski L, et al. Acoustic band structure of periodic elastic composites [J]. Physical Review Letters, 1993, 71(13): 2022.
[2] Liu Z, Chan C T, Sheng P.Analytic model of phononic crystals with local resonances [J]. Physical Review B, 2005, 71(1): 014103.
[3] Lai Y, Zhang Z Q. Large band gaps in elastic phononic crystals with air inclusions [J]. Applied physics letters, 2003, 83(19): 3900-3902.
[4] 王刚.声子晶体局域共振带隙机理及减振特性研究[D].长沙:国防科技大学, 2005.
WANG Gang.Research on the mechanism and the vibration attenuation characteristic of locally resonant band gap in phononic crystals [D].Chang Sha:National university of defense technology,2005.
[5] Liu Z, Zhang X, Mao Y, et al. Locally resonant sonic materials[J]. Science, 2000, 289(5485): 1734-1736.
[6] 郁殿龙.基于声子晶体理论的梁板类周期结构振动带隙特性研究[D].长沙：国防科学技术大学, 2006.
YU Dian-long. Research on the vibration band gaps of periodic beams and plates based on the theory of phononic crystals[D].Chang Sha: National university of defense technology,2006.
[7] 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 Yong.Locally resonant structures:Band gap tuning and properties of vibration and noise reduction[D]. Chang Sha: National university of defense technology,2012.
[8] Flannelly W D. Dynamic antiresonant vibration isolator[P]: U.S. Patent 3,322,379. 1967-5-30.
[9] Rita A D, McGarvey J H, Jones R. Helicopter rotor isolation evaluation utilizing the dynamic antiresonant vibration isolator [J]. Journal of the American Helicopter Society, 1978, 23(1): 22-29.
[10] Braun D. Development of antiresonance force isolators for helicopter vibration reduction[J]. Journal of the American Helicopter Society, 1982, 27(4): 37-44.
[11] Braun D. Vibration isolator particularly of the antiresonance force type: U.S. Patent 4,781,363 [P]. 1988-11-1.
[12] Ivovich V A, Savovich M K. Isolation of floor machines by lever-type inertial vibration corrector[J]. Proceedings of the Institution of Civil Engineers-Structures and Buildings, 2001, 146(4): 391-402.
[13] Platus D L. Vibration isolation system[P]: U.S. Patent 3,606,233. 1971-9-20.
[14] Yilmaz C, Kikuchi N. Analysis and design of passive band-stop filter-type vibration isolators for low-frequency applications[J]. Journal of Sound and Vibration, 2006, 291(3): 1004-1028.
[15] 方俊鑫，陆栋. 固体物理学[M]. 上海：上海科学技术出版社，1980.
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