To realize a broadened band gap as a potential application of vibration control in the electric vehicle powertrain system requires, a novel configuration of locally resonant (LR) beam with multi-oscillators attached is proposed, in which two types of oscillators are periodically and alternately attached at identical intervals. An analytical model is proposed based on transfer matrix method, which is validated by a finite element simulation. The band gaps in flexural vibration generated by this novel structure are investigated by the analytical model. The band gap coupling effect is observed and the influence of the intervals and oscillator parameters are discussed. The novel configuration effectively enlarges the range of band gaps in flexural vibrations.
HuangHSunC (2009) Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density. New Journal of Physics11: 013003.
7.
HuangHSunCHuangG (2009) On the negative effective mass density in acoustic metamaterials. International Journal of Engineering Science47: 610–617.
8.
HusseinMIHulbertGMScottRA (2006) Dispersive elastodynamics of 1D banded materials and structures: analysis. Journal of Sound and Vibration289: 779–806.
9.
HusseinMIHulbertGMScottRA (2007) Dispersive elastodynamics of 1D banded materials and structures: design. Journal of Sound and Vibration307: 865–893.
10.
KittelCMcEuenP (1976) Introduction to solid state physics, New York: Wiley.
11.
KushwahaMSHaleviPDobrzynskiL (1993) Acoustic band structure of periodic elastic composites. Physical Review Letters71: 2022–2025.
12.
LangleyR (1996) The response of two-dimensional periodic structures to point harmonic forcing. Journal of Sound and Vibration197: 447–469.
13.
LiuLHusseinMI (2012) Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance. Journal of Applied Mechanics-Transactions of the Asme79: 17.
14.
LiuZChanCShengP (2005) Analytic model of phononic crystals with local resonances. Physical Review B71: 014103.
15.
LiuZYZhangXXMaoYW (2000) Locally resonant sonic materials. Science289: 1734–1736.
16.
MaceB (1980) Periodically stiffened fluid-loaded plates, I: Response to convected harmonic pressure and free wave propagation. Journal of Sound and Vibration73: 473–486.
17.
MeadD (1973) A general theory of harmonic wave propagation in linear periodic systems with multiple coupling. Journal of Sound and Vibration27: 235–260.
18.
MeadD (1975a) Wave propagation and natural modes in periodic systems: I. Mono-coupled systems. Journal of Sound and Vibration40: 1–18.
19.
MeadD (1975b) Wave propagation and natural modes in periodic systems: II. Multi-coupled systems, with and without damping. Journal of Sound and Vibration40: 19–39.
20.
MeadD (1996) Wave propagation in continuous periodic structures: research contributions from Southampton, 1964–1995. Journal of Sound and Vibration190: 495–524.
21.
MeadDZhuDBardellN (1988) Free vibration of an orthogonally stiffened flat plate. Journal of Sound and Vibration127: 19–48.
22.
MeadDJ (1970) Free wave propagation in periodically supported, infinite beams. Journal of Sound and Vibration11: 181–197.
23.
MeadDJ (2009) The forced vibration of one-dimensional multi-coupled periodic structures: an application to finite element analysis. Journal of Sound and Vibration319: 282–304.
24.
PhaniASWoodhouseJFleckN (2006) Wave propagation in two-dimensional periodic lattices. The Journal of the Acoustical Society of America119: 1995–2005.
25.
RaoSS (2010) Mechanical Vibrations (5th Ed.), New Jersey: Printice Hall.
26.
RivinEI (2003) Passive Vibration Isolation, New York: Asme Press.
27.
RomeoFLuongoA (2002) Invariant representation of propagation properties for bi-coupled periodic structures. Journal of Sound and Vibration257: 869–886.
28.
RomeoFLuongoA (2003) Vibration reduction in piecewise bi-coupled periodic structures. Journal of Sound and Vibration268: 601–615.
29.
RuzzeneMBazA (2000) Control of wave propagation in periodic composite rods using shape memory inserts. Journal of Vibration and Acoustics122: 151–159.
30.
RuzzeneMScarpaFSorannaF (2003) Wave beaming effects in two-dimensional cellular structures. Smart Materials and Structures12: 363.
31.
SigalasMEconomouE (1992) Elastic and acoustic wave band structure. Journal of Sound and Vibration158: 377–382.
32.
StrasbergMFeitD (1996) Vibration damping of large structures induced by attached small resonant structures. The Journal of the Acoustical Society of America99: 335–344.
33.
Sun J-H, Lan C-W, Kuo C-Y, et al. (2012) A ZnO/silicon Lamb wave filter using phononic crystals. Frequency Control Symposium (FCS), 2012 IEEE International. IEEE, pp. 1-4.
34.
ThompsonD (2008) A continuous damped vibration absorber to reduce broad-band wave propagation in beams. Journal of Sound and Vibration311: 824–842.
WangJ (2009) Study on Instantaneous Vibration of Electric Motor Powertrain Mounting System of Vehicle. PhD Thesis, Tongji University, Shanghai, China.
38.
WangZYZhangPZhangYQ (2013) Locally Resonant Band Gaps in Flexural Vibrations of a Timoshenko Beam with Periodically Attached Multioscillators. Mathematical Problems in Engineering. 10.
39.
WenQHZuoSGWeiH (2012) Locally resonant elastic wave band gaps in flexural vibration of multi-oscillators beam. Acta Physica Sinica61: 7.
40.
WenXSWenJHYuDL (2009) Phononic Crystals, Beijing: National Defense Industry Press.
41.
XiaoYWenJHWangG (2013) Theoretical and Experimental Study of Locally Resonant and Bragg Band Gaps in Flexural Beams Carrying Periodic Arrays of Beam-Like Resonators. Journal of Vibration and Acoustics-Transactions of the Asme135: 17.
YuDLLiuYZWangG (2006a) Flexural vibration band gaps in Timoshenko beams with locally resonant structures. Journal of applied physics100: 5.
44.
YuDLLiuYZZhaoHG (2006b) Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom. Physical Review B73: 5.
