In this paper, the vibration band gap properties of a two-dimensional square lattice are studied using the spectral element method. Before assembling the spectral equations of whole structures, the spectral stiffness matrices of the tensional and bending elements are established. The frequency responses of the lattices are calculated and compared with those obtained by the finite element method. It can be observed that the results in the spectral element method are more accurate, especially in high frequency ranges. The frequency band gap properties are analyzed based on the accurate frequency responses. The effects of the material and structure parameters on the band gap properties are investigated.
AnJShenJ (2013) A spectral-element method for transmission eigenvalue problems. Journal of Scientific Computing57: 670–688.
2.
ChenT (2013) Investigations on flexural wave propagation of a periodic beam using multi-reflection method. Archive of Applied Mechanics83: 315–329.
3.
DoyleJF (1997) Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, New York: Springer.
4.
GaoQYaoWAWuFZhangHWLinJHZhongWXHowsonWPWilliamsFW (2013) An efficient algorithm for computing the dynamic responses of one-dimensional periodic structures and periodic structures with defects. Computational Mechanics52: 525–534.
5.
HuangYLiuSZhaoJ (2013) Optimal design of two-dimensional band-gap materials for uni-directional wave propagation. Structural and Multidisciplinary Optimization48: 487–499.
6.
JianILeeU (2012) Spectral element analysis of the axial-bending-shear coupled vibrations of composite Timoshenko beams. Journal of Composite Materials46: 2811–2828.
7.
LanMWeiP (2013) Band gap of piezoelectric/piezomagnetic phononic crystal with graded interlayer. Acta Mechanica. DOI: 10.1007/s00707-013-0984-1.
8.
LeeU (2001) Dynamic characterization of the joints in a beam structure by using spectral element method. Shock and Vibration8: 357–366.
9.
LeeU (2009) Spectral Element Method in Structural Dynamics, Singapore: John Wiley & Sons.
10.
LiLChenTWuJWangX (2013) A discretized multi-freedom-degree model for predicting the lowest local resonant gap in phononic structures. Journal of Vibration and Control. DOI: 10.1177/1077546313479988.
11.
MadeoANeffPGhibaIDPlacidiLRosiG (2013) Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps. Continuum Mechanics and Thermodynamics. DOI: 10.1007/s00161-013-0329-2.
12.
MalmJSchlatter, Philipp, FischerPFHenningsonDS (2013) Stabilization of the spectral element method in convection dominated flows by recovery of skew-symmetry. Journal of Scientific Computing57: 254–277.
13.
NarisettiRKLeamyMJRuzzeneM (2010) A perturbation approach for predicting wave propagation in one-dimensional nonlinear periodic structures. Journal of Vibration and Acoustics132: 031001.
14.
NarisettiRKRuzzeneMLeamyMJ (2011) A perturbation approach for analyzing dispersion and group velocities in two-dimensional nonlinear periodic lattices. Journal of Vibration and Acoustics133: 061020.
15.
SalehiHAryadoustMShoushtariMZ (2013) Investigation the effect of lattice angle on the band gap width in 3D phononic crystals with rhombohedral(I) lattice. Applied Physics A: Materials Science & Processing. DOI: 10.1007/s00339-013-8084-6.
16.
TimoshenkoSPGereJM (1972) Mechanics of Materials, New York: Van Nostrand-Reinhold.
17.
WangYZLiFMKishimotoKWangYSHuangWH (2009) Elastic wave band gaps in magnetoelectroelastic phononic crystals. Wave Motion46: 47–56.
18.
WuZJLiFMWangYZ (2013a) Study on vibration characteristics in periodic plate structures using the spectral element method. Acta Mechanica224: 1089–1101.
19.
WuZJLiFMWangYZ (2013b) Vibration band gap behaviors of sandwich panels with corrugated cores. Computers and Structures129: 30–39.
20.
WuZJLiFMWangYZ (2014) Vibration band gap properties of periodic Mindlin plate structures using the spectral element method. Meccanica49: 725–737.
21.
WuZJWangYZLiFM (2013c) Analysis on band gap properties of periodic structures of bar system using the spectral element method. Waves in Random and Complex Media23: 349–372.
