Numerical and experimental analysis of the vibration and band-gap properties of elastic beams with periodically variable cross sections

References

• Richards D , Pines DJ . Passive reduction of gear mesh vibration using a periodic drive shaft. J Sound Vib. 2003;264:317–342.10.1016/S0022-460X(02)01213-0
   Web of Science ®Google Scholar
• Li FM , Song ZG . Vibration analysis and active control of nearly periodic two-span beams with piezoelectric actuator/sensor pairs. Appl Math Mech. 2015;36:279–292.10.1007/s10483-015-1912-6
   Google Scholar
• Carta G , Giaccu GF , Brun M . A phononic band gap model for long bridges. The ‘Brabau’ bridge case. Eng Struct. 2017;140:66–76.10.1016/j.engstruct.2017.01.064
   Web of Science ®Google Scholar
• Junyi L , Ruffini V , Balint D . Measuring the band structures of periodic beams using the wave superposition method. J Sound Vib. 2016;382:158–178.10.1016/j.jsv.2016.07.005
   Web of Science ®Google Scholar
• Casadei F , Beck BS , Cunefare KA , et al . Vibration control of plates through hybrid configurations of periodic piezoelectric shunts. J Intell Mater Syst Struct. 2012;23(10):1169–1177.10.1177/1045389X12443014
   Web of Science ®Google Scholar
• Han L , Zhang Y , Li XM , et al . Flexural vibration reduction of hinged periodic beam–foundation systems. Soil Dyn Earthquake Eng. 2015;79:1–4.10.1016/j.soildyn.2015.08.014
   Web of Science ®Google Scholar
• Yin J , Peng HJ , Zhang S , et al . Design of nacreous composite material for vibration isolation based on band gap manipulation. Comput Mater Sci. 2015;102:126–134.10.1016/j.commatsci.2015.01.032
   Web of Science ®Google Scholar
• Brillouin L . Wave propagation in periodic structures. 2nd ed. Dover; s1953.
   Google Scholar
• Mead DJ . Free wave propagation in periodically supported infinite beams. J Sound Vib. 1970;11(2):181–197.10.1016/S0022-460X(70)80062-1
   Web of Science ®Google Scholar
• Mead DJ , Parthan S . Free wave propagation in two-dimensional periodic plates. J Sound Vib. 1979;64(3):325–348.10.1016/0022-460X(79)90581-9
   Web of Science ®Google Scholar
• Gonella S , Ruzzene M . Homogenization of vibrating periodic lattice structures. Appl Math Model. 2008;32:459–482.10.1016/j.apm.2006.12.014
   Web of Science ®Google Scholar
• Yu DL , Wen JH , Shen HJ , et al . Propagation of flexural wave in periodic beam on elastic foundations. Phys Lett A. 2012;376:626–630.10.1016/j.physleta.2011.11.056
   Web of Science ®Google Scholar
• Yu DL , Wen JH , Shen HJ , et al . Propagation of steady-state vibration in periodic pipes conveying fluid on elastic foundations with external moving loads. Phys Lett A. 2012;376:3417–3422.10.1016/j.physleta.2012.09.041
   Web of Science ®Google Scholar
• Xu YL , Chen CQ , Tian XG . Phonon-polariton and band structure of electro-magneto-acoustic SH wave propagation oblique to the periodic layered piezoelectric structures. Phys Lett A. 2013;377:895–902.10.1016/j.physleta.2013.02.003
   Web of Science ®Google Scholar
• Heckl MA . Coupled waves on a periodically supported Timoshenko beam. J Sound Vib. 2002;252(5):849–882.10.1006/jsvi.2001.3823
   Web of Science ®Google Scholar
• Wu ZJ , Wang Y-Z , Li F-M . Analysis on band gap properties of periodic structures of bar system using the spectral element method. Waves Random Complex Media. 2013;23:349–372.10.1080/17455030.2013.830798
   Web of Science ®Google Scholar
• Wu ZJ , Li FM , Wang YZ . Vibration band gap behaviors of sandwich panels with corrugated cores. Comput Struct. 2013;129:30–39.10.1016/j.compstruc.2013.08.009
   Web of Science ®Google Scholar
• Wu ZJ , Li FM , Zhang C . Vibration band-gap properties of three-dimensional Kagome lattices using the spectral element method. J Sound Vib. 2015;341:162–173.10.1016/j.jsv.2014.12.038
   Web of Science ®Google Scholar
• Li FM , Zhang CZ , Liu CC . Active tuning of vibration and wave propagation in elastic beams with periodically placed piezoelectric actuator/sensor pairs. J Sound Vib. 2017;393:14–29.10.1016/j.jsv.2017.01.038
   Web of Science ®Google Scholar
• Liu Y , Gao LT . Explicit dynamic finite element method for band-structure calculations of 2D phononic crystals. Solid State Commun. 2007;144:89–93.10.1016/j.ssc.2007.08.014
   Web of Science ®Google Scholar
• Zuo SL , Li FM , Zhang C . Numerical and experimental investigations on the vibration band-gap properties of periodic rigid frame structures. Acta Mech. 2016;227:1653–1669.10.1007/s00707-016-1587-4
   Web of Science ®Google Scholar
• Wang YZ , Li FM , Kishimoto K . Effects of the initial stress on the propagation and localization properties of Rayleigh waves in randomly disordered layered piezoelectric phononic crystals. Acta Mech. 2011;216(1–4):291–300.10.1007/s00707-010-0371-0
   Web of Science ®Google Scholar
• Wang YZ , Li FM , Kishimoto K , et al . Wave localization in randomly disordered layered three-component phononic crystals with thermal effects. Arch Appl Mech. 2010;80(6):629–640.10.1007/s00419-009-0329-7
   Web of Science ®Google Scholar
• Li FM , Wang YS . Wave localization in randomly disordered multi-coupled multi-span beams on elastic foundations. Waves Random Complex Media. 2006;16(3):261–279.10.1080/17455030600758552
   Web of Science ®Google Scholar
• Yesilce Y , Catal HH . Free vibration of semi-rigidly connected piles embedded in soils with different subgrades. Int J Struct Stab Dyn. 2008;8(2):299–320.10.1142/S0219455408002661
   Web of Science ®Google Scholar
• Yesilce Y , Catal HH . Free vibration of piles embedded in soil having different modulus of subgrade reaction. Appl Math Model. 2008;32(5):889–900.10.1016/j.apm.2007.02.015
   Web of Science ®Google Scholar
• Shen HJ , Wen JH , Yu DL , et al . The vibrational properties of a periodic composite pipe in 3D space. J Sound Vib. 2009;328:57–70.10.1016/j.jsv.2009.07.032
   Web of Science ®Google Scholar
• Xu YL , Zhou XL , Wang W , et al . On natural frequencies of non-uniform beams modulated by finite periodic cells. Phys Lett A. 2016;380:3278–3283.10.1016/j.physleta.2016.07.057
   Web of Science ®Google Scholar