CHEN Qi-yong, HU Shao-wei, ZHANG Zi-ming. Research on the Vibration Property of the Beam on Elastic Foundation Based on the PCs Theory[J]. Applied Mathematics and Mechanics, 2014, 35(1): 29-38. doi: 10.3879/j.issn.1000-0887.2014.01.004
Citation: CHEN Qi-yong, HU Shao-wei, ZHANG Zi-ming. Research on the Vibration Property of the Beam on Elastic Foundation Based on the PCs Theory[J]. Applied Mathematics and Mechanics, 2014, 35(1): 29-38. doi: 10.3879/j.issn.1000-0887.2014.01.004

Research on the Vibration Property of the Beam on Elastic Foundation Based on the PCs Theory

doi: 10.3879/j.issn.1000-0887.2014.01.004
  • Received Date: 2013-08-26
  • Rev Recd Date: 2013-09-03
  • Publish Date: 2014-01-15
  • Axial loads imposed on the structure influence the vibration properties and cause the change of vibration resistance functions. Theory about the band gap properties of phononic crystals (PCs) were used to study the flexural vibration band gaps of an Euler beam on elastic foundation. A flexural vibration model of the infinite periodic PCs Euler beam was established, which was under the actions of axial force and Winkler foundation. A modified transfer matrix (MTM) method was applied to calculate the band structure of the beam. The change tendency of the band structure were estimated on the basis of the band structure. Results show that axial loads influence the band gaps and band frequency ranges. Axial tensile loads elevate the band gap frequencies, but the base band gaps remain unchanged; axial compressive loads lower the band gap frequencies, and the base band gap frequencies drop when the amplitudes of the compressive loads increase. Meanwhile, the Euler beam model was numerically simulated, and the results were matched with the analytical ones. Through adjusting the magnitude of the axial loads, different band frequency ranges and effects of vibration reduction could be achieved.
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