Free transverse vibration in periodically hinged identical beams on elastic foundations: a single material phononic crystal

Abstract

Unlike the common phononic crystals (PCs) with different materials, the infinite periodically hinged identical beams on elastic foundations, considered as a special “single material” PC, also have transverse vibration band gaps (BGs). The modified transfer matrix method is proposed to calculate the band structure of this system. The propagation of transverse vibration of such a system with aluminium beams and soil foundation is studied. The results show that the system gives wider BGs than the common PC case at low frequency. The influence of the stiffness of foundation and geometrical parameters is analyzed to obtain a wider first BG. The frequency responses of the 6‐cell periodically hinged aluminium beams (solid line) and common aluminium‐epoxy PC beam (dashed line) on a foundation. The hinged case has wider low BGs with stronger attenuation. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Flexural vibration reduction of phononic crystal floating bridge

“…where The eigenvalue problems which contain the frequency dispersion relations of the indentically hinged and two-component rigid connected, section-hinged and cell-hinged PC floating bridges could be given, after using the Bloch's theorem [20]. Sovling the eigenvalue problems, the corresponding frequency dispersion relations and BGs ranges could be obtained.…”

Vibration attenuation in two-link flexible mechanical arms with periodic composite materials

“…PCs have wide potential applications such as noise control, new acoustic device, wireless communication, [28][29][30] vibration attenuation in beam, and beamfoundation systems and plate. [31][32][33][34][35][36] Inspired by the concept of PCs, we introduce the periodic composite materials to the flexible mechanical arms system, which would be a potential way to eliminate the vibration in mechanical arms system. In this article, first, we present the detailed derivation based on TMM and calculate the band structure in the mechanical arms with PCs as a theoretical solution.…”

Regulating elastic bandgaps in two‐dimensional lattice grid by periodical cut‐off operations

“…Recently, the propagation of elastic waves in periodic structures has received considerable attention . Bandgaps (BGs), within which there can be no propagation of elastic waves, exist.…”