Propagation of flexural wave in periodic beam on elastic foundations

The propagation properties of flexural wave in the periodic beam on elastic foundations are studied theoretically. The wavenumbers and traveling wave characteristics in the beam on elastic foundations are analyzed. Basing on the equations of motion, the complex band structures and frequency response function are calculated by the transfer matrix method. And the Bragg and locally resonant gaps properties and the effects are researched. A gap with low frequency and wide range can exist in a beam on elastic foundations. -- Highlights: ► The flexural wave will be attenuate while frequency is under some pivotal frequency value. ► The effect on the pivotal frequency in two gap mechanism is different. ► A low frequency and wide range gap with strong attenuation can exist in this structure.