Abstract The idea of periodic stucture of phononic crystals is introduced to the physical design of the beam, and the propagation of coupled flexural-torsional vibration in the periodic Timoshenko beam composed of two kinds of materials including warping effect is investigated. Based on the equation of coupled flexural-torsional vibration of beam, the band structure of such a beam are presented by making use of the transfer matrix theory. The transmission characteristic of vibration of the finite periodic beams is simulated by using finite element method, which shows vibration attenuation in the range of frequency agrees well with the band gap. Comparing with the band structure obtained from the condition ignoring the warping effect, the result has shown that it may be getting the meaningless result if igoring the warping deformation.
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