Study on Tunable Band Gap of Flexural Vibration in a Phononic Crystals Beam with PBT

Low-frequency flexural vibration plays a significant role in beam vibration control. To efficiently attenuate the propagation of flexural vibration at a low-frequency range, this paper proposes a new type of a phononic crystals beam with an adjustable band gap. The governing equations of flexural vibration in a periodic beam are established based on the Euler theory and Timoshenko theory. The band structures are calculated by the plane wave expansion method, the attenuation properties and transmission response curves with a finite periodic beam are calculated by the spectral element method and finite element method. The effects of the elastic foundation and axial stress on band gaps are discussed in detail, and the regulation of the temperature field on the band gap is emphatically studied. The theoretical and numerical results show that the elastic foundation and axial stress have significant influence on the band gap, and the location and width of the band gaps can be adjusted effectively when the Young's modulus of PBT is changed by a varying temperature. The results are very useful for understanding and optimizing the design for composite vibration isolation beams.