Locally Resonant Band Gaps in Flexural Vibrations of a Timoshenko Beam with Periodically Attached Multioscillators

A new beam structure with periodically attached multioscillators is proposed based on the idea of locally resonant (LR) phononic crystals (PCs) to reduce flexural vibrations in the frequency-multiplication ranges. Wave band structures of the new beam are derived by using the transfer matrix method. The multiple band gaps in the beam are then verified by the frequency response function (FRF), which is calculated through the finite element method. In addition, simplified models are proposed, which contribute to the calculation of the edge frequencies of the band gaps and enhance the understanding of the LR mechanism of PCs. The accuracy of the simplified models is proven by comparing them with the results derived from the analytical model under different beam structure parameters. The results suggest that lower frequencies and ranges of frequency multiplications can be achieved in the band gaps which are obtained from the new beam structure with multioscillators in a unit cell. Therefore, the ideas presented in this paper have the potential to be used in developing new devices with frequency-multiplication characteristics for vibration isolation or noise control in aerospace and civil structures.