科研之友
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摘要
This paper systematically studies wave attenuation and band structure in functionally graded corrugated phononic crystal beams. The unit cell of the corrugated beam consists of the functionally graded parts and the homogeneous part. Considering the Timoshenko beam theory, the periodic boundary condition, and the particular coordinate transformation relation, the elastodynamic equation of functionally graded composite corrugated phononic crystal beams is established and discretized with the higher-order spectral elements. Based on Hamilton's principle and Fourier transformation, a semi-analytical approach for the corrugated beam is proposed in the framework of the Bloch theorem, which can provide the exact explicit complex solutions. Besides, the accuracy and convergence of the proposed method are discussed by comparison with the classical methods. The underlying mechanism that induces bandgaps and wave attenuation are demonstrated by analyzing the complex band structure of the corrugated phononic crystal beam. The results indicate that the appearance of bandgaps is the manifestation of exponentially decreasing transmission of evanescent waves in the corrugated beam. By tuning the superlattice configuration of the beam, customized bandgaps and broadband wave attenuation with lower frequency domain can be realized flexibly. Additionally, it can be observed that all elastic waves become evanescent modes by introducing the structural loss factor into the phononic crystal beam. This work gives several exciting and interesting results. A new thought has been developed for designing advanced acoustic materials and manipulating wave motion, which has much potential in functional acoustic devices with unique properties.
