Dispersion and band gaps of elastic guided waves in the multi-scale periodic composite plates

This paper presents dispersive behaviors and band gap characteristics of the multi-scale periodic composite plate reinforced with grapheme platelets (GPLs) and fibers. The plate consists of a laminated composite structure and an isotropic part. The material properties are measured by the layer-wise distribution of graphene platelets (GPLs) in nanocomposite matrix and fiber content in the laminated composite. Based on the first order shear deformation plate theory, Bloch theorem and the higher-order spectral elements, a semi-analytical approach is proposed for wave analysis of the periodic laminated composites. Considering the periodic boundary and analytic integration through the thickness, elastodynamic wave equation is established on the middle surface of the periodic unit cell, and then transformed into a one-dimensional problem by the Fourier transformation along the wave propagation direction, which improves the calculation efficiency. A second-order polynomial eigenvalue problem with regard to wave dispersion is obtained. Besides, the accuracy of the proposed approach is analyzed and the layer number of the nanocomposite laminate is determined. Various significant parameters including weight content of GPLs, fiber volume fraction and lattice size of the plate are taken into account to investigate guided wave propagation in the multi-phase periodic composite plates. The results indicate that full band gaps can be realized in the periodic multi-scale composite phononic crystal plates and partial band gaps appear in both in-plane and out-of-plane wave modes. The addition of reinforcements can efficiently regulate the center frequency and width of full and partial band gaps by changing GPLs content and fiber volume. Moreover, the variation of lattice parameter of the periodic composite plate has significant impact on the first full band gap. This work can provide guidelines to the developments of novel composite structures, acoustic devices and the applications in structural health monitoring.