## 5 Conclusions  
In this paper, the dynamic behaviors of FG-GPLs-reinforced plates are analyzed based on the first-order shear deformation theory within the framework of the state space. The method of reverberation-ray matrix (MRRM) is utilized to obtain the natural frequencies and dispersion spectra. By using the dual coordinates to avoid big number computation and eliminating the inversion of the zero matrix, MRRM can determine a solution which is inherently numerically stable. The free vibration and dispersion relation are revealed with a detailed examination of the influence of the GPLs weight fractions, GPLs size, distribution patterns, boundary conditions and aspect ratios. Numerical results show that the weight fraction and size of GPLs can improve the natural frequencies, and all the dispersion curves can be considerably affected by changing the graphene weight fraction, while only the flexural modes of the dispersion curves are sensitive to the graphene distribution, the boundary conditions and aspect ratios. It is envisaged that the present analysis can provide guidelines to design novel, better-performing composite structures. Conceptualization, Y.Z. and J.Z. ; funding acquisition, Y.Z. and J.Z. ; methodology, Y.Z. and D.L. ; writing--original draft, Y.Z. ; writing--review and editing, D.L. and J.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the Natural Science Foundation of China (11402002, 12072322), the Hebei Provincial Natural Science Foundation of China (A2021409004), the Hebei Provincial Higher Education Science and Technology Research Project--Top Young Talents Project (BJ2019059), the Hebei Provincial Introduced Oversea Scholars Foundation of China (C20210109). * (12) [PERSON]; [PERSON]; [PERSON] Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method. _Compos. Struct._**2018**, _193_, 281-294. [CrossRef]
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