Analysis of natural frequency for bioinspired functional gradient plates

Biological materials-fish scales exhibit ultra-flexibility due to its functionally graded materials. Inspired by the hierarchical gradient structure of fish scales, a new flexible gradient model that can adequately describe the characteristics of the bioinspired hierarchical structures is proposed in this work. To assess the flexibility of the proposed gradient model, a combination of extended finite element method (XFEM) and stabilized discrete shear gap (DSG) is established to analyze the vibration of bioinspired gradient plates with/without cracks. The DSG technique is employed to eliminate the shear locking phenomenon, while the XFEM is used for a mesh-independent modelling of crack. The combined approach is applicable to both moderately thick and thin plates, and is insensitive to mesh distortion. Functionally gradient plates take two types: power law function (Type I) and bioinspired hierarchical mode (Type II). For Type I, the natural frequencies decrease by increasing the gradient factor, i.e., the exponent of the power law. When the gradient factor is larger than one, the improvement of the plate stiffness by material gradient is restricted. For Type II, the natural frequencies are mostly independent of the step smoothing factor, yet quite sensitive to the number of step layers, providing an additional degree of freedom in tailoring the material properties. In addition, the natural frequencies of the bioinspired gradient plate are lower than that of the homogeneous ceramic plate. By using Type II, the stiffness of the plate can be reduced effectively, making the plate prone to deformation, which coincides with the flexible scale design. Therefore, the present study provides an incisive method and instructive guideline for a new era of artificially designed flexible materials inspired by natural (or biological) materials and structures.