Free vibration characteristics of three-phases functionally graded sandwich plates using novel nth-order shear deformation theory

In this study, the authors investigate the free vibration behavior of three -phases functionally graded sandwich plates using a novel nth -order shear deformation theory. These plates are composed of a homogeneous core and two face -sheet layers made of different functionally graded materials. This is the novel type of the sandwich structures that can be applied in many fields of mechanical engineering and industrial. The proposed theory only requires four unknown displacement functions, and the transverse displacement does not need to be separated into bending and shear parts, simplifying the theory. One noteworthy feature of the proposed theory is its ability to capture the parabolic distribution of transverse shear strains and stresses throughout the plate's thickness while ensuring zero values on the two free surfaces. By eliminating the need for shear correction factors, the theory further enhances computational efficiency. Equations of motion are established using Hamilton's principle and solved via Navier's solution. The accuracy and efficiency of the proposed theory are verified by comparing results with available solutions. The authors then use the proposed theory to investigate the free vibration characteristics of three -phases functionally graded sandwich plates, considering the effects of parameters such as aspect ratio, side -to -thickness ratio, skin -core -skin thicknesses, and power -law indexes. Through careful analysis of the free vibration behavior of three -phases functionally graded sandwich plates, the work highlighted the significant roles played by individual material ingredients in influencing their frequencies.