A Three-variable Isogeometric Model for Free Vibration Analysis of Triply Periodic Minimal Surface Plates

Abstract

Triply Periodic Minimal Surface (TPMS) architectures offer an optimal balance of minimal weight and superior mechanical resilience. Consequently, they have emerged as excellent candidates for advanced engineering applications, including aerospace and biomedical structures. To better understand their vibrational behavior, this study presents an effective framework dedicated to the free vibration analysis of TPMS-based plates. The computational model employs isogeometric analysis (IGA) in conjunction with a higher-order plate theory. This approach efficiently reduces the required independent variables to three while automatically satisfying stress-free boundary conditions. The reliability of this numerical approach is first confirmed through benchmark comparisons. Subsequently, the study investigates the vibrational characteristics of plates modeled with Gyroid, Primitive, and I-graph and Wrapped Package-graph (IWP) architectures. A key focus is placed on the impact of architectural variation. Therefore, uniform (Uni.), symmetric (Sym.), and asymmetric (Asym.) porosity distributions along the plate's thickness are systematically analyzed. The computational results indicate a profound sensitivity of the natural frequencies to both the selected porosity distribution functions and the underlying TPMS geometries. Ultimately, these findings demonstrate the critical role of these parameters in optimizing lightweight, high-performance structural designs.