Design and Simulation of Innovative Applications Based on Triply Periodic Minimal Surfaces

Triply Periodic Minimal Surfaces (TPMS) are mathematically defined by a combination of trigonometric functions and characterized by having a zero mean curvature. They can be repeated in three spatial directions, forming continuous and periodic structures. Such properties make TPMS ideal for advanced engineering applications requiring optimized mechanical performance and lightweight solutions. While their realization was once constrained by traditional manufacturing techniques, recent advances in additive manufacturing, which now enable their production, have significantly increased the interest on these structures in various areas of research and industry. The present thesis explores the mechanical and acoustic applications of Triply Periodic Minimal Surfaces (TPMS), focusing on their feasibility for real-world engineering solutions. After analyzing the mathematical and geometrical properties of TPMS—including functionally graded and hybrid structures—we have studied beams with sinusoidal inertia inspired by TPMS-based variations, highlighting the effect of inertia oscillations on the buckling behavior. Additionally, we have investigated the use of TPMS as a novel design concept for airless tires, demonstrating promising mechanical performance. Finally, TPMS-based structures are proposed as innovative matching layers for ultrasonic transducers, showcasing their potential to optimize energy transmission efficiency and control acoustic band gaps.