تحلیل ورق‌های سبک‌وزن با ساختار TPMS: ارتباط بین تخلخل، نسبت جرمی و فرکانس طبیعی با استفاده از تئوری تغییرشکل مرتبه‌بالا

This study investigates the free vibration behavior of TPMS-based porous plates—specifically IWP, Primitive, and Gyroid architectures—using a higher-order shear deformation theory. After determining the key morphological parameters governing each structure, the dimensionless natural frequencies were obtained analytically via Navier’s solution. Subsequently, the vibrational response was analyzed by varying geometric and mass-related parameters—including the in-plane aspect ratio, the relative mass ratio, and the porosity coefficient.
The results demonstrate that the Gyroid structure exhibits the highest natural frequency under all conditions, showing a remarkable stiffness-to-density ratio. In contrast, the Primitive structure displays the lowest frequency and greater sensitivity to porosity, making it well-suited for energy absorption applications. The IWP architecture demonstrates intermediate performance; notably, at higher relative mass ratios, its behavior closely approaches that of Gyroid, positioning it as a balanced and reliable option for practical engineering designs.
These findings establish a precise framework for the targeted design of lightweight structures with tailored vibrational characteristics, enabling optimized performance in aerospace, automotive, and biomedical applications.