Numerical and Experimental Modal Analyses of Re-Entrant Unit Cell-Shaped Frames

This study investigates the dynamic behavior of re-entrant unit cell-shaped steel frames through numerical and experimental modal analyses. Inspired by re-entrant honeycomb structures, individual frame units were modeled to explore how natural frequencies vary with beam cross-sectional dimensions and frame angles. Twenty distinct frame models, incorporating four cross-sectional sizes (4×4 mm, 8×8 mm, 12×12 mm, and 16×16 mm) and five main frame angles (120°, 150°, 180°, 210°, and 240°), were developed using 3D modeling and finite element analysis (FEA) tools. The first eight natural frequencies and corresponding mode shapes were extracted for each model. The results revealed that lower modes exhibit global bending and torsional behaviors, whereas higher modes demonstrate increasingly localized deformations. The natural frequencies decrease by approximately 180° in the straight frame configuration and increase in the hexagonal configurations, highlighting the critical influence of the frame geometry. Increasing the cross-sectional size consistently enhances the dynamic stiffness, particularly in hexagonal frames. A quadratic polynomial surface regression analysis was performed to model the relationship between natural frequencies, cross-sectional dimensions, and frame angles, achieving high predictive accuracy (R² > 0.98). This regression model provides an efficient design tool for predicting vibrational behavior and optimizing frame configurations without extensive simulations. Experimental modal analyses validated the numerical results, confirming the effectiveness of the modeling approach. Overall, this study offers a comprehensive understanding of the dynamic characteristics of re-entrant frame structures and proposes practical design strategies for improving vibrational performance, particularly in applications such as machine foundations, vibration isolation systems, and aerospace structures.