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

This study investigates the dynamic behaviors 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, and the first eight natural frequencies and corresponding mode shapes were extracted for each model. The results reveal that lower modes exhibit global bending and torsional behaviors, whereas higher modes demonstrate increasingly localized deformations. It is found that the natural frequencies decrease 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 of the natural frequency with the cross-sectional dimension and frame angle, achieving high predictive accuracy (R2 > 0.98). The experimental validation results were in good agreement with the numerical results, with discrepancies generally remaining below 7%. The developed regression model provides an efficient design tool for predicting vibrational behaviors and optimizing frame configurations without extensive simulations; furthermore, experimental modal analyses validated the numerical results, confirming the effectiveness of the model. Overall, this study provides a comprehensive understanding of the dynamic characteristics of re-entrant frame structures and proposes practical design strategies for improving vibrational performance, which is particularly relevant in applications such as machine foundations, vibration isolation systems, and aerospace structures.