Fractal Metamaterial Beams: Tuning Dynamic Stiffness and Vibration Attenuation

Despite recent advances in metamaterials, experimental studies addressing the dynamic behavior of waveguide-type fractals manufactured by means of additive manufacturing remain scarce, limiting understanding of their performance in real-world vibration control. This study investigates the dynamic behavior of fractal waveguide beams based on Sierpinski geometry through combined experimental and analytical approaches. Beams with iterations i = 0–3 were fabricated via stereolithography and tested under a doubly clamped configuration subjected to harmonic excitation. The dynamic response was captured using an accelerometer and analyzed in both time and frequency domains using Fast Fourier Transform. A single-degree-of-freedom mass–spring model was employed to estimate dynamic stiffness and validate experimental results. The findings reveal that fractal geometry significantly influences vibrational behavior, producing a nonlinear and non-monotonic evolution of stiffness and energy dissipation. The highest-order fractal beam exhibited the greatest vibration attenuation and resonance frequency (27.2 Hz), despite having the lowest effective mass, demonstrating an optimized stiffness-to-mass ratio. Spectral area analyses confirmed that energy dissipation increases with fractal complexity, enabling identification of transitions between stiffness- and inertia-dominated regimes. By identifying these regimes, this work provides a framework for engineering lightweight, adaptive structures for advanced vibration attenuation and tunable mechanical vibration control applications.