Reversely Superposing Low-Frequency Bragg Bandgap and High-Frequency Locally Resonant Bandgap for Broadband Vibration Reduction of Flexible Metamaterials

Flexible structures, like slender rods, beams and pipelines suffer from dense modal distributions, making broadband vibration suppression highly challenging. Metamaterial bandgaps provide a viable solution, though traditional methods-using low-frequency locally resonant bandgap and high-frequency Bragg bandgap-are either narrowband or demand impractical mass ratios. This study introduces a reverse strategy using a slender pipeline as a flexible model. We synergistically couple a low-frequency Quasi-Bragg bandgap (0-129 Hz, zero-frequency bandgap) from periodic clamps with a high-frequency locally resonant bandgap using lightweight resonators (similar to 10% mass ratio). We analyze the origin of each bandgap and the edge frequencies, through waves, vibration, and mode shapes, then examine the influence of system parameters to analyze the modulation patterns of the bandgaps to widen the bandgaps. Specifically, we find that nonperiodic clamps can broaden the low-frequency bandwidth, and further superposing Bragg bandgap and locally resonant bandgap can broaden the desired high-frequency bandwidth. Experiments considering different additional resonators, lattice constant, bandgap coupling, and nonperiodic supports are established to validate the theory. By combining different effects in experiment, we achieve substantial (20-60 dB) and nearly full-band (0-800 Hz) vibration reduction. This work establishes a robust framework for designing flexible metamaterials, offering a highly effective vibration control strategy for critical infrastructure.