A Functionally Arranged Phononic Crystal Rod Enabling Ultra-Wideband Vibration Attenuation and Orderly Frequency Distillation

Abstract

In this study, a functionally arranged phononic crystal rod, incorporating sub-periodic structures featuring distinct lattice constants, is designed. This rod seamlessly combines two distinct capabilities: highly efficient broadband vibration suppression and orderly frequency distillation. In the pursuit of this design, the dispersion characteristics of a periodic rod are first analytically calculated to determine the precise cut-on and cut-off frequencies of the resulting band gaps. Following this, the transmission of longitudinal waves traveling through a finite functionally arranged rod is elucidated. Based on these calculations, careful parameter selection yields a compact configuration for a functionally arranged phononic crystal rod, boasting an exceptionally wide band gap spanning frequencies from 100 Hz to 10,000 Hz. Finite element simulations vividly demonstrate its ultra-broadband vibration attenuation capability, nonsymmetrical wave propagation behavior, and orderly frequency distillation phenomenon. Our study underscores the advantages of employing constituent materials with a higher impedance ratio in obtaining a more compact topological structure while preserving the broadband required for vibration attenuation. This research provides essential insights for tackling the need for broadband vibration suppression in engineering and also sets the stage for achieving orderly frequency extraction and energy localization.