Double-beam metastructure with inertially amplified resonators for flexural wave attenuation

Abstract

A new type of double-beam metastructure with periodically attached inertially amplified (IA) resonators is designed to attenuate the flexural wave propagation in the low-frequency range. An analytical approach based on the spectral element method (SEM) and the Wittrick-Williams algorithm is developed. The results of SEM show superior accuracy and an order of magnitude higher computational efficiency compared to the finite element method (FEM). Employing the developed approach, the wave attenuation behavior is presented as a function of the parameters including truss angle, beam thickness, IA mass, spring, and damper location to exhibit the perfect adjustability of bandgaps realized by the proposed structure. The local resonance bandgap frequencies are effectively lowered under the effect of inertial amplification. In addition, the damping amplification is also achieved by the IA structure, which is advantageous for extending the wave attenuation range. Finally, multibody dynamics numerical simulations are carried out to validate the reliability of the theoretical method and the rationality of simplifications used in the theoretical derivation. Furthermore, the formation mechanism of bandgaps is revealed by exploring the eigenmode shape on dispersion curves to obtain a thorough understanding of the structure.