Dissipative Multiresonant Pillared and Trampoline Metamaterials with Amplified Local Resonance Bandgaps and Broadband Vibration Attenuation

The present study deals with the analysis of dissipative multiresonant pillared and trampoline effect-enhanced elastic metamaterials for the amplification of local resonance bandgaps. The study is conducted through a finite element-based numerical technique and substantiated with a discrete mass-in-mass analytical model. The band structures and wave dispersion characteristics of the multiresonant pillars erected on a thin elastic plate foundation are analyzed. Compared to a single-resonant metamaterial, this multiresonant structure innovatively creates wider bandgaps due to the coupling of resonance frequencies of the pillar modes with the base plate. For trampoline metamaterials, a periodic array of holes is made inside the plate. The holes forge the plate to work as a compliance base that enhances the system resonance frequency through intensive vibration of pillar-plate structure resulting in further amplified local resonance bandgaps. The enlargement of bandgaps also depends upon the height of the pillar and diameter of holes. Extremely wide low-frequency bandgaps can be achieved for a larger pillar height and a bigger hole diameter. Through a frequency response study, reported bandgaps are compared and an infinite unit cell model (band structure) is validated. The introduction of material loss factor (material damping) resulted in a broadband vibration attenuation zone spread throughout the frequency spectrum. Compared to a standard multiresonant pillared-plate model, the bandgap amplification caused by the trampoline effect induces a relatively larger bandwidth, and this superior characteristic together with the dissipative nature of the medium may facilitate potential design outcomes for manipulating subwavelength metamaterial properties over a broad range of frequencies.