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

The present study deals with the analysis of dissipative multi-resonant 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 multi-resonant pillars erected on a thin elastic plate foundation is analyzed. Compared to a single-resonant metamaterial, this multi-resonant structure innovatively creates wider bandgaps due to the coupling of resonance frequencies of the pillar modes with the base plate. For trampoline metamaterials, 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 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 multi-resonant 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 frequency.