Dissipative Elastic Metamaterials based Multi-Resonant Pillared and Trampoline Metamaterials with Broadband Vibration Attenuation Zone

Composite periodic structures based elastic metamaterials with peculiar effective dynamic material characteristics and fantastic wave manipulation properties to completely impede or amplify the propagation of elastic/acoustic waves have become an active research area since last two decades. The present study deals with the novel idea of dissipative elastic metamaterials with trampoline effect and metadamping phenomena. A unit cell of the multi-resonant composite pillared-plate structure is considered and trampoline effect is introduced through drilling periodic array of holes inside the plate. The holes reduce the stiffness of the plate and intensify the vibration between pillar-plate structure that results into deeper and wider local resonance bandgaps at subwavelength frequency regime. Installation of the holes further inculcate springboard effect that results into vibration of both pillar and plate structures. The coupling of the multi-resonant modes further enhances local resonance phenomena that results into wider and deeper bandgaps as compare to single resonant counterpart. The study is based on analytical and numerical model with finite and infinite periodic unit cell structures. The band structures with bandgaps for multi-resonant pillared-plate structure and trampoline metamaterials are presented side-by-side and amplification of local resonance bandgaps due to trampoline effect is reported. The obtained bandgaps are optimized through geometric and material parameter investigation and their effects on bandgaps are discussed. The findings of infinite unit cell model are validated through finite element based frequency response studies and excellent agreement is achieved between both models. Damping flattened the resonance peaks and expand the local resonance bandgaps throughout the frequency spectrum. Multi-resonant trampoline metamaterials based such extremely wide and subwavelength frequency bandgaps can find potential design outcomes for manipulating subwavelength metamaterials properties over a wide frequency spectrum.