ELASTIC WAVE BANDGAP TAILORING IN METAMATERIALS: NUMERICAL AND EXPERIMENTAL INVESTIGATIONS

Abstract

Phononic metamaterials exhibit unconventional and unusual approaches to control the subwavelength elastic/acoustic waves. Among various properties, the propagation of elastic waves is restricted over a frequency range known as bandgap. To achieve such bandgap phenomena, the metamaterials must be constructed by periodic unit cells with constituent materials of single phase or multiphase. The phononic crystal type bandgap metamaterials are realized primarily by harnessing Bragg’s scattering mechanism; nonetheless, it delivers bandgap at a high frequency level. In contrast, phononic materials dependent on local resonance mechanism are called Locally Resonant Metamaterials (LRMs), which exhibit the low frequency bandgap two orders of magnitude lower than the phononic crystals. Particularly, in LRMs bandgap emerges due to negative effective mass at dipole resonance, and negative effective stiffness near quadrupole/monopole resonances. Manipulating the interaction of the resonances is the key in achieving wide and low frequency bandgap. In recent years, several attempts have been made in this context; however, accomplishing wide and low frequency bandgap with smaller unit cell sizes remains challenging. Further, the presence of variable bandgap with externally applied deformation is highly desirable for different elastic wave propagation or mitigation related phenomena. Accordingly, for tailoring of bandgap the interplay of resonances with applied deformation must be investigated for various periodic units. At first, we developed a single phase metamaterial having periodically arranged divergent shaped star units for low frequency and wide bandgap. The simulation results demonstrate that the metamaterial exhibits an uninterrupted and extended bandgap of 10.92 kHz from 2 to 13 kHz frequency regime. We fabricated the structure based on numerical findings, elastic wave transmission characteristics have been analyzed using experimental techniques. Further, expanding the bandgap in the entire sonic range with single phase metamaterial is of major concern for broad frequency bandgap applications. Consequently, exploiting spatial periodicity, a single phase lattice subjected to local resonance mechanism is configured towards achieving a large frequency bandgap in sonic range. Numerical simulations reveal the presence of a comprehensive bandgap of 18 kHz in the 2 to 22 kHz range with systematically localizing the same constituent material in the lattice. Bloch wave modes unravel the involvement of dipole, monopole, and quadrupole resonances for wide and connected bandgaps. The existence of salient bandgaps is experimentally validated by analyzing the mechanical wave transmission. Moreover, once fabricated, the elastic wave bandgap metamaterials have fixed bandgap due to constant geometric configuration and hence limiting the number of intended usages. Thereby, tunability of bandgap in favor of its broadening and closing can extend their applicability for the next generation phononic devices. Although various attempts are made using multi-fields such as magnetic, electric and thermal etc., mechanical deformation based tunable bandgap is of great interest. Nonetheless, achieving tunability in terms of broadening or terminating the bandgap in multiphase LRM remains a challenging task. Subsequently, we propose LRM by integrating two-dimensionally periodically arranged square unit cells consisting of soft coated hard inclusion embedded in a polymer scaffold. We develop the numerical methodologies; firstly, the quasi-static nonlinear finite element framework to solve displacement field under applied external loading. Secondly, a linearized elasto-dynamics based finite element scheme is outlined to examine the dispersion response of deformed periodic unit cells. Further, analyzing the symmetry group of the unit cell under deformed state for a series of loading, we extract the bandgap responses. Moreover, to correlate the widening and terminating of bandgap with applied deformation, the presence of strong and weak coupling of locally resonant mode to dipole vibration modes are described. Afterwards, single phase phononic material has capability to produce a significant bandgap owing to the presence of dipole, monopole, and quadrupole resonances. We explore the alteration of bandgap in single phase symmetric and asymmetric star shaped structures with applied deformation. Simulation results reveal that the metamaterial exhibits a tailorable elastic wave bandgap with applied deformation. We extract the dispersion responses by considering the symmetry group of unit cell under applied deformation. We fabricated the structure based on numerical findings, and different levels of uniaxial tensile deformation are applied using inhouse developed mechanical device. Subsequently, with experimental technique elastic wave transmission characteristic has been extracted at various sets of applied deformation. Experimental observations are in good agreement with numerically predicted bandgaps. Finally, tailoring of bandgap with applied deformation is explained by cooperation and noncooperation of dipole and quadrupole/monopole resonances to the locally resonant vibration mode.