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Acoustic metamaterials allow for creating selective pass- and stop-bands on the frequency spectrum. We demonstrate the possibility of designing acoustic metamaterials as core-shell 2D-phononic media with an extremely simple morphology, the frequency spectrum of which contains many real-time tunable bandgaps. The connected shells of such metamaterials form a grid with square cells filled with nuclei partitionable into two subsystems. Both subsystems are characterized by their frequency spectra, and it is the coupling between them that generates the bandgaps. If the structural elements of the metamaterial are built based on magnetoelastomers, then bandgaps can be easily controlled by an external magnetic field that changes the elastic moduli of shells/cores. We have shown the possibility of manipulating single bandgaps in different parts of the spectrum, and simultaneous control of all bandgaps up to their complete disappearance. This manipulation can be carried out, specifically, with no change in the maximum achievable frequency in the metamaterial. The results obtained can be used for selective filtering of damaging wave components, active control of seismic or blast waves, sonar systems, ultrasound imaging, impact-resistant structures, and noise cancellation protocols. The physical concepts developed are extendable to 3D-structures in a similar fashion so can benefit a wider community.

Introducing multi-resonator microstructure into phononic metamaterials provides more flexibility in bandgap manipulation. In this work, 3D-acoustic metamaterials of the body- and face-centered cubic lattice systems encompassing nodal isotropic multivibrators are investigated. Our main results are: (1) the number of bandgaps equals the number, n, of internal masses as each bandgap is a result of the classical analog of the quantum level-repulsion mechanism between internal and external oscillations, and (2) the upper boundary frequencies, ωupper2i, i = 1, 2, ⋯, n, of the gaps formed coincide with eigen-frequencies, ωint;i2 ≠ 0, of the isolated multivibrator, ωupper2;i = ωint; i2, and the lower boundary frequencies, ωlower2,i2, are in good agreement with estimations as (), where represent the eigen-frequencies of the multivibrator when its external shell is motionless. The morphologies of the set of dispersion surfaces, ωm2(k), m = 1, 2, …, 6, in the corresponding passbands are similar to each other and to that of the set of dispersion surfaces, ωext; m2(k), obtained through the exclusion of internal masses. Thus, the problem of analyzing the acoustic properties of the complicated system is reduced to the study of two simple sets {ωint; i2} and , along with {ωext; m2(k)}, the morphology of which depends only on the type of lattice symmetry. This splitting renders controlled phononic bandgaps formation in homogeneous multi-resonator metamaterials feasible.

Modern armour graded thin steel plates benefit from significant elastic strength with high elastic energy storage capacity, which contributes to dissipation of total impulse from extensive blast loads within the bounds of the elastic region. Higher elastic energy storage capability mitigates the probability of catastrophic damage and ensuing large deformations compared to the conventional graded metallic panels. While blast assessment of such structures is important to design and application of protective systems, limited studies are available on their response to localised blasts. The present paper aims at deducing, from the minimization of Föppl-von Kármán (FVK) energy functional, the dynamic response of localised blast loaded thin elastic square plates undergoing large deformations. The presumed blast load function is a multiplicative decomposition of a prescribed continuous piecewise smooth spatial function and an arbitrary temporal function which may assume various shapes (e.g. rectangular, linear, sinusoidal, exponential). A kinematically admissible displacement field and the associated stress tensor were considered as a truncated cosine series with multiple Degrees-of-Freedom (DoF's). From the prescribed displacement field, having simply supported boundary conditions, useful expressions for stress tensor components were delineated corresponding to a unique mode and a series of differential equations were derived. The explicit solutions were sought using the Poincaré-Lindstedt perturbation method. The closed form solutions of each mode were corroborated with the numerical FE models and showed convergence when the first few modes were considered. The influence of higher modes, however, on the peak deformation was negligible and the solution with 3 DOF's conveniently estimated the blast response to a satisfactory precision.