Topological defects (including disclinations and dislocations) which commonly exist in various materials have shown an amazing ability to produce excellent mechanical and physical properties of matters. In this paper, disclinations and dislocations are firstly introduced into the valley-polarized elastic phononic plate. Deformation of the lattice yields the interface expressing as the topologically protected wave guiding, due to the valley-polarized phase transition of phononic crystals (PnCs) across the interface. Then, disclinations are introduced into the Wannier-type elastic phononic plate. The deformation of the lattice yielded by disclinations produces a pentagonal core with the local five-fold symmetry. The topological bound states are well localized around the boundaries of the pentagonal cores with and without the hollow regions. The topological interface state and the topological bound state immunize against the finite sizes and the moderate disturbances of plates, essentially differing from the trivial defect states. The discovery of topological defect states unveils a new horizon in topological mechanics and physics, and it provides a novel platform to implement large-scale elastic devices with robust topological waveguides and resonators.
We introduce a class of two-dimensional non-resonant single-phase phononic materials and investigate its peculiar dispersion characteristics. The material consists of a thin plate-like structure with an embedded periodic lattice of Acoustic Black Holes. The use of these periodic tapers allows achieving remarkable dispersion properties such as Zero Group Velocity in the fundamental modes, negative group refraction index, bi-refraction, and mode anisotropy. The dispersion properties are numerically investigated using a three-dimensional supercell plane wave expansion method. The effect on the di…
Based on the formalism developed by Psarobas et al [Phys. Rev. B 62, 278(2000)], which using the multiple scattering theory to calculate properties of simple phononic crystals, we propose a very simple method to study the NaCl-type phononic crystal. The NaCl-type phononic crystal consists of two kinds of non-overlapping elastic spheres with different mass densities, $L\acute{a}me$ coefficients and radius following the same periodicity of the ions in the real NaCl crystal. We focus on the (001) surface, and view the crystal as a sequence of planes of spheres, each plane of spheres has identical…
We investigate the effect of small spatiotemporal modulations in subwavelength-dimensioned phononic crystals with large band gaps, on the frequency spectrum for elastic waves polarized in the plane of periodicity. When the radius of cylinders periodically placed inside a matrix of highly-contrasting elastic properties is time-varying, we find that due to the appearance of frequency harmonics throughout the spectrum, the notion of a band gap is destroyed in general, although with the appropriate tuning of parameters, in particular the modulation frequency, it is possible that some band-gap regi…
We report a new type of phononic crystals with topologically non-trivial bandgaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern number of 1 and 2, indicating that these structures support single and multi-mode edge elastic waves immune to back-scattering. These robust one-way phono…
Distinct from the phononic valley pseudo-spin, the real physical spin of elastic waves adds a novel tool-kit capable of envisaging the valley-spin physics of topological valley phononic crystals from a local viewpoint. Here, we report the observation of local elastic valley spin as well as the hidden elastic spin-valley locking mechanism overlooked before. We demonstrate that the selective one-way routing of valley phonon states along the topological interface can be reversed by imposing the elastic spin meta-source at different interface locations with opposite valley-spin correspondence. We …
The resonance modes and the related effects to the transmission of elastic waves in a two dimensional phononic crystal formed by periodic arrangements of a two blocks unit cell in one direction are studied. The unit cell consists of two asymmetric elliptic cylinders coated with silicon rubber and embedded in a rigid matrix. The modes are obtained by the semi-analytic method in the least square collocation scheme and confirmed by the finite element method simulations. Two resonance modes, corresponding to the vibration of the cylinder along the long and short axes, give rise to resonance reflec…
Different omnidirectional refractive devices for flexural waves in thin plates are proposed and numerically analyzed. Their realization is explained by means phononic crystal plates, where a previously developed homogenization theory is employed for the design of graded index refractive devices. These devices consist of a circular cluster of inclusions with properly designed gradient in their radius. With this approach, the Luneburg and Maxwell lenses and a family of beam splitters for flexural waves are proposed and analyzed. Results show that these devices work properly in a broadband freque…
Beta-PtO2 is a useful transition metal dioxide, but its fundamental thermodynamic and elastic properties remain unexplored. Using first-principles calculations, we systematically studied the structure, phonon, thermodynamic and elastic properties of beta-PtO2. The lattice dynamics and structural stability of beta-PtO2 under pressure were studied using the phonon spectra and vibrational density of states. The vibrational frequencies of the optical modes of beta-PtO2 increase with elevating pressure; this result is comparable with the available experimental data. Then, the heat capacities and th…
The localization of waves in two-dimensional clusters of scatterers arranged in relatively twisted lattices is studied by multiple scattering theory. It is found that, for a given frequency, it is always possible to find localized modes for a discrete set of rotation angles, analogous to the so-called "magic angles" recently found in two-dimensional materials like graphene. Similarly, for small rotations of the lattices, a large number of resonant frequencies is found, whose position strongly depends on the rotation angle. Moreover, for angles close to those that make the two lattices commensu…
We study the effect of planar defects in phononic crystals of spherical scatterers. It is shown that a plane of impurity spheres introduces modes of vibration of the elastic field localized on this plane at frequencies within a frequency gap of a pure phononic crystal; these show up as sharp resonances in the transmittance of elastic waves incident on a slab of the crystal. A periodic arrangement of impurity planes along a given direction creates narrow impurity bands with a width which depends on the position of these bands within the frequency gap of the pure crystal and on the separation be…
In this work we theoretically study the interface acoustic states of resonators on a thin plate with topologically protected and conventional designs. Topologically protected interface state is first analyzed by employing the conception of breaking inversion symmetry within the unit cell of a honeycomb lattice for cylindrical and spherical resonators; we further demonstrate the robustness of the wave propagation along a zig-zag path containing sharp corners, defect and disorder. The wave propagation ceases to be preserved if we increase the degree of disorder along the zig-zag path. In paralle…
We experimentally investigate the valley-Hall effect for interfacial edge states, highlighting the importance of the modal patterns, between geometrically distinct regions within a structured elastic plate. These experiments, for vibration, are at a scale where detailed measurements are taken throughout the system and not just at the input/output ports; this exposes the coupling between geometrically distinct modes that underlie the differences between wave transport around gentle and sharp bends.
Spectral gaps in the vibrational modes of disordered solids are key design elements in the synthesis and control of phononic metamaterials that exhibit a plethora of novel elastic and mechanical properties. However, reliably producing these gaps often require a high degree of network specificity through complex control optimization procedures. In this work, we present as an additional tool to the existing repertoire, a numerical scheme that rapidly generates sizeable spectral gaps in absence of any fine tuning of the network structure or elastic parameters. These gaps occur even in disordered …
The band structure in phononic crystals (PCs) is usually affected by the deformations of their soft components. In this work, hyperelastic transformation media is proposed to be integrated in the PCs'design, to achieve stable elastic band-gaps which is independent with finite mechanical deformations. For a one-dimensional (1D) PC, we demonstrate the semi-linear soft component can keep all elastic wave bands unchanged with the external deformation field. While for neo-Hookean soft component, only S-wave bands can be precisely retained. The change of the P-wave bands can be predicted by using a …
A full band gap of the longitudinal mode of elastic waves centered near 2.8 MHz with a width of ~ 1 MHz has been observed in the phononic crystals made of body centered tetragonal tungsten carbide spheres imbedded in aluminum matrix. Two defects states in the band gap due to a 7-sphere defect cluster with silicon nitride spheres have also been observed. Transmitted pressure field pattern clearly shows that at the defect state frequencies the ultrasonic waves transmitted through the doped crystal are emitted from the defect cluster.
We report an experimental study of the elastic properties of a two-dimensional (2D) colloidal crystal subjected to light-induced substrate potentials. In agreement with recent theoretical predictions [H.H. von Gruenberg and J. Baumgartl, Phys. Rev. E 75, 051406 (2007)] the phonon band structure of such systems can be tuned depending on the symmetry and depth of the substrate potential. Calculations with binary crystals suggest that phononic band engineering can be also performed by variations of the pair potential and thus opens novel perspectives for the fabrication of phononic crystals with …
We quantize the elastic modes in a plate. For this, we find a complete, orthogonal set of eigenfunctions of the elastic equations and we normalize them. These are the phonon modes in the plate and their specific forms and dispersion relations are manifested in low temperature experiments in ultra-thin membranes.
An effective medium theory for resonant and non-resonant metamaterials for flexural waves in thin plates is presented. The theory provides closed-form expressions for the effective parameters of arrangement of inclusions or resonators in thin plates as a function of the filling fraction of the inclusions, their physical properties and the frequency. It is shown that positive or negative effective elastic parameters are possible depending on the symmetry of the resonance but, unlike it happens for bulk elastic waves, the responsible for the negative mass density behaviour is the monopolar term,…
Material surface may have a remarkable effect on the mechanical behavior of magneto-electro-elastic (or multiferroic) structures at nano-scale. In this paper, a surface magneto-electro-elasticity theory (or effective boundary condition formulation), which governs the motion of the material surface of magneto-electro-elastic nano-plates, is established by employing the state-space formalism. The properties of anti-plane shear (SH) waves propagating in a transversely isotropic magneto-electro-elastic plate with nano-thickness are investigated by taking surface effects into account. The size-depe…
Platonic crystals (PCs) are the elastic plate analogue of the photonic crystals widely used in optics, and are thin structured elastic plates along which flexural waves cannot propagate within certain stop band frequency intervals. The practical importance of PCs is twofold: these can be used either in the design of microstructured acoustic metamaterials or as an approximate model for surface elastic waves propagating in meter scale seismic metamaterials. Here, we make use of the band spectrum of PCs created with very small clamped holes, the nails of the title, to achieve surface wave reflect…
Highly confined Love modes are demonstrated in a phononic crystal based on a square array of etched holes in SiO 2 deposited on the ST-cut quartz. An optimal choice of the geometrical parameters contributes to a wide stop-band for shear waves' modes. The introduction of a defect by removing lines of holes leads to the nearly flat modes within the band gap and consequently paves the way to implement advanced designs of electroacoustic filters and high-performance cavity resonators. The calculations are based on the finite element method in considering the elastic and piezoelectric properties of…
We rigorously derive a Kirchhoff plate theory, via $Γ$-convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin sheet. The heterogeneity in the elastic properties of the material results in a spontaneous strain that depends on both the thickness and the plane variables $x'$. At the same time, the spontaneous strain is $h$-close to the identity, where $h$ is the small parameter quantifying the thickness. The 2D Kirchhoff limiting model is constrained to the set of isometric immersions of the mid-plane of the plate into $\mathbb…
It is known that design of elastic cloaks is much more challenging than the design idea for acoustic cloaks, cloaks of electromagnetic waves or scalar problems of anti-plane shear. In this paper, we address fully the fourth-order problem and develop a model of a broadband invisibility cloak for channelling flexural waves in thin plates around finite inclusions. We also discuss an option to employ efficiently an elastic pre-stress and body forces to achieve such a result. An asymptotic derivation provides a rigorous link between the model in question and elastic wave propagation in thin solids.…
