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Film/substrate structures are often seen in nature and engineering and their characteristic mechanical behaviors facilitating widespread application prospects. Surface patterns of film/substrate structures significantly affect the propagation of elastic waves. This paper investigates elastic wave propagation in the thin film/substrate periodic structure with sinusoidal surface patterns through the uniaxial tension. Based on the Bloch wave theory and numerical simulation, diverse bandgaps are triggered and the overall frequency range of the bandgaps shifts upward with the increase of the tensile strain, which demonstrates that tensioning the bilayer is a reliable and robust way for manipulating bandgaps. Band properties and bandgap evolution by various geometric and material parameters are discussed systematically, including various surface sinusoidal amplitudes, thickness of the substrate and various density or modulus ratio. The underlying mechanism of the exciting results in reversal design and regulation of structural geometry is revealed and is explained by using the spring-mass model. This work can provide new thought and insight for controlling wave propagation and promoting potential applications of the film/substrate systems and devices. [ABSTRACT FROM AUTHOR]

We investigate a one-dimensional discrete binary elastic superlattice bridging continuous models of superlattices that showcase a one-way propagation character, as well as the discrete elastic Su–Schrieffer–Heeger model, which does not exhibit this character. By considering Bloch wave solutions of the superlattice wave equation, we demonstrate conditions supporting elastic eigenmodes that do not satisfy the translational invariance of Bloch waves over the entire Brillouin zone, unless their amplitude vanishes for a certain wave number. These modes are characterized by a pseudo-spin and occur only on one side of the Brillouin zone for a given spin, leading to spin-selective one-way wave propagation. We demonstrate how these features result from the interplay of the translational invariance of Bloch waves, pseudo-spins, and a Fabry–Pérot resonance condition in the superlattice unit cell. [ABSTRACT FROM AUTHOR]

This work examines elastic wave propagation phenomena in open-cell foams with the use of the Bloch wave method and finite element analysis. Random foam topologies are generated with the Surface Evolver and subsequently meshed with Timoshenko beam elements, creating open-cell foam models. Convergence studies on band diagrams of different domain sizes indicate that a representative volume element (RVE) consists of at least 8³ cells. Wave directionality and energy flow features are investigated by extracting phase and group velocity plots. Explicit dynamic simulations are performed on finite size domains of the considered foam structure to validate the RVE results. The effect of topological disorder is studied in detail, and excellent agreement is found between the wave behavior of the random foam and that of both the regular and perturbed Kelvin foams in the low-frequency regime. In higher modes and frequencies, however, as the wavelengths become smaller, disorder has a significant effect and the deviation between regular and random foam increases significantly. [ABSTRACT FROM AUTHOR]

Magneto-electro-elastic (MEE) heterogeneous materials with periodic microstructure are investigated, with special focus on the particular case of a layered MEE material. By exploiting the transfer matrix method in combination with the Floquet–Bloch boundary conditions, the frequency dispersion spectrum can be derived by solving an eigenproblem, involving a 12 × 12 transfer matrix with palindromic characteristic polynomial. In particular, by assuming the cubic symmetry of layers, the problems involving longitudinal and transverse elastic waves are uncoupled. This circumstance has the advantage of simplifying the treatment and the size of the subproblems to be solved, corresponding to a 4 × 4 transfer matrix for the longitudinal case, and a 8 × 8 transfer matrix of the transverse problem, both characterized by palindromic characteristic polynomials. Afterward, a dynamic multi-field continualization approach is proposed to investigate wave propagation in MEE layered periodic material by matching the Z -transform of the vector collecting the nodal fields to the two-sided Laplace transform of the same vector at the macroscale. The continualization technique allows identifying multi-field integral-type non-local continua as well as multi-field generalized gradient-type (higher-order) non-local continua. Finally, to verify the accuracy of the proposed approach, the dispersion curves derived from the continualization technique are compared with the curves provided by the Floquet–Bloch theory. • Magneto-Electro-Elastic periodic microstructured materials are investigated. • Transfer matrix method is applied to obtain complex frequency dispersion spectra. • A dynamic multi-field continualization scheme of layered MEE is conceived. • Multi-field generalized gradient-type (higher-order) non-local continua are identified. [ABSTRACT FROM AUTHOR]

The periodic cellular topology characterizing the microscale structure of a heterogeneous material may allow the finest functional customization of its acoustic dispersion properties. The paper addresses the free propagation of elastic waves in micro-structured cellular materials. Focus is on the alternative formulations suited to describe the wave propagation in the material, according to the classic canons of solid or structural mechanics. Adopting the centrosymmetric tetrachiral microstructure as prototypical periodic cell, the frequency dispersion spectrum resulting from a synthetic lagrangian beam-lattice formulation is compared with its counterpart derived from different continuous models (high-fidelity first-order heterogeneous and equivalent homogenized micropolar continuum). Asymptotic perturbation-based approximations and numerical spectral solutions are cross-validated. Adopting the low-frequency band gaps of the material band structures as functional targets, parametric analyses are carried out to highlight the descriptive limits of the synthetic models and to explore the enlarged parameter space described by high-fidelity models. The final tuning of the mechanical properties of the cellular microstructure is employed to successfully verify the wave filtering functionality of the tetrachiral material. [ABSTRACT FROM AUTHOR]

Propagation of anti-plane waves through a discrete square lattice and through a continuous fibrous medium is studied. In the long-wave limit, for periodically heterogeneous structures the solution can be periodic or anti-periodic across the unit cell. It is shown that combining periodicity and anti-periodicity conditions in different directions of the translational symmetry allows one to detect different types of modes that do not arise in the purely periodic case. Such modes may be interpreted as counterparts of non-classical waves appearing in phenomenological theories. Dispersion diagrams of the discrete square lattice are evaluated in a closed analytical from. Dispersion properties of the fibrous medium are determined using Floquet-Bloch theory and Fourier series approximations. Influence of a viscous damping is taken into account. [ABSTRACT FROM AUTHOR]

• Bloch waves propagation in periodic thermodiffusive layered materials is studied • Trasfer matrix method is exploited to determine material frequency band structure • Palindromic characteristic polynomial is solved in terms of Floquet multipliers • Homogeneous and inhomoegenous waves propagation are investigated • Effects of thermodiffusive coupling on elastic waves propagation are studied The dynamic behaviour of periodic thermodiffusive multi-layered media excited by harmonic oscillations is studied. In the framework of linear thermodiffusive elasticity, periodic laminates, whose elementary cell is composed by an arbitrary number of layers, are considered. The generalized Floquet-Bloch conditions are imposed, and the universal dispersion relation of the composite is obtained by means of an approach based on the formal solution for a single layer together with the transfer matrix method. The eigenvalue problem associated with the dispersion equation is solved by means of an analytical procedure based on the symplecticity properties of the transfer matrix to which corresponds a palindromic characteristic polynomial, and the frequency band structure associated to wave propagating inside the medium is finally derived. The proposed approach is tested through illustrative examples where thermodiffusive multilayered structures of interest for renewable energy devices fabrication are analyzed. The effects of thermodiffusion coupling on both the propagation and attenuation of Bloch waves in these systems are investigated in detail. [ABSTRACT FROM AUTHOR]

• The elastic wave propagation in imass embedded pre-stressed regular and re-entrant hexagonal lattices is investigated. • The Bloch theorem in combination with the finite element method is introduced to obtain the band structures of the proposed lattice systems. • Veering phenomena and zero-frequency band gaps are identified in the band strucutre diagrams. • The Hurty-Craig-Bampton model reduction method is introduced to analyze the in-plane dynamics of the embedded hexagonal structures. This paper investigates the elastic wave propagation, mode veering, and in-plane vibration of pre-stressed hexagonal lattice embedded in an elastic medium and composed of axially loaded Timoshenko beams with attached point masses. The frequency band structure of the lattice system is obtained by solving the corresponding eigenvalue problem based on the Bloch theorem and the finite element method. The parametric study is performed by investigating the effects of the pre-stress magnitude, stiffness of elastic medium, and attached point masses on the band structure of a lattice unit cell. For simulating the free vibration behavior of the proposed lattices with different topologies, the Hurty-Craig-Bampton method is introduced to reduce the number of degrees of freedom. Based on the reduced finite element model, the natural frequencies are determined for various boundary conditions. The additional interface reduction technique, called system-level reduction, has been observed to achieve accurate results compared to that of the full model. Numerical experiments demonstrated a significant influence of the additional masses, pre-stress, and stiffness of elastic medium on Bloch waves and eigenvalues of the proposed lattice systems. The effects of different parameters on the emergence of mode veering phenomenon and band gaps are investigated in detail. [ABSTRACT FROM AUTHOR]