Search

This article presents a multifield asymptotic homogenization scheme for the analysis of Bloch wave propagation in non-standard thermoelastic periodic materials, leveraging on the Green-Lindsay theory that accounts for two relaxation times. The procedure involves several steps. Firstly, an asymptotic expansion of the micro-fields is performed, considering the characteristic size of the microstructure. By utilizing the derived microscale field equations and asymptotic expansions, a series of recursive differential problems are solved within the repetitive unit cell Q. These problems are then expressed in terms of perturbation functions, which incorporate the material's geometric, physical, and mechanical properties, as well as the microstructural heterogeneities. The down-scaling relation, which connects the microscopic and macroscopic fields along with their gradients through the perturbation functions, is then established in a consistent manner. Subsequently, the average field equations of infinite order are obtained by substituting the down-scaling relation into the microscale field equations. To solve these average field equations, an asymptotic expansion of the macroscopic fields is performed based on the microstructural size, resulting in a sequence of macroscopic recursive problems. To illustrate the methodology, a bi-phase layered material is introduced as an example. The dispersion curves obtained from the non-local homogenization scheme are compared with those generated from the Floquet-Bloch theory. This analysis helps validate the effectiveness and accuracy of the proposed approach in predicting the wave propagation behavior in the considered non-standard thermoelastic periodic materials. [Display omitted] • Multifield asymptotic homogenization scheme in non-standard thermoelasticity. • Bloch wave propagation in periodic Cauchy materials is investigated. • The Green-Linsdsay model accounting for two relaxation times is leveraged. • Higher order approximations of complex frequency band structures are obtained. • Illustrative examples, validating the accuracy of the approach, are performed. [ABSTRACT FROM AUTHOR]

Magneto-electro-elastic (MEE) materials are attracting an increasing amount of scientific interest in physics, for their valuable potential in the functional management of mechanical-to-magnetoelectric energy conversions. The present paper focuses on heterogeneous MEE media – artfully realized by virtue of the periodic repetition of a multi-phase elementary cell – which represent promising solutions to passively control the propagation of multifield Bloch waves. Specifically, the linear continuum model governing the coupled free dynamics of a cellular non-dissipative MEE material is formulated for the unbounded three-dimensional domain. Then, the governing equations are specialized for a periodic layered waveguide with perfect inter-layer interfaces. The Floquet–Bloch decomposition is employed to analytically determine the uni-modular transfer matrix of the heterogeneous multi-layered cell. The related eigenproblem, governed by a palindromic characteristic polynomial in the Floquet multipliers, is solved in closed form to analyze the dispersion properties in the real-valued frequency domain and complex-valued wavenumber domain. Alternatively, a perturbation scheme is outlined to asymptotically approximate the exact eigensolutions. The dispersion spectra, composed of propagation and attenuation branches, are parametrically investigated for a two-layered periodic waveguide. The corresponding band structures are assessable a priori by leveraging the formal analogy with the stability analysis for non-autonomous dynamical systems. As main findings, slow-propagating quasi-shear-elastic waves and fast-propagating quasi-magneto-electric waves are found to dominate the low-frequency and high-frequency ranges, respectively, although some crossing points between the respective spectral branches can be detected. Quantitatively different but qualitatively similar behaviors of propagation and/or attenuation are observed for the quasi-shear-elastic waves and quasi-magneto-electric waves. Consequently, pass–pass, pass–stop and stop–stop bands of frequencies can be recognized and tuned by varying the key physical parameters. This rich spectral scenario opens the way for the functional customization of MEE-based metafilters or metapropagators, purposely designed to govern the transfer, localization, conversion, harvesting of energy across large frequency ranges. • Free wave propagation through a periodic non-dissipative MEE material is studied • The dispersion properties of periodic layered waveguide are analytically derived • Floquet multipliers are derived by solving the palindromic characteristic polynomial • Perturbation scheme is outlined to asymptotically approximate the eigensolutions • Pass–pass, pass–stop and stop–stop bands of frequencies can be recognized and tuned [Display omitted] [ABSTRACT FROM AUTHOR]

• Complex band structures are calculated by considering partial open-pore interfaces. • The first avoided crossing vanishes with the increase of pore blockage coefficient. • The first avoided-crossing becomes wide with the increase of the porosity. Complex band structures of the longitudinal wave propagation normally in fluid-saturated porous periodic structure with partial open-pore interfaces are calculated. The results show that the first avoided crossing gradually vanishes with the increase of the pore blockage coefficients. [Display omitted] The propagation of waves in fluid-saturated porous periodic structures is significantly affected by the interface condition between adjacent layers. We consider in this paper the partial-open pore interface condition between adjacent layers in a one-dimensional fluid-saturated porous phononic crystal. A transfer matrix method is devised to obtain both the complex band structure and the poroelastic Bloch waves of the crystal. Spectral transmission through a finite structure is further computed by a stiffness matrix method. Attention is restricted to normal incidence of longitudinal waves. The influence of the pore blockage, a parameter of the partial-open pore interface condition, and of porosity and viscosity are investigated. The value of the pore blockage is found to influence significantly both the dispersion of poroelastic waves but also the partition of wave energy between solid skeleton and pore fluid. The effects of porosity and viscosity in the case of the partial-open pore interface condition are similar to what was previously obtained in the fully open pore case. [ABSTRACT FROM AUTHOR]

• The Dirichlet-to-Neumann map method is extended to compute the band structures of 2D viscoelastic phononic crystals where the shear modulus of the viscoelastic matrix material is dependent of the frequency. • The relaxation time and the final-initial modulus ratio determine the main influence domain of the viscosity and the amplitude of the shear modulus. • The complex band structures are computed for different viscosity parameters and the wave propagation and attenuation with the change of the viscosity are analyzed. • Based on the storage shear modulus, the band structures are studied and compared with that of the purely elastic case. • The effects of various parameters on the band structures of viscoelastic phononic crystals are discussed. The effects of viscosity on the band-baps of two-dimensional (2D) viscoelastic phononic crystals are studied by the Dirichlet-to-Neumann (DtN) map method. The viscoelastic phononic crystals are composed of square or triangular lattices of elastic circular solid cylinders in a viscoelastic solid matrix. Time-harmonic anti-plane transverse (SH) waves are considered and the standard linear solid model is used to describe the viscoelastic behavior of the matrix material, in which the shear modulus depends on the frequency. Based on the DtN map constructed by using the cylindrical wave expansions, a linear eigenvalue problem related to the Bloch wave vector is formulated, which involves relatively small matrices. By using real frequencies and complex-valued wave vectors, the complex band structures are computed for different viscosity parameters, and the wave propagation and attenuation characteristics in dependence of the viscosity are analyzed. Then based on the storage shear modulus, real band structures for the Pb/epoxy phononic crystals with viscosity in the square and triangular lattices are studied, and the effects of the different viscoelastic material parameters and other relevant influencing parameters on the band-gaps are discussed. The results show that the viscosity of the matrix material affects the location and the width of the band-gaps. This fact provides an alternative way to tune the band-gaps of phononic crystals by adjusting the viscoelastic parameters combined with other influencing parameters. Band structures of the Pb/epoxy phononic crystal in the square lattice (a) and triangular lattice (b) for different (τ=1×10-5 s) [Display omitted] [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]