Analytical Solution of Stationary Coupled Thermoelasticity Problem for Inhomogeneous Structures

A mathematical statement for the coupled stationary thermoelasticity is given on the basis of a variational approach and the contact boundary problem is formulated to consider inhomogeneous materials. The structure of general representation of the solution from the set of the auxiliary potentials is established. The potentials are analyzed depending on the parameters of the model, taking into account the restrictions associated with additional requirements for the positive definiteness of the potential energy density for the coupled problem in the one-dimensional case. The novelty of this work lies in the fact that it attempts to take into account the effects of higher order coupling between the gradients of the temperature fields and the gradients of the deformation fields. From a mathematical point of view, this leads to a change in the roots of the characteristic equation and affects the structure of the solution. Contact boundary value problems are formulated for modeling inhomogeneous materials and a solution for a layered structure is constructed. The analysis of the influence of the model parameters on the structure of the solution is given. The features of the distribution of mechanical and thermal fields in the region of phase contact with a change in the parameters, which are characteristic only for gradient theories of coupled thermoelasticity and stationary thermal conductivity, are discussed. It is shown, for example, that taking into account the additional parameter of connectivity of gradient fields of deformations and temperatures predicts the appearance of rapidly changing temperature fields and significant localization of heat fluxes in the vicinity of phase contact in inhomogeneous materials.

Hearing the shape of a drum for light: isospectrality in photonics

The independent tailoring of wave quantities lays the foundation for controlling wave phenomena and designing wave devices. The concept of isospectrality, which suggests the existence of systems that provide identical spectra, has inspired a novel route to the spectrum-preserved engineering of wave–matter interactions in photonics, acoustics, and quantum mechanics. Recently, in photonics, constructing isospectral optical structures has become an emerging research topic to handle the intricate spectral responses of the systems composed of many-particles or inhomogeneous materials. The cornerstones in this field have stimulated the realization of non-Hermitian systems with real eigenspectra, one-dimensional structures exhibiting higher-dimensional physics, and novel engineering methodologies for broadband devices such as phase-matched multiplexers and multimodal lasing platforms. Here we review recent achievements based on isospectrality in photonics. We outline milestones in two different subfields of supersymmetric photonics and interdimensional isospectrality. We illustrate that isospectrality has paved the way for the independent control of wave quantities, showing great potential for the analytical and platform-transparent design of photonic systems with complex structures and materials.

Free Vibrations and Impact Resistance of a Functionally Graded Honeycomb Sandwich Plate

The functionally graded honeycomb has the characteristic of light weight, low density, high impact resistance, noise reduction, and energy absorption as a kind of new composite inhomogeneous materials. It has the advantages of both functionally graded materials and honeycombs. In this paper, a functionally graded honeycomb sandwich plate with functionally graded distributed along the thickness of the plate is constructed. The equivalent elastic parameters of the functionally graded honeycomb core are given. Based on Reddy’s higher-order shear deformation theory (HSDT) and Hamilton’s principle, the governing partial differential equation of motion is derived under four simply supported boundary conditions. The natural frequencies of the graded honeycomb sandwich plate are obtained by both the Navier method from the governing equation and the finite element model. The results obtained by the two methods are consistent. Based on this, the effects of parameters and graded on the natural frequencies of the functionally graded honeycomb sandwich plate are studied. Finally, the dynamic responses of the functionally graded honeycomb sandwich plate under low-speed impacts are studied. The results obtained in this paper will provide a theoretical basis for further study of the complex dynamics of functionally graded honeycomb structures.

A Theoretical Model For Predicting The Surface Topography of Inhomogeneous Materials After Shot Peening

Shot peening is widely used in engineering as a classical strengthening process. Although many studies on shot peening have been done, most have focused on homogeneous target materials. In this paper, a theoretical model is proposed for predicting the surface morphology of inhomogeneous target materials. The topography of target materials after single-shot impact is calculated on the basis of energy conservation and Hertz contact theory, and the final three-dimensional surface topography after multiple-shot impact is obtained through superposition. Single-shot and random multiple-shot finite element models are used to show the advantages of the proposed model over the existing theoretical model for homogeneous target materials. The roughness is found to increase with the shot velocity and shot radius.

Thermoelastic instability during sliding of inhomogeneous materials with different thermophysical properties

The conditions for the appearance of thermoelastic instability are determined by modeling of the frictional heating during sliding of the surface of an inhomogeneous material having a periodic structure, consisting of elements with different thermophysical properties. Cases of the absence of wear and steady-state wear conditions with a linear dependence of the wear rate on the applied pressure and sliding speed are considered. Keywords: inhomogeneous material, matrix, fiber, thermoelastic instability, wear, periodic structure. [email protected]

Three-Dimensional Broadband and Isotropic Double-Mesh Twin-Wire Media for Meta-Lenses

Lenses are used for multiple applications, including communications, surveillance and security, and medical instruments. In homogeneous lenses, the contour is used to control the electromagnetic propagation. Differently, graded-index lenses make use of inhomogeneous materials, which is an extra degree of freedom. This extra degree of freedom enables the design of devices with a high performance. For instance, rotationally symmetric lenses without spherical aberrations, e.g., the Luneburg lens, can be designed. However, the manufacturing of such lenses is more complex. One possible approach to implement these lenses is using metamaterials, which are able to produce equivalent refractive indices. Here, we propose a new type of three-dimensional metamaterial formed with two independent sets of wires. The double-mesh twin-wire structure permits the propagation of a first mode without cut-off frequency and with low dispersion and high isotropy. These properties are similar to periodic structures with higher symmetries, such as glide symmetry. The variations of the equivalent refractive index are achieved with the dimension of the meandered wires. The potential of this new metamaterial is demonstrated with simulated results of a Luneburg meta-lens.

Investigation of the Properties of Powder Materials Using Computer Modeling

Granulometric characteristics of structurally inhomogeneous materials based on full-scale mounds of a powder mixture of different fractional composition are established. Regularities of backfilling of powder particles of different shapes and sizes are revealed, and changes in the polydispersity of powder particles within each fraction are justified. It is proved that with a decrease in the average particle size of structurally inhomogeneous AlCu2 materials in a single fraction, the size spread relative to this value of other particles increases. The results of calculating the porosity of backfills with particles of various shapes (round, triangular, and square) depending on the cross-sectional area of the lobules are presented. A three-dimensional diagram is constructed that shows the relationships between the fractional composition of powder particles, their average diameter, and the degree of inhomogeneity of homogeneous bronze AlCu2.