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This study employs the wave dispersion relation of periodic structures to demonstrate the dual resonance mechanism occurring as a train traverses a series of bridges. Dual resonance occurs when the resonant speeds of both the train and the bridge coincide, leading to resonance in the bridge and progressively amplifying the train’s responses from the front to the rear carriages. This phenomenon involves a complex interaction between the bridge’s temporal resonance and the train’s spatial periodicity. This interaction creates a unique spatiotemporal vibration pattern. To understand the wave dispersion in this periodically coupled system, we model it as two interconnected spring-mass systems connected by contact springs. The analytical approach allows us to identify the key parameters governing the wave dispersion relation and wave-transmitting phenomena between two periodic structures. The wave dispersion analysis reveals that continuous beams have broader passbands, allowing them to transmit more waves and vibrations from moving trains than simply supported beams. This reduces resonance and leads to smoother system performance for continuous beams. Consequently, when a train travels on an equal-span continuous bridge at its resonance speeds, its vibrations can be efficiently transmitted to the bridge through these passbands, thereby mitigating resonance.

Single crystals of AgCuS, ${\mathrm{\text{Ag}}}_{1.55}{\mathrm{\text{Cu}}}_{0.45}\mathrm{\text{S}}$, ${\mathrm{\text{Ag}}}_{1.55}{\mathrm{\text{Cu}}}_{0.45}\mathrm{\text{S}}$ and ${\mathrm{\text{Ag}}}_{1.55}{\mathrm{\text{Cu}}}_{0.45}\mathrm{\text{S}}$ compounds were synthesized using the Bridgman method. The crystal structures and phase transitions were studied by X-ray diffraction (XRD) method in the high temperature ranges. The monoclinic, orthorhombic, hexagonal and cubic phases were observed in the temperature range of $300\mathrm{\text{K}}\le T\le 870\mathrm{\text{K}}$. Thermal expansion coefficients were calculated for different phases according to the lattice parameters. It was determined that the values of thermal expansion coefficients differ in different planes depending on the space group and symmetry.

The reduction of the periodicity of phononic crystals (PnCs) usually leads to the decrease of band gap (BG) width. However, a systematic study of the relationship between the unit cell and the supercell in the proposed hybrid stepped PnCs shows that the BG width can be increased in special cases. How the periodicity of PnCs affects the final BG characteristics is important for the design of PnCs with high structural performance. Supercell of PnCs with imperfections from the rotation of the unit cell was used to demonstrate the relationship between the unit cell and the supercell, which was further used for the wave attenuations of the proposed hybrid stepped PnCs. The rotation angle and the number of the rotating scatterers can be controlled for better structural performance for the PnCs. The different changes of the equivalent stiffness corresponding to the starting and the end frequencies lead to the increase of the BG width when the ration angle of the unit cell is $35^{\circ }$ in the supercell composed of zigzag scatterers and cross scatterers. The rotation of the unit cell in the supercell leads to the decrease of the starting frequency.

A two-variable polynomial invariant of non-oriented doubly periodic structures is proposed. A possible application of this polynomial for the classification of textile structures is suggested.

The pantograph-catenary system is essential to the operation of modern railways. The overhead catenary system serves to deliver steady electric power to the trains running on the railways. The propagation of waves in the catenary system can be significantly affected by its interaction with the pantograph. To investigate the wave transmission via the contact wires of a catenary system, a simplified model composed of a pre-tensioned wire suspended by periodic spring supports is adopted. For a periodic structure with wider band gaps (or stop bands), a larger cluster of frequencies of the transmitting waves can be filtered out. This is beneficial to the maintenance of the catenary system as unwanted vibrations have been reduced. To widen the band gaps, a resonator can be equipped on each of the spring supports for attenuation of a wider range of transmitting waves in the pre-tensioned wire. In this study, a unit cell conceived as the spring–resonator–wire unit is adopted to formulate the dispersion equation in closed form, from which the critical condition for widening the band gaps is derived. In addition, the moving pantograph is modeled as a moving force. From the exemplar study, it was shown that the installation of proper resonators on a catenary system can increase the gap bandwidth, such that the pantograph-induced wave transmission in the contact wires will be attenuated or filtered out.

This study investigates the effect of different unit cells on the mechanical performance of porous implant. Three shapes of unit cells (Diamond 30(DO30), Octet truss 30(OT30), and Rhombic dodecahedron 30(RD30)) were selected, which have the same relative density. Corresponding models of single pore (SP), repeating pores (RP) and porous implant (PI) were created. Using finite element methodology, mechanical performances of three classes of models under the conditions of pressure and torsion were simulated based on the same static load (SP: 50N, 0.125N$\cdot$m; RP: 200N, 0.5N$\cdot$m; PI: 200N, 0.5N$\cdot$m), respectively. Results demonstrated that RP showed consistent mechanical performances with SP: OT30 displayed the lowest stresses, displacements, and strains under the conditions of pressure and torsion, and conversely DO30 always resulted in the highest magnitudes. For the case of PI, mechanical performances were different from SP and RP: implant with shape of RD30 resulted in the lowest stress (275.2MPa) under the condition of pressure, but displacement (2.236e$-$002mm) and strain (3.050e$-$003) of OT30 were the largest; under the condition of torsion, stress sequence was same as SP and RP, but DO30 provided the highest strain (2.437e$-$003), RD30 displayed the largest displacement (1.508e$-$002mm). Unit cell influences mechanical performance of porous implant directly, and the implant outline and incomplete structure may also affect it. It could not select pore simply by the right type of unit cell, and surface area is an important parameter as well as pore size.

The compaction of a package of monosized spherical solid grains by rate-independent plasticity deformation is examined in this paper through the use of both yield design homogenization method and finite element simulation. Both modes of compaction, isostatic and closed die, are considered. In this study, the arrangement of powder consists of hexagonal array of identical spherical grains touching each other in its initial state. During the compaction process the response of the powder compacts is monitored in terms of behaviors of appropriate representative unit cells subject to axisymmetrical loading conditions. The kinematic approach of the yield design homogenization method has been used to determine external estimates of macroscopic strength criteria of powders at various stages of compaction. The obtained upper bound estimates are based on consideration of discontinuous incompressible velocity fields satisfying conditions of homogeneous strain rate. The shapes and sizes of the macroscopic yield surfaces are determined at various stages of compaction and it has been found that they depend upon the loading history as well as the relative density of the compact. Finite element simulations similar to those of Ogbonna N. and Fleck N. A. [1995] "Compaction of an array of spherical particles," Acta Metall. Mater.43(2), 603–620. have also been performed in order to (i) obtain the deformation modes as well as the evolution of the deformation mechanism of the powder compact during the whole process of compaction; (ii) derive the evolution of contact sizes between adjacent grains; (iii) examine the dependence of the macroscopic yield surface upon the degree of compaction, using the "yield probing technique" Gurson, A. L. and Yuan, D. W. [1995] A Material Model for a Ceramic Powder Based on Ultrasound, TRS Bend Bar, and Axisymmetric Triaxial Compression Test Results (ASME, New York), pp. 57–68, and (iv) validate, to some extent, the results provided by the kinematic approach.

In this paper, the numerical homogenization technique is used to evaluate the representative volume element and to compute the effective transverse thermal properties of unidirectional fibers reinforced composites. Three unit cells are constructed including square, hexagonal and random arrangement. The results obtained by finite element analysis showed the effect of unit cells configurations on the prediction of effective transverse thermal properties of unidirectional fibers composites for a wide range of fiber volume fractions and contrasts of properties. The numerical results are compared to available analytical models in the thermal conductivity of composites and experimental test results from the literature.