Narrow Results

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.

We consider a family of Schrödinger operators supported by a periodic chain of loops connected either tightly or loosely through connecting links of the length $\ell >0$ with the vertex coupling which is non-invariant with respect to the time reversal. The spectral behavior of the model illustrates that the high-energy behavior of such vertices is determined by the vertex parity. The positive spectrum of the tightly connected chain covers the entire halfline while the one of the loose chain is dominated by gaps. In addition, there is a negative spectrum consisting of an infinitely degenerate eigenvalue in the former case, and of one or two absolutely continuous bands in the latter. Furthermore, we discuss the limit $\ell \to 0$ and show that while the spectrum converges as a set to that of the tight chain, as it should in view of a result by Berkolaiko, Latushkin, and Sukhtaiev, this limit is rather non-uniform.

Stainless steel surface was irradiated by linear polarized laser (800 nm, 35 fs, 4 Hz and 0.7 J/cm²) with different pulse numbers. Environmental scanning electron microscope (ESEM/EDS) was used for detailed morphology, microstructure and composition studies. The wettability of irradiated steel surface was tested by Interface Tensiometer JC-2000X and compared with untreated stainless steel. Results showed that micro/nanostripes with different periods were formed. The period increased with the increasing pulse numbers from 450 nm for 90 pulses to 500 nm for 180 pulses. The orientation of those stripes was parallel with the laser beam polarization. Nanoparticles were observed on those periodic structures. EDS indicated that the atomic ratio of Cr increased and the atomic ratios of Fe and Ni decreased after laser irradiation, which may enhance the corrosion resistance due to the Cr-rich layer. The prepared structure exhibited hydrophobic property without further treatment. The formation mechanism of micro/nanoperiodic structures was also explored.

We proposed a kind of unit cell composed of simple steel plate structures in this work. A variety of acoustic phenomena including anomalous refraction, asymmetric transmission, acoustic splitting and acoustic focusing were realized by coding the unit cells with different splicing modes. The transformation from plane acoustic wave to vortex acoustic wave was also realized by using the coding method of three-dimensional rotation. This work increased the functionality of the unit cell and provided a method for the design of sub-wavelength acoustic devices.

The aim of this paper is to give an account of some problems considered in the past years in the setting of Discrete Dynamical Systems and Iterative Functional Equations, some new research directions and also state some open problems.

Nonlinear propagation of optical pulses of finite transverse widths through periodic structures with and without defects is investigated numerically and the subject of investigation is a stack of alternating linear and cubically nonlinear layers of submicron thicknesses is considered. The simulations are based on a modified equation for the pulse envelope and modified boundary conditions where both the diffraction and possible focusing of the pulse are taken into account. The simulations demonstrate an essential influence of defects within the periodic structure on the nonlinear propagation of optical pulses when the carrier frequency is chosen within the stop-band of the structure with the defect.

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.

The variation principle widely used in structural dynamics analysis allows us to transform the differential equation of the boundary value problem into a functional with extreme value. In recent years, it has been applied to the band-gap analysis of periodic structures. However, for periodic beam-plate composite structures with periodic and ordinary boundaries, it is relatively difficult for the traditional energy methods, such as the Rayleigh–Ritz method, to construct the displacement functions that satisfy boundary conditions. Hence, a hybrid solution is proposed in this paper to account for various boundary conditions of the periodic beam-plate composite structure. Specifically, the displacement functions constructed by the plane wave series can automatically satisfy the periodic boundary conditions. With the ordinary boundaries modeled by artificial springs, the spectral functions conforming to arbitrary boundary conditions are used to represent the displacement functions. The proposed solution is used to solve the band-gap problems of CRTS-III and CRTS-II slab ballastless tracks in China, and the accuracy of the solution is verified by comparing the calculated results with numerical simulations. In addition, through band-gap formation mechanism analysis, the frequency range of propagating flexural waves in each track component is accurately evaluated, which provides a theoretical basis for refined structural vibration reduction in the future. The solution proposed in this paper is flexible and convenient, which can be extended to a more complex band-gap analysis of periodic structures.

Train vibrations are the primary concern in environmental engineering and civil engineering. It is significantly imperative to find new methods for reducing and isolating vibrations. The locally resonant metamaterials (LRMs) propose a novel method and concept for reducing train vibration. However, the accurate and quick design structures of LRMs based on vibration characteristics are still an issue. Thus, this study presents a novel inverse design model of three-component locally resonant metamaterial barriers (LRMBs) for vibration reduction based on deep learning. The bandgap characteristics and vibration modes of the LRMB are investigated by using the improved plane wave expansion (IPWE) and finite element method (FEM). Besides, the gradient-combined LRMBs are proposed based on time–frequency features of measured vibration caused by trains and the novel inverse design model, and a two-dimensional finite element model coupling with infinite element boundaries is established to study the reduction efficiency of the gradient-combined LRMBs. And the performances of different LRMBs are fully analyzed in time and frequency domains. The results show that the novel inverse design model can be successfully used to design the LRMB based on vibration features. Moreover, the gradient-combined LRMBs have better isolation performance.

In this paper, a two-scale coupled higher order finite element method of thermo-elastic effect in composites with small periodicity is presented. Some finite element approximate errors corresponding to higher order two-scale finite element method are analyzed, and one matched and improved higher order numerical approximate error is obtained.

In this paper, an efficient numerical approach is proposed to study free and forced vibration of complex one-dimensional (1D) periodic structures. The proposed method combines the advantages of component mode synthesis (CMS) and wave finite element method. It exploits the periodicity of the structure since only one unit cell is modelled. The model reduction based on CMS improves the computational efficiency of unit cell dynamics, avoiding ill-conditioning issues. The selection of reduced modal basis can reveal the influence of local dynamics on global behavior. The effectiveness of the proposed approach is illustrated via numerical examples.

This paper deals with the deduction of new homogenized models for the flexural wave in bi-periodic beams. According to the homogenization theory, the long-wave assumption is used and the valid frequency range of homogenized models is limited to the first Bragg band gap. However, the classical homogenization method, whose idea is taking the component’s mean values as effective material properties, has limitations in mimicking the dispersive behavior and the real valid frequency range is far less than the limit. Thus, enriched homogenized models, derived by the multi-scale asymptotic homogenization method, are proposed to provide more accurate homogenization models with larger real valid frequency range. The new homogenized models are validated by investigating the dispersion relation in the infinite case and the frequency response function in the finite case. Wave finite element method (WFEM) are used to provide associated references. A parametric study is carried out in the infinite case while two different boundary conditions are considered in the finite case.

In this paper, the analytical homogenization method of Periodic Discrete Media (HPDM) and the numerical Condensed Wave Finite Element Method (CWFEM) are employed to study the wave propagation in two-dimensional periodic beam lattices. The validity of the HPDM is re-evaluated using the wave propagation feature identified by the CWFEM. Particular attention is paid to the polarization direction of the waves. The wave propagation in two directions is investigated while characteristic wave propagation features such as local resonance, veering and locking phenomena are observed. Complementary results are deduced from the two methods.