Narrow Results

The traditional dynamic analysis method is less efficient in the global and local vibrations analysis of long-span bridge structures. Therefore, to meet the need for an efficient solution of the refined analysis model of the train–track–bridge coupled system (TTBCS), a new hybrid dynamic model of the TTBCS based on the transfer matrix method (TMM) is proposed in this paper. It can solve the local high-frequency vibration response of the track structure and the global and local vibrations responses of the bridge structure simultaneously, accurately, and efficiently. First, according to the periodic characteristics of track and bridge structure, the periodic repeating parts are divided into cellular structures. For the bridge subsystem, fine cells are established to achieve the accurate solution of local vibration, and the rest of the super element cells are established by model condensation technology, which can significantly reduce the number of cells and save the transmission time. The state vector transfer model of the track and bridge subsystem is established based on the TMM, and the coupling calculation is realized by combining rail bridge force. The train system adopts the model of 10degrees of freedom and realizes the coupling with the rail system through the wheel–rail interaction force. With the movement of train load, the track and bridge cells established by the hybrid dynamic model approach (HMA) dynamically update the arrangement information, which not only realizes the calculation of ultra-long track based on a fixed number of track cells, but also moves the fine cell models of bridge with the change of load position. These dynamic update measures reduce both the number of cells and transfer solutions, save the transfer time, and further improve the calculation efficiency. Taking CRH-2 EMU passing through a 3-span simply supported steel truss bridge as an example, the results and time-consuming of the direct stiffness method, TMM, and HMA are compared, and the accuracy and efficiency of the hybrid model are proved.

The coupling of beam and arch in bridge engineering introduces intricate dynamic responses. To more efficiently and comprehensively evaluate the coupling dynamic characteristics of arch bridge, this study examines the natural frequencies and dynamic responses of a beam–spring–arch coupling structure under moving loads/oscillators. A mathematical model of the coupling structure is formulated, with the corresponding partial differential equations derived using Hamilton’s principle. The transfer matrix method is employed to establish state vector connections for each segment of the structure, leading to the derivation of a frequency equation to calculate natural frequencies based on specific boundary conditions. Modal functions are determined by transferring the state vectors of each segment, and the Galerkin method is used to discretize the first six-order vibration in the form of ordinary differential equations. The study explores the characteristics of free vibration modes and natural frequencies, and numerically calculates the dynamic responses of the coupling structure under moving loads/oscillators. Responses for the first six modes are superimposed, and the effects of key parameters on the dynamic response are analyzed. The calculated natural frequencies show less than 5% deviation from those obtained via finite element models. The oscillator mass block displacement exhibits an inverted M-shape. Increased structural stiffness raises natural frequencies and induces a curve veering phenomenon. While higher stiffness can reduce oscillator displacement during movement, it does not entirely eliminate member response and may amplify displacement in certain sections. The developed coupling dynamics model and findings provide guidance for the stiffness design of beams, arches, and supporting components, as well as for the vibration reduction of arch bridges.

By combining the inertial amplification (IA) mechanism and Bragg scattering mechanisms, a metamaterial periodic Timoshenko beam with IA is designed to enhance the capability of flexural vibration reduction in the low-frequency range. The band structures of flexural vibration band gap (BG) are calculated using the transfer matrix method (TMM). The results based on the Euler–Bernoulli and Timoshenko beam theory are compared to show the necessity of using the Timoshenko beam model for small slenderness ratio beams. The formation mechanism of the BG of the proposed periodic Timoshenko beam with the IA mechanism is revealed theoretically. The vibration experiments with different excitation approaches are carried out to validate the theoretical results. The effects of the beam and IA mechanism parameters on the BG properties are investigated and the rules of parameter influences are discovered. It can be found that increasing the Segment II length, decreasing the Segment I and Segment III length and thickness, and increasing the IA mass and angle are beneficial for reducing low-frequency vibrations. This research will contribute to the development of innovative smart materials and structures for vibration and noise reduction.

An analytical method for calculating the dynamic stiffness of rubber isolator with multi-rigid-flexible bodies and various coupling deformation modes is proposed. The three-dimensional transfer matrices are reduced to two-dimensional representation for calculations, based on the excitation direction of the isolator and the deformation modes of the rubber components, which reduces computational costs. The metal and rubber components in the isolator are treated as rigid and flexible bodies, respectively, and the transfer matrices of each component are derived in conjunction with continuous system theory. The deformation of the rubber components involves shear, bending, longitudinal, and torsional motions. The frequency-dependent complex elastic modulus of the rubber material is obtained from dynamic shear tests and fitted to a five-parameter fractional derivative model. The extended transfer matrix method is employed to solve for the frequency-dependent nonlinear dynamic stiffness of the isolator in three translational directions. Finally, the proposed method is validated through a combination of finite element analysis and dynamic stiffness testing, and the influences of material and geometric parameters are analyzed.

Sensitivity analysis is an essential step for the optimization design of mechanical systems. To improve the efficiency of sensitivity analysis based on the multibody system transfer matrix method, this study proposes a fast calculation method (FCM) and its operator formulas for any order derivative of the overall transfer matrix (DOTM). First, the formulas for the $p$-order DOTM are derived by the definition-based method (DM). To reduce the computational time complexity, a FCM for DOTM is established through directly differentiating the recursive formula of the overall transfer matrix for chain mechanical systems and reducing the computational time complexity from $O(n^{p+1})$ in DM to $O(n)$ in FCM. Then, to simplify the deduction process of DOTM for the chain mechanical systems and branch mechanical systems, the operator formulas for FCM are established by defining and applying a successive derivative operator and a combinatorial product operator. The operator formulas reveal the calculation rules similar to the automatic assembly theory for the overall transfer matrix in branch systems. Meanwhile, the proposed method and operator formulas are also applicable to a general mechanical system containing closed-loops. Finally, the natural frequency sensitivity of a chain multibody system, frequency response sensitivity of a branch system and the natural frequency sensitivity of a complex mechanical system demonstrate that the proposed FCM has remarkably higher computation efficiency than DM and is user-friendly to be realized with a computer.

Hybrid nanocomposite thin films, composed of inorganic colloidal quantum dots (CQDs) embedded in a matrix of organic conjugated polymer, have shown promise as a method for room-temperature infrared detection due to the three-dimensional confinement of the CQD and significantly lower dark currents compared to inorganic detectors. However, in order to improve device performance, the excited charges must be efficiently promoted out of the CQD, which is surrounded by an insulating surface ligand. These short, organic molecules, which are required to prevent agglomeration of CQDs in solution, have been shown to inhibit charge transfer into and out of the CQD. In this work, the transfer matrix method is utilized to calculate the quantized energy levels and wavefunctions in the conduction band of the CdSe CQD for a variety of surface ligand materials. These results are used to calculate the absorption coefficient for a size distribution of CQDs and are compared with measured Fourier Transform Infrared absorbance spectra. Finally, the effect of the ligand on the calculated absorption coefficient will be used to optimize the design for an infrared photoconductor.

The effect of tube geometry on quantum transport in carbon nanotube electron resonators is studied analytically by developing a transfer matrix method. The conductance of metallic chiral nanotubes not only shows oscillating variations as a function of gate voltage with rapid and slow periods, but also exhibits a conductance gap and some resonance conductance peaks in the gap region. These features depend on to a high degree on both tube diameter and chirality and thus provide an experimental means for structure appraisal of the nanotube devices.

We designed the one-dimensional photonic quasi-crystals (1D PQCs) arrays for application to the flat-band (FB) pass filters using a transfer matrix method (TMM). In this work, the PQCs of the combinations of SiO₂-TiO₂ and SiO₂-ITO were designed with the centre wavelength of 1.550 µm at an incident angle of 8°. The width of flat-transmission bands increases with increasing the number of cavity. For a SiO₂/TiO₂–based PQC with 3-cavity structure, the FB-width was evaluated to be about 0.7 nm and the insertion loss was approximately 0.3 dB. In addition, the band-center wavelength exhibited a blue shift with an increase of incident angle and their band widths are uniform for specific θ_i-ranges. An application of this FB-pass filter to a wavelength division multiplexing (WDM) device was also proposed. We believe that the PQC-based devices could be comprehensively applied to the new conceptional optical passive and active devices.

A layered structure model is proposed for microwave dielectric properties of nonhomogeneous hydrogen plasma in carbon nanotubes (CNTs) film. Using the transfer matrix method for solving electromagnetic wave propagation equation, the microwave attenuation of the film is calculated in the range of 0–30 GHz under different conditions. It is found theoretically that with the increase of hydrogen plasma nonhomogeneity, the frequency bandwidth of strong microwave absorption by the film increases markedly. The application of a moderate static magnetic field can effectively improve microwave attenuation properties of hydrogen plasma in CNTs. The numerical results are in good agreement with the available experimental data.

We study physical properties of the symmetric diamond chain with delocalized interstitial spins. We derive an exact solution of the model and characterize the phases of the system at zero temperature. On the basis of this solution, we examine its magnetic and thermal properties as well. The case of nonconserved electron number is then considered. There are phases, which we term as nonclassical, for which electrons in Hubbard dimers are in quantum entangled states. We finally study quantum entanglement depending on Hamiltonian parameters and temperature.

In the present work, we propose that a one-dimensional quantum heterostructure composed of magnetic and non-magnetic (NM) atomic sites can be utilized as a spin filter for a wide range of applied bias voltage. A simple tight-binding framework is given to describe the conducting junction where the heterostructure is coupled to two semi-infinite one-dimensional NM electrodes. Based on transfer matrix method, all the calculations are performed numerically which describe two-terminal spin-dependent transmission probability along with junction current through the wire. Our detailed analysis may provide fundamental aspects of selective spin transport phenomena in one-dimensional heterostructures at nanoscale level.

Based on the photon localization and the photonic bandgap characteristics of photonic crystals (PCs), one-dimensional (1D) ring mirror-defect photonic crystal structure is proposed. Due to the introduction of mirror structure, a defect cavity is formed in the center of the photonic crystal, and then the resonant transmission peak can be obtained in the bandgap of transmission spectrum. The transfer matrix method is used to establish the relationship model between the resonant transmission peak and the structure parameters of the photonic crystals. Using the rectangular air gate photonic crystal structure, the dynamic monitoring of the detected gas sample parameters can be achieved from the shift of the resonant transmission peak. The simulation results show that the Q-value can attain to 1739.48 and the sensitivity can attain to 1642 nm ⋅ RIU${}^{-1}$, which demonstrates the effectiveness of the sensing structure. The structure can provide certain theoretical reference for air pollution monitoring and gas component analysis.

By using the transfer matrix method (TMM), we theoretically explore the transmittance properties and cutoff frequency of one-dimensional photonic crystal (1DPCs) within the terahertz frequency region. The present structure consists of high-temperature superconductor and semiconductor layers. The results of the calculations represent the effects of various parameters on the cutoff frequency. We have used the two-fluid model as well as the Drude model to describe the permittivity of superconductor and semiconductor. Further, we consider that the permittivity of both the materials is depending on the hydrostatic pressure. The present results show that with the increasing of different parameters as the operating temperature, the thickness of semiconductor, and the filling factor of semiconductor, then the cutoff frequency shift to lower frequencies regions. By the increasing of superconductor thickness, hydrostatic pressure, doping concentration and filling factor of the superconductor, we found the cutoff frequency shifts to higher frequency regions. These results indicate that cutoff frequency can be modified through these different parameters. Finally, the present design could be useful for many optical systems as the optical filter, reflector and photoelectronic applications in the Terahertz regime.

Photonic crystal is a dielectric structure arranged according to certain rules, and its excellent electromagnetic wave characteristics can be used to manufacture a lot of kinds of photonic crystal devices. In this paper, a defect is introduced into the photonic crystal, and the transfer matrix method is used to study the relationship between the liquid concentration and the peak value of the liquid transmission at the electromagnetic wave length when the defect is a mixture of ethanol and glycol. The results show that by observing and measuring the position of the peak transmittance of the mixed liquid, the substance content of the liquid mixture, that is, the concentration, can be inferred. The accuracy of this method is compared with the experimental results, which shows that this method has high accuracy. This method is simple and easy to operate. This result opens up a new direction for the application of photonic crystals.

In this study, we have scrutinized the frequency gap generation by changing the geometrical parameters of a one-dimensional phononic crystal. For this purpose, we have calculated the transmission coefficient of an incident acoustic wave by using the transfer matrix method. We have retained and fixed the total length of the system and changed the system internal geometry not to increase the system length too much. Another reason was to adjust the phononic band gaps and get the desired transmission properties by finding the optimum internal geometry without increasing or decreasing the total length of phononic crystals. In addition, we also propose few structures with the opportunity of applications in acoustical devices such as sonic reflectors. Our results can also be of high interest to design acoustic filters in the case that transmission of certain frequencies is necessary.

The boundary conditions of the moving layered medium are analyzed and the expressions of electromagnetic field are deduced. The reflection and transmission coefficients in fixed coordinates are obtained by using the covariance characteristic of Maxwell Equations. It is very complicated to apply boundary conditions many times in analyzing a multi-layer slab. In this paper, the results obtained from the boundary conditions of single-layer slab are analogous with those obtained by the transfer matrix method. Through improvement and generalization, the transfer matrix method can be used to calculate the moving multi-layer slabs. It can be applied to calculate the reflection and transmission coefficients of one-dimensional moving photonic crystal as well as deal with TM and TE polarization for the oblique incident. The zero reflection points of TM and TE polarization for layered slab are calculated. The results calculated in this study are matching well with the reference. It shows that the reflection oscillation enhances with the increase of $\beta$ and layer number, while the changing rule of reflections about TM polarization is relatively complex. The reflections of both TE wave and TM wave are all related to the incidence angle.

In this research, a one-dimensional photonic crystal with such a novel and simple design is introduced to serve as an efficient reflector for infrared (IR) wavelengths. The construction of the proposed photonic crystal design based on the gyroidal geometry is the mainstay of this research to investigate the total reflectivity through a wide band of IR wavelengths. In this regard, [Air/(A/B)¹⁰/substrate] is indeed the configuration of the suggested photonic crystal structure. The layer symbols, A and B represent two layers of silver with a gyroidal configuration in host materials of titanium dioxide and silicon, respectively. Meanwhile, our numerical findings demonstrate the existence of a cutoff feature at a wavelength of 1$\mu$m of the propagating electromagnetic waves. Moreover, the filling fraction of sliver through layers (A) and (B) provides a substantial role in the tunability of the cutoff frequency and the reflectivity of the structure as well. Then, we have taken into account how the host material’s thicknesses and refractive indices will affect the proposed structure’s reflectance. In particular, the refractive index of the host material could lead to a significant variation of the permittivities of the considered materials. Finally, we think that the proposed structure may be of a great interest in a variety of physical and engineering applications including the optical reflectors, smart windows and solar cells applications as well.

This work presents an innovative platform of a multi-channel one-dimensional photonic crystal (1-DPC) based on blood refractive index data of different patients in the aspect of the main protein components like hemoglobin. This photonic crystal (PC) contains a defect center infiltrated with plasma using a microorder size syringe. When binary silica and III–V semiconductor (InSb) materials are combined, they increase the refractive index difference between the alternate layers of the composite material, resulting in a wide photonic band gap (PBG). We use the well-known transfer matrix method (TMM) to observe the reflectance of various blood samples that were previously published. We assess and contrast the influence of different refractive index data on the dynamic shift in PBG calculation for novel superior and resourceful sensor in the prevention of microscopic organisms such as SARS-CoV-2, the virus linked with COVID-19. Yet, the performance of this PC has more moral content and unlimited casting efficacy in the face of an incurable virus.

The reflected properties of one-dimensional frequency-dependent metallic-dielectric photonic crystals are investigated when disorders are introduced for the first time. It is demonstrated that disordered metallic-dielectric photonic crystal provides remarkably high reflection range compared with the corresponding period metallic-dielectric one when the degree of disorder is moderately chosen, and a wider stop band will be obtained with the increasing of periods. At last, the reflected properties influenced by incident angle for different polarizations are also calculated and discussed.

This paper tackles anti-reflection coating structure for silicon solar cell where conductive nanoparticle (CNP) film is sandwiched between a semi-infinite glass cover and a semi-infinite silicon substrate. The transmission and reflection coefficients are derived by the transfer matrix method and simulated for values of unit cell sizes, gab widths in visible and near-infrared radiation. We also illustrated the dependence of the absorption, transmission and reflection coefficients on several angles of incidence of the transverse magnetic polarized (TM) waves. We found out that reflection decreases by the increase of incident angle to 50${}^{\circ }$. If nanoparticles are suitably located and sized at gab width of 3.5 nm, unit cell of 250 nm and CNP layer thickness of 150 nm, the absorptivity of the structure achieves 100%.