Superposition Of Modes Research Articles

Train–Track–Bridge Dynamic Interaction on a Bowstring-Arch Railway Bridge: Advanced Modeling and Experimental Validation

This article describes the validation of a 3D dynamic interaction model of the train-track-bridge system on a bowstring-arch railway bridge based on experimental tests. The train, track, and bridge subsystems were modeled on the basis of large-scale and highly complex finite elements models previously calibrated on the basis of experimental modal parameters. The train-bridge dynamic interaction problem, in the vertical direction, was efficiently solved using a dedicated computational application (TBI software). This software resorts to an uncoupled methodology that considers the two subsystems, bridge and train, as two independent structures and uses an iterative procedure to guarantee the compatibility of the forces and displacements at the contact points at each timestep. The bridge subsystem is solved by the mode superposition method, while the train subsystem is solved by a direct integration method. The track irregularities were included in the dynamic problem based on real measurements performed by a track inspection vehicle. A dynamic test under traffic actions allowed measuring the responses in the bridge, track, and vehicles, which were synchronized by GPS systems. The test results demonstrated the occurrence of upward displacements on the deck, which is a characteristic of structures with an arch structural behavior, as well as an alternation of tensile/compressive stresses between the rail and deck due to the deck-track composite effect. Furthermore, the acceleration response of the bridge proved to be significantly influenced by the train operating speed. The validation procedure involved comparing the dynamic responses obtained from the train-bridge interaction model, including track irregularities, and the responses obtained experimentally, through the test under traffic actions. A very good correlation was obtained between numerical and experimental results in terms of accelerations, displacements, and strains. The contributions derived from the parametric excitation of the train, the global/local dynamic behavior of the bridge, and the excitation derived from the track irregularities were decisive to accurately reproduce the complex behavior of the train-track-bridge system.

Role of fractional high harmonics with non-integer OAM on the generation of a helical attosecond pulse train.

Extreme-ultraviolet pulses of attosecond duration carrying orbital angular momentum (OAM) can be produced by spectrally filtering vortex high harmonics generated in a gas medium. Here we reveal that fractional high harmonics (FHHs) with non-integer OAM generated by a short duration Laguerre-Gaussian laser beam are origins for the change of helical attosecond pulse train (APT) with azimuthal angle. We show that these harmonics have gap and minimum structures in the annular intensity profile and discontinue phase distribution along azimuthal angle. And each FHH can be expressed as a superposition of OAM modes with integer topological charges. Features of FHH can be identified by coherently combining selected OAM modes. We also uncover that these features are formed after FHH is propagated in gas medium and in vacuum. We finally demonstrate that the generation of FHHs and the dependence of helical APTs on azimuthal angle are changed by varying the macroscopic condition.

Improved Response Spectrum Method Based on Real-Complex Hybrid Modal Superposition for Base-Isolated Structures

A novel real-complex hybrid modal response spectrum method (RCHM-RSM) based on the modal superposition of the superstructure is proposed for base-isolated (BI) structures in this paper. In contrast to the traditional analysis method, the method can increase the accuracy of the structural response and avoid complex calculations. Additionally, the direct use of the damping matrix of superstructures for BI structures was found to cause an overestimation of the damping effect and consequently underestimate the deformation of the superstructure. Thus, a new scheme is proposed for determining the damping matrix for BI structures, and general expressions of the damping matrix of the superstructure and the damping constant of the isolation layer are presented. Using the proposed method to construct the damping matrix of BI structures, the equivalent load associated with the coupling damping between the structure and support can be determined when the displacement–velocity input model (D–VIM) is adopted. Analytical expressions of structural matrices are presented for a shear-type model of a BI structure, and a numerical investigation is conducted to demonstrate the feasibility and effectiveness of the proposed methods. The results show that the proposed method (RCHM-RSM) has the advantages of simple calculations and high accuracy. The numerical results obtained also confirm that the direct use of the damping matrix of superstructures for the BI structure will underestimate the superstructure response, while the displacement input model (DIM) overestimates the deformation of the isolation layer and underestimates superstructure responses, the analysis results by using D–VIM are consistent with the acceleration input model (AIM), so the D–VIM should be used instead of the DIM.

TUNNEL REACTION TO GROUND MOVEMENT USING A SIMPLIFIED MODEL

Purpose: the analysis is performed by modal superposition of the response of a simplified model containing connected bending and shear beams supported by Winkler-type springs.
 Objective: to present a simplified model using coupled Bernoulli and shear beams supported by Winkler-type springs for the systematic identification of tunnels subject to earthquake-induced ground motions. A model formulation is introduced and closed-form solutions for the modal characteristic equation and mode shape are derived.
 Research methods: the formulation of the model is introduced and closed-form solutions are derived for the equation of modal characteristic and mode shape. The latter are checked by the results of numerical models. A system identification algorithm is then presented, demonstrating its ability to recover the model parameters when the recorded acceleration time intervals along the tunnel are perturbed by noise and sensor locations change. The presented framework can be used for initial and simple recovery of tunnel response in the presence of monitoring data or for planning monitoring campaigns in newly constructed or existing tunnels.
 Main results: using a simple genetic algorithm and the proposed simplified model, it was shown that system identification can be performed for variable conditions. The model was tested for two different earthquakes of different frequencies, and the influence of the distribution of sensors along the length of the tunnel was also parametrically investigated. The test results were intentionally compromised by adding white Gaussian noise with a variance equal to that observed during ground motion. It was observed that for values ​​of α >3.0 (ie, when the effect of the shear beam is significant), the model parameters can be successfully recovered. Therefore, for such conditions, the proposed approach can be used to recover important tunnel dynamic properties (e.g., T1 or α) as well as soil-structure interaction by tracking kb changes after earthquakes. For values ​​< 3, a Bernoulli beam with a Winkler basis is a valid representation, while observing differences with a model involving a Pasternak basis are marginal.
 Scientific novelty: another approach to parametric system identification using simplified models. For tunnels, such models usually consist of beams on independent Winkler-type springs, including both numerical and analytical schemes. However, the seismic response of the continuum (i.e., soil) can be better modeled by including a transverse beam above the Winkler foundation, which allows interaction between individual springs, rather than using a single layer of independent springs. In geotechnical seismic resistance, a similar approach was used to assess the seismic response of pile foundations and retaining walls.
 Conclusions and practical challenge: different sensor distributions and reduced number of sensors did not lead to significant differences in the final results. This first shows that sensor position is not the dominant parameter for the case of five sensors along the length of the tunnel, fixed at both ends, and uniform soil conditions and other assumptions made in the paper. Further tests should be performed on real data and sensors to examine the impact of other aspects such as sensor noise.
 Key words: winkler springs, soil; soil; model; system identification algorithm is presented.

Terahertz wideband quarter wave plate based on freestanding grating structures

Wideband metasurfaces usually have increased structure complexity as compared to their narrowband counterparts, by integrating multiple in-plane or cascaded resonant structures. We propose a dielectric grating structure as a quarter-wave plate with alleviated structure complexity and wide bandwidth at terahertz frequencies, by simply enlarging the period from subwavelength to superwavelength scale. From the modal theory, the superwavelength grating supports more than one waveguide modes. The superposition of the fundamental mode and higher-order mode with diverse dispersion characteristics is used to engineer the spectral response and to achieve a wideband linear-to-circular polarization conversion, which is validated by experimental study.

Simulation study on the influence of wheel irregularity on the vertical dynamics of wheel–rail interaction for high-speed railway track using bond graph

Dynamic interaction between train wheel and high-speed slab is an important issue when evaluating the contact force at the wheel–rail interface under the influence of an irregularity either on the train wheel or on the rail. In this paper, an influence of amplitude of irregularity along with the vehicle speed on the dynamics of wheel–rail interaction for high-speed railway tracks is being analyzed. For this purpose, single-wheel high-speed railway (HSR) track interaction models are developed using the bond graph modeling technique. The HSR track model consists of two layers of beam, i.e., rail and concrete slab. Both the rail and slab track is modeled using the Euler–Bernoulli beam theory. The Hertzian contact theory at the wheel–rail interface has been considered for this analysis. The vertical dynamic interaction between a train wheel and a high-speed slab track is compiled in the time domain using a bond graph approach coupled with a technique known as modal superposition. Irregularity present on the wheel is characterized as smooth, moderate, and severe depending upon the variation of irregularity amplitude. An expeditious increase of maximum contact force has been observed between the speed range of 200 and 250 km/h. Beyond the speed of 250 km/h, there is a gradual increment of contact force up to its peak value. When the train speed is beyond 288 km/h, there is a gradual decrease in maximum contact force. This kind of several other useful dynamic responses in terms of wheel acceleration and wheel–rail overlap are also evaluated.

Structural Dynamics and Vibration Analysis of the MDOF Systems

Because the vibration of buildings plays an important role in resisting an earthquake, we need some methods to analyze the vibration of the MDOF systems. This paper proposes a method to analyze the structural dynamics and vibration of the MDOF systems by using the “modal superposition method” and the “Duhamel integral”. We set the system consisting of mass, stiffness, and damping to correspond to actual situations. The results obtained in this research include the E.O.M: natural frequency and mode shape of the building model, which can show the resonance of the building. Based on our analysis, designers can make a more appropriate design of buildings that can reduce the mortality in the earthquake.

Generation of OAM-carrying space-time wave packets with time-dependent beam radii using a coherent combination of multiple LG modes on multiple frequencies.

Space-time (ST) wave packets, in which spatial and temporal characteristics are coupled, have gained attention due to their unique propagation characteristics, such as propagation invariance and tunable group velocity in addition to their potential ability to carry orbital angular momentum (OAM). Through experiment and simulation, we explore the generation of OAM-carrying ST wave packets, with the unique property of a time-dependent beam radius at various ranges of propagation distances. To achieve this, we synthesize multiple frequency comb lines, each assigned to a coherent combination of multiple Laguerre-Gaussian (LGℓ,p) modes with the same azimuthal index but different radial indices. The time-dependent interference among the spatial modes at the different frequencies leads to the generation of the desired OAM-carrying ST wave packet with dynamically varying radii. The simulation results indicate that the dynamic range of beam radius oscillations increases with the number of modes and frequency lines. The simulated ST wave packet for OAM of orders +1 or +3 has an OAM purity of >95%. In addition, we experimentally generate and measure the OAM-carrying ST wave packets with time-dependent beam radii. In the experiment, several lines of a Kerr frequency comb are spatially modulated with the superposition of multiple LG modes and combined to generate such an ST wave packet. In the experiment, ST wave packets for OAM of orders +1 or +3 have an OAM purity of >64%. In simulation and experiment, OAM purity decreases and beam radius becomes larger over the propagation.

Direct generation of orthogonally polarized dual-wavelength orbital Poincaré modes at 639 nm and 721 nm in a blue-diode pumped Pr:YLF laser

We report on the first, to the best of our knowledge, direct generation of orthogonally polarized dual-wavelength laser with orbital Poincaré (OP) modes at 639 nm and 721 nm in a blue-diode pumped Pr:YLF laser. Beyond the single-wavelength emission, dual-wavelength laser can be approached by adjusting the tilt angle of the output mirror in the critical cavity. In addition, either monochromatic or bi-chromatic orbital Poincaré modes, including Hermite-Gaussian (HG) modes, Laguerre-Gaussian (LG) modes and Hermite-Laguerre Gaussian (HLG) modes can be directly generated by simple off-axis pump scheme and displacement of the output mirror. Moreover, hybrid eigenmodes with S-shape beam profile resulting from dual singularities at the wavefront are observed, as well as the mode switching along with the increase of the pump power. Meanwhile, these composite modes are replicated by simulations using the coherent superposition of higher order HG modes. This work may shed new light on the dual-wavelength laser at visible regime with various modes for potential applications.

Photonic spin Hall effect using hybrid Tamm plasmon polariton

Here, we report a photonic spin Hall effect (PSHE), i.e., splitting of opposite spin in a transverse direction using a multi-layered metallo-dielectric heterostructure by hybridization of a Tamm plasmon polariton and a surface plasmon polariton. The underlying mechanism of PSHE is also explained using the concept of superposition of normal and abnormal modes in the circular-polarization basis. It is revealed that the spin-dependent transverse shift for the proposed hybrid structure is enormously high owing to the transverse shift of ∼18 μm. The PSHE is found to be strongly dependent on the number of bi-layers of the structure and the analyte refractive index, which provides an additional degree of freedom for tailoring the device performance. Therefore, this study opens a pathway for developing next-generation photonic spin Hall devices in the fields of spin photonics, optical sensing, and optical communications.

Experimental and numerical analysis of damping behavior of iron graphite composite in machine tool joint

Iron graphite (FeGr) composite is a potential design material for machine tools to increase vibration damping without additional energy. Previous studies focused on the isolated composite’s properties rather than their damping effect as a passive damper to assembled components. There is currently no effective model using real mode superposition (RMS) method for demonstrating the damping behavior of FeGr composites in a multi-material structure. This paper presents a local damping description for a finite element model with RMS assuming constant loss factor for all modes to simulate the damping behavior of FeGr composites and their contribution to system damping and a test rig to identify the model parameters for typical machine tool boundary conditions. The influence of FeGr spacers with 0, 20%, 40%, and 60% graphite content on eigenfrequency and on damping of the test rig was measured, and the results were used to identify the damping model. The agreement of eigenfrequencies and damping ratio between measurement and simulation proves the effectiveness of the parameterized damping model predicting the mode-dependent damping behavior of FeGr in machine tool joints. The material analysis indicates that increasing the graphite content of FeGr composites from 0 to 60% amplifies the system damping from 0.03% to 0.6% at first bending mode. The interface pressure in a tightly fastened FeGr joint affects the system damping significantly. When designing machine tools, the surface condition of FeGr composite cannot be overlooked. FeGr dominates system damping and shows better damping performance at high vibration amplitudes.

Exploring the effect of transverse patterns on the temporal characteristics in self-mode-locked Nd: YVO[formula omitted] lasers

We investigate the influence of transverse mode distribution on the self-mode-locked (SML) states by employing off-axis pumping in an Nd:YVO4 laser with a linear concave-plano cavity. The higher-order transverse modes in the cavity are excited by adjusting the off-axis pumping displacement, and the dependence of the time characteristics of the SML laser on the transverse modes is analyzed. When the laser cavity length is 50 mm, and the off-axis displacement is adjusted offsets in the radial x and y directions to be (0,0) μ m, (45,58) μ m, and (80,0) μ m, the laser is operated in the longitudinal SML state with a repetition rate of 2.72 GHz, the amplitude modulation mode-locked pulse with a modulation frequency of 0.68 GHz and a repetition rate of 2.72 GHz, and the total-self-mode-locked with a repetition rate of 0.68 GHz, respectively. The corresponding transverse mode patterns are TEM00, TEM00+TEM01+TEM10 superposition, and TEM00+TEM10+TEM20 superposition. Finally, numerical simulations reconstruct the experimental mode-locked pulse and the corresponding transverse mode patterns based on the theory of coherent superposition of laser modes.

Reconstruction of dynamic wind forces on a transmission steel lattice tower using aeroelastic wind tunnel test data

This article reports a methodology for estimating dynamic wind forces on a steel lattice tower by using limited structural displacements. The methodology involves combining the modal state-space system model and a Kalman filter-based algorithm. For convenient application, the equivalent concentrated forces are taken as the inversing objects, representing the distributed wind forces on a lattice tower. The corresponding equivalent cantilever model of the lattice tower is utilized, in which the stiffness matrix is estimated by a modified flexibility approach. Based on the modal superposition principle, the dynamic wind forces in physical space are reconstructed using the identified input modal wind forces. The scheme of the dynamic wind force reconstruction is designed in detail. A typical transmission steel lattice tower is considered, and the aeroelastic wind tunnel experiments are performed. The performance and effectiveness of the proposed scheme are investigated based on numerical simulations and wind tunnel tests. It is indicated that the reconstructed dynamic wind forces can produce equivalent dynamic responses to the actual. Besides, it performs robustly on the effect of measurement noise. Although the modal force identification is sensitive to the modeling error of structural natural frequency, the effect can be judged according to the change in the power spectra of the identified modal force. The proposed inversing approach can serve as a useful tool to evaluate dynamic wind forces on steel lattice towers with limited response measurements.

Numerical simulation of vortex-induced vibrations of inclined flexible risers subjected to uniform current

The vortex-induced vibrations (VIVs) of a flexible riser at four different inclination angles (θ) subjected to a uniform current were numerically simulated by using three-dimensional Large-Eddy-Simulation (LES). A weak coupling method was adopted for addressing the fluid-structure interaction, where the fluid domain was calculated by the commercial code ANSYS Fluent, while the structural response was calculated by the mode superposition method. The sensitivity of the vibration to grid refinement was checked, and the numerical simulation accuracy was validated by comparison to experimental results. The effects of the θ on the VIV of the flexible cylinder were investigated. The cross-flow vibration is found to decrease with increasing θ, while the in-line vibration does not show the same variation. Figure-eight shaped orbital trajectories are observed in four different θ cases. If θ attains a specific value, the vortex shedding separates into two different modes (i.e., straight vortex and hairpin vortex) along the flexible cylinder. With increasing θ, the hairpin vortex tubes gradually become the dominant vortex shedding mode.

Forced Frequency Response Analysis of a Gudgeon Pin

In this study, forced frequency response analysis was applied on the gudgeon pin. Ansys Mechanical 19.2 program was used to analyze the vibration on the gudgeon pin. Once completed in the finite element analysis, a note from the modal results, the model's natural frequencies range from 38721 to 79346 Hertz for the first 12 modes. According to the modal analysis results, the gudgeon pin will not be subjected to resonance during working. Therefore, a frequency scan including modal analysis is required to detect resonant frequencies that may coincide with the natural frequencies of the first 12 modes obtained in modal analysis. Consequently, harmonic analysis has been solved using the mode superposition method with 50 intervals with 1000 Hz steps in the range of 30000-80000 Hz. To dampen the resonant frequencies, harmonic analyzes were repeated using six different constant damping ratios, and the results were compared.

Influence of cut-out shape on the dynamic behavior of carbon nanotubes reinforced functionally graded plates

This research investigates the effects of cut-out on the dynamic behaviour of functionally graded carbon nanotube reinforced composite (FGCNTRC) plates. Finite element method (FEM) is utilized and SHELL181 type element of the ANSYS Workbench 17.2 program is utilized. To understand the vibration characteristics of the FG plates, various shapes of cut-outs such as triangular, square, rectangular, hexagonal, circular etc are considered. For comparison, solid FGCNTRC plate is modeled and natural frequencies of plates integrated with cut-outs of different shapes are determined using free vibration study. The mode superposition method is used to address the harmonic response analysis problem keeping the damping ratio constant. The stress, phase changes and displacement responses for definite frequency ranges have been used to interpret the findings. To learn more about the effects of cut-outs on the dynamic response, the plates are designed considering various grading patterns. The findings show that the shape of cut-outs significantly affects the harmonic responses as well as the fundamental frequency of the FG plates and are also depending on the grading patterns of these plates.

Performance evaluation of nonlinear energy scavenging overlay networks

SummaryThis paper investigates a nonlinear energy scavenging overlay network (NLESON) wherein a primary source (PS) communicates with a primary destination (PD) probably under aid of a secondary source (SS) who communicates with a secondary destination (SD). SS is a power‐constrained device, and thence, its operation relies on energy harvested by a practical nonlinear energy scavenger. To support PS and exploit the harvested energy at most, SS adaptively switches between single and superposition modes where the single mode allows SS to transmit solely its signal with the entire harvested energy and the superposition mode asks SS to transmit both—its signal and amplified primary signal—with different power fractions. Moreover, for increasing the probability of successfully decoding primary signal at PD and SD, which then reduces considerably primary interference on secondary signal in the superposition mode, we leverage both direct channels (PS‐PD and PS‐SD) and apply both signal combining paradigms (maximum ratio combining and selection combining). The outage/throughput performance of the NLESON is assessed quickly through the proposed closed‐form expressions over shadowed fading channels. Various results exposed the effectiveness of the aforementioned solutions for the NLESON and their flexibility in controlling system performance.

The Application of Fast Multipole Boundary Element Method to the Calculation of Slamming Load of Three-Dimensional Elastic Sphere

An efficient fluid-structure interaction (FSI) method is established to quickly and accurately calculate the fluid load of three-dimensional (3D) elastic structure in the process of water slamming. In this method, the boundary element method (BEM) and computational structural dynamics (CSD) are coupled by thin plate spline (TPS) interpolation method and flow field reconstruction. In order to improve the calculation efficiency, the fast multipole algorithm is introduced into the BEM, the finite element mesh of the wetted part of the structure is directly used as the flow field boundary, and the structural dynamic response is analyzed by the direct integration method of state equation based on modal superposition. The numerical results are compared with the results of Nisewanger’s sphere water entry test and the existing literature, which proves the accuracy of the numerical calculation method established in this paper. The effects of time-domain iteration step size, mesh size, slamming velocity, fluid density and structural elastic effect on water slamming load are studied. The results show that the slamming velocity and fluid density have a great influence on the simulation results; the iteration step size has little influence on the accuracy of simulation calculation, and the mesh size has a certain influence on the accuracy of simulation calculation; elastic effect reduces the peak value of slamming load, considering elastic effect is necessary for accurate calculation of slamming load.

Accurate mode decomposition with the combination of the matrix analytic and the SPGD algorithm

The matrix analytic algorithm (MAA) offers excellent abilities in fast mode decomposition (MD) of multimode fibers. However, with the growth of the number of superposition modes, the residual error of the MAA becomes enlarged. In this case, it is not able to realize satisfactory MD due to the trade-off between the number of modes and the decomposition accuracy. In this paper, we propose a new, to the best of our knowledge, MD algorithm by introducing the stochastic parallel gradient descent (SPGD) algorithm to MAA. Specifically, the approximate value of the amplitude and relative phase is first obtained by MAA; then, the approximate value is used to obtain the accurate amplitude and relative phase iteratively through the SPGD method. The MAA-SPGD is helpful in avoiding accuracy degradation as the number of modes increases. With the introduction of SPGD, at the mode number of 50, the average value of the cross-correlation between the original and reconstructed image reduces from 0.25 to 0.02 for the difference from 1. Due to the appropriate initial iteration value from the MAA, the MAA-SPGD eliminates the local optimum, which reveals the stability and reliability features in MD.

Displacement field reconstruction technique for plate-like structures based on model superposition method

To achieve real-time sensing and deformation reconstruction of flexible plate structure, a 3D reconstruction technique based on a quasi-distributed fiber grating sensor network and order-optimized modal superposition method is proposed. Graphic visualization is introduced to the field of deformation monitoring, then the displacement field reconstruction of the typical structure of spacecraft is realized. Firstly, a finite element model of the four-sided fixed-supported plate structure is constructed, and the conversion matrix of surface strain and displacement are obtained based on modal analysis, and then the modal parameters are optimized through static simulation experiments; Secondly, the influence of the number and position of sensors on the reconstruction accuracy is studied, then a high-density distributed fiber grating sensor network is attached to the surface of the plate to construct an experimental FBG model of the spacecraft; Finally, concentrated loads are applied to the structure at different positions, and structure’s surface strain information is collected by FBG network, then the morphological reconstruction of the deformed structure is realized based on the improved model superposition method, which proves the feasibility of the algorithm. The results show that the reconstruction method’s average absolute error is less than 0.13 mm, so this method can be used to displace field reconstruction problems of flexible structures.