In-plane Modes Research Articles

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

Numerical Analysis of Different Influencing Factors on the In-Plane Failure Mode of Unreinforced Masonry (URM) Structures

The research work herein presented is aimed at investigating the effects of different influencing factors on the in-plane failure mode of unreinforced masonry (URM) structures. Firstly, the in-plane stress failure criterion cited in this paper was introduced, and the corresponding judgment procedure was demonstrated. Then, various finite element models considering different influencing factors were established, which included the aspect ratio of pier (η), stiffness ratio of pier to spandrel (ρ) and vertical load (σ). Furthermore, the in-plane stress failure criterion that we introduced was used to evaluate the failure modes of each model. The main findings of the simulations were as follows: under the condition of (η ≤ 1.0), three failure modes emerged in all models, which included pier, mixed and spandrel failure modes, with the gradual increase in ρ. Once the value of η exceeded 1.0, all models exhibited the pier failure mode regardless of whether the value of ρ increased or decreased. Moreover, under the identical aspect ratio (η = 1.0), the failure modes of the models altered regularly with the increase in the value of σ (from 0.3 MPa to 0.6 MPa), which transferred from pier failure to mixed failure, and from mixed failure to spandrel failure. The research results not only provide theoretical reference for the design of new masonry buildings, but also provide technical guidance for the judgement and prediction of failure modes of existing masonry buildings.

Stability of two-dimensional complex plasma monolayers in asymmetric capacitively coupled radio-frequency discharges.

In this article, the stability of a complex plasma monolayer levitating in the sheath of the powered electrode of an asymmetric capacitively coupled radio-frequency argon discharge is studied. Compared to earlier studies, a better integration of the experimental results and theory is achieved by operating with actual experimental control parameters such as the gas pressure and the discharge power. It is shown that for a given microparticle monolayer at a fixed discharge power there exist two threshold pressures: (i) above a specific pressure p_{cryst}, the monolayer always crystallizes; (ii) below a specific pressure p_{MCI}, the crystalline monolayer undergoes the mode-coupling instability and the two-dimensional complex plasma crystal melts. In between p_{MCI} and p_{cryst}, the microparticle monolayer can be either in the fluid phase or the crystal phase: when increasing the pressure from below p_{MCI}, the monolayer remains in the fluid phase until it reaches p_{cryst} at which it recrystallizes; when decreasing the pressure from above p_{cryst}, the monolayer remains in the crystalline phase until it reaches p_{MCI} at which the mode-coupling instability is triggered and the crystal melts. A simple self-consistent sheath model is used to calculate the rf sheath profile, the microparticle charges, and the microparticle resonance frequency as a function of power and background argon pressure. Combined with calculation of the lattice modes the main trends of p_{MCI} as a function of power and background argon pressure are recovered. The threshold of the mode-coupling instability in the crystalline phase is dominated by the crossing of the longitudinal in-plane lattice mode and the out-of plane lattice mode induced by the change of the sheath profile. Ion wakes are shown to have a significant effect too.

Charge density wave and pressure-dependent superconductivity in the kagome metal CsV3Sb5 : A first-principles study

The kagome metals $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, and Cs) have received intensive research interest due to the presence of charge density waves (CDWs), ${\mathbb{Z}}_{2}$ topological surface states, and intriguing pressure-dependent superconductivity. Using first-principles calculations, here we study the origin of the CDW order in ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ and its superconducting properties under pressure up to 45 GPa. We reveal that the momentum-dependent electron-phonon coupling (EPC) effect plays an important role in the formation of the CDW order. Upon compression, the movement of the van Hove singularity, which induces the change in the density of states at the Fermi level, as well as the redistribution of the EPC, can explain the experimentally observed double superconducting domes. The main contribution to the EPC is varied from in-plane vibrational modes in superconducting area I (2--15 GPa) to out-of-plane modes in superconducting area II (15--45 GPa). Our observations clarify the origin of the CDW order and shed some light on understanding the experimental observations of pressure-dependent superconductivity in ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$.

Kekulé Lattice in Graphdiyne: Coexistence of Phononic and Electronic Second-Order Topological Insulator.

Topological physics has been extensively studied in different kinds of bosonic and Fermionic systems, but the coexistence of topological phonons and electrons in one single material has seldom been reported. Recently, graphdiyne has been proposed as a two-dimensional (2D) electronic second-order topological insulator (SOTI). In this work, we found that graphdiyne is equivalent to Kekulé lattice, also realizing a 2D phononic SOTI in both out-of-plane and in-plane modes. Depending on edge terminations, the characterized topological corner states can be either inside or outside the bulk gap and are tunable by the local corner potential. Most remarkably, a unique selectivity of space and symmetry is revealed in the electron-phonon coupling between the localized phononic and electronic topological corner states. Our results not only demonstrate the phononic higher-order band topology in a real carbon material but also provide an opportunity to investigate the interplay between phononic and electronic higher-order topological states.

Charging effects on the vibrational properties of Au and Au2 on MgO(100)

Vibrational spectra of charge-neutral and charged Au and Au2 on MgO(100) were investigated using ab-initio density functional perturbation theory. The calculated vibrational spectra showed vibrational features associated with the charge states of Au and Au2 on MgO(100). Further analyses of surface in-plane and normal phonon modes of Au and Au2 on MgO(100) were performed to extract vibrational features involving the Au modes. These features provide important information for experimentally explaining the charge states of Au and Au2 on MgO(100).

Anisotropic phonon transport in van der Waals nanostructures

Phonon transport in van der Waals materials behaves strong anisotropic and size-dependent properties. With the help of molecular dynamics simulation, nonequilibrium Green's function, and Monte Carlo simulation methods, it is demonstrated that when the structure size is smaller than the phonon mean free paths, the thermal conductivity cannot be simply predicted by the classical anisotropic model. For thin van der Waals nanowires, the cross-plane phonon modes dominate heat transfer process along arbitrary crystalline directions except the in-plane direction, which makes phonons transport in zigzag way. Increasing the structure size, the in-plane phonon modes gradually dominate heat transfer process along arbitrary crystalline directions except the cross-plane direction. A phenomenological model based on the modified Boltzmann transport equation is put forward to describe anisotropic phonon transport in the van der Waals nanostructures when the structure size is smaller than the phonon mean free paths, which fits well with the molecular dynamics results.

Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations

The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.

In-Plane Shear and Interlaminar Fracture Toughness Properties of MWCNT stitch Para-aramid/Phenolic Nanocomposites

In-plane shear and mode‒II interlaminar fracture toughness properties of three-dimensional nanostitch para-aramid/phenolic composites were experimentally studied. Introducing the nanostitching yarn into nanocomposites slightly enhanced their shear strengths and the interlaminar fracture toughness (GIIC) due to the through-the-thickness reinforcement which was provided by micro filament TOWs and nanotubes. In-plane shear failure mode was predominantly irregular shear hackle marks in the phenolic resin and fibrillar peeling on the fiber due to in-plane shear deformation. However, the failure mode of interlaminar fracture toughness was mainly shear hackles in the interlayer region of the nanostitch composite. Carbon nanotubes in the phenolic resin and filament TOWs probably reduced the stress clustering via friction-debonding-pull-out-sliding as a form of stick-slip. These failure mechanisms probably arrested the crack growth and suppressed delamination in the through-the-thickness fiber reinforced zone. As a result, nanostitch aramid composite showed damage tolerance characteristic.

Transient Analysis of Micro/Nano Plates by Moving Finite Element Method

The paper deals with transient analysis of homogeneous as well as FGM (functionally graded material) thin micro/nano plates subjected to transversal dynamic loading. within the highergrade continuum theory of elasticity. The microscopic structure of material is reflected in this higher-grade continuum theory via one material coefficient called the micro-length scale parameter. Furthermore the material can be composed of two micro-constituents what is included in the employed continuum model by functional gradation of the Young’s modulus through the plate thickness with assuming power-law dependence of volume fractions of micro-constituents on the transversal coordinate. The high order derivatives of field variables are eliminated by decomposing the original governing partial differential equations (PDE) into the system of PDEs with lower order derivatives. For the numerical implementation, the weak formulation is proposed with novel Moving Finite Element approximation method of spatial variations of field variables. The semi-discretized equations of motion yield a system of ordinary differential equations which can be solved by standard time stepping techniques. Several numerical simulations are devoted to study the influence of micro-length scale parameter as well as the parameters of gradation of Young’s modulus on coupled bending and in-plane deformation response modes.

Tuning the Anisotropic Thermal Transport in {110}-Silicon Membranes with Surface Resonances.

Understanding the thermal transport in nanostructures has important applications in fields such as thermoelectric energy conversion, novel computing and heat dissipation. Using non-homogeneous equilibrium molecular dynamic simulations, we studied the thermal transport in pristine and resonant Si membranes bounded with {110} facets. The break of symmetry by surfaces led to the anisotropic thermal transport with the thermal conductivity along the [110]-direction to be 1.78 times larger than that along the [100]-direction in the pristine structure. In the pristine membranes, the mean free path of phonons along both the [100]- and [110]-directions could reach up to ∼100 µm. Such modes with ultra-long MFP could be effectively hindered by surface resonant pillars. As a result, the thermal conductivity was significantly reduced in resonant structures, with 87.0% and 80.8% reductions along the [110]- and [100]-directions, respectively. The thermal transport anisotropy was also reduced, with the ratio decreasing to 1.23. For both the pristine and resonant membranes, the thermal transport was mainly conducted by the in-plane modes. The current work could provide further insights in understanding the thermal transport in thin membranes and resonant structures.

Electromechanical response of laterally clamped piezoelectric wafers: Absence of in-plane mechanical resonances in the electromechanical impedance spectrum

We discuss the electromechanical response characteristics of laterally clamped piezoelectric wafers. The impedance spectra (both magnitude and phase) obtained from finite element simulations of uniformly polarized free and clamped circular and square wafers are first presented. It is observed that the magnitude and phase of the impedance spectrum for free piezoelectric wafers shows all the in-plane extensional modes as electromechanical resonances, while that for a clamped wafer does not show any of them. However, it is also shown that the spectrum corresponding to the out-of-plane displacement on the surface of the wafer actually shows the in-plane resonances for both free and clamped wafers. In other words, it is found that the clamped wafer shows in-plane mechanical resonances but these do not appear in the electromechanical impedance spectrum. This observation is then generalized and explained using an analytical model for thin piezoelectric wafers of arbitrary shape. In particular, it is shown that the impedance spectrum of laterally clamped piezoelectric wafers of any arbitrary shape do not show in-plane extensional modes as electromechanical resonances. Moreover, the impedance spectrum of a laterally clamped wafer is shown to depend only on its area and thickness but not its shape. The above findings are relevant to measurement techniques that rely explicitly on the characteristics of the impedance spectrum observed for a piezoelectric wafer. In addition, the absence of resonances resulting from lateral clamping allows for broadband operation of piezoelectric wafers as sensors and actuators for applications such as ultrasonic range finding, underwater acoustics and acoustic imaging.

Broadband high-efficiency near-infrared graphene phase modulators enabled by metal–nanoribbon integrated hybrid plasmonic waveguides

Abstract The phase modulator is a key component in optical communications for its phase modulation functions. In this paper, we numerically demonstrate a variety of ultra-compact high-efficiency graphene phase modulators (GPMs) based on metal–nanoribbon integrated hybrid plasmonic waveguides in the near-infrared region. Benefiting from the good in-plane mode polarization matching and strong hybrid surface plasmon polariton and graphene interaction, the 20 μm-length GPM can achieve excellent phase modulation performance with a good phase and amplitude decoupling effect, a low insertion loss around 0.3 dB/μm, a high modulation efficiency with V π L π of 118.67 V μm at 1.55 μm, which is 1–3 orders improvement compared to the state-of-the-art graphene modulators. Furthermore, it has a wide modulation bandwidth of 67.96 GHz, a low energy consumption of 157.49 fJ/bit, and a wide operating wavelength ranging from 1.3 to 1.8 μm. By reducing the overlap width of the graphene–Al2O3–graphene capacitor, the modulation bandwidth and energy consumption of the modulator can be further improved to 370.36 GHz and 30.22 fJ/bit, respectively. These compact and energy-efficient GPMs may hold a key to various high-speed telecommunications, interconnects, and other graphene-based integrated photonics applications.

A Macro‐Distinct Element Model (M‐DEM) for simulating in‐plane/out‐of‐plane interaction and combined failure mechanisms of unreinforced masonry structures

AbstractIn the seismic analysis of unreinforced masonry (URM) structures, the modeling of out‐of‐plane (OOP) modes and their mechanical interaction with in‐plane (IP) loaded components are typically neglected when using simplified numerical methods. Although this may result in unconservative predictions, the high computational expense entailed by more refined approaches is often prohibitive for applied researchers and practitioners. To overcome these limitations, the demonstrated capabilities of a recently developed low‐cost Macro‐Distinct Element Model (M‐DEM) to simulate IP and OOP modes are extended in this work towards the modeling of IP/OOP interaction and combined failure mechanisms of URM assemblies. In the M‐DEM framework, shear and flexural damage are accounted for by zero‐thickness interface spring layers, whose layout is determined a priori as a function of the masonry texture, while crushing failure is modeled through homogenized finite element macro‐blocks. To adapt and validate this M‐DEM scheme to model IP/OOP interaction, past experiments on full‐scale C‐, U‐, and I‐shaped URM specimens tested under quasi‐static loading were simulated. The shake‐table response of a full‐scale C‐shaped URM assembly with openings was also numerically simulated up to collapse, representing a major improvement over previous macro‐element methods. After the comparison with experimental tests, a parametric investigation of the response of reference URM walls under combined IP/OOP actions was conducted, and the influence of previous IP damage on one‐ and two‐way OOP bending capacity is quantified. This aspect, despite being widely identified as of relevant interest, has only been marginally investigated in previous research, both experimentally and numerically.

Vibronic spectrum of 2-(2'-hydroxyphenyl)benzoxazole

UV-vis absorption spectrum of 2-(2'-hydroxyphenyl)benzoxazole is calculated for the transitions to the first and second excited states using the Franck-Condon approximation and harmonic model for vibrations. The largest intensity of vibronic transitions to the first electronic state is found for an in-plane deformation mode that changes mutual position of the benzoxazole and phenyl fragments; for the stretching vibration involving the aromatic rings and the bond linking the benzoxazole and phenyl moieties. For the second electronic state the vibrations are the deformation modes of oxazole and phenyl rings, stretching vibrations involving the bonds of the nitrogen atom and the bond linking the benzoxazole and phenyl moieties.

Modal characteristics of coupled MEMS resonator array under the effect of residual stress

The residual stress introduced in the packaging process of the mode localized MEMS sensors will shift the eigenfrequencies of their coupled resonator array, thereby affecting the function of the device. In this paper, the influence of residual stress on the modal characteristics of MEMS resonator array is analyzed by laser Doppler method, and the local vibration of coupling beam with 432 nm amplitude is measured by stroboscopic method. The theoretical model and finite element model of the resonator array considering residual stress are established. The results show that the in-plane mode of the resonator is coupled with the local mode of the coupling folded beam under the residual tensile stress of 83.3 MPa. The effect of residual stress on the eigenfrequencies of different modes differs by 14.47 times. The in-plane mode eigenfrequency of one of the resonators increases by 170.5% under the effect of residual stress.

Different optical characteristics between monolayer and bilayer WS2 due to interlayer interaction

In this research Raman spectroscopy and photoluminescence (PL) spectroscopy measurements reveal different optical characteristics between monolayer (1 L) and bilayer (2 L) WS2 due to the interlayer interaction. First, ultralow frequency (ULF) Raman spectra indicate that 2 L WS2 shows additional shear mode (S) and layer-breathing (LB) mode in comparison with 1 L WS2. The 2 L WS2 has the in-plane vibration mode E2g1 red-shifted while the out-plane vibration mode A1g blue-shifted. Then, both direct transition (DT) and indirect transition (IT) emission are observed in the PL spectra for 2 L WS2 while only DT for 1 L WS2. The PL signal corresponding to localized excitons, that is measured as a low energy side tail with the DT emission, is more prominent for 1 L WS2 at low temperature of 7 K. The DT emission and IT emission show opposite variation trend as the temperature increases from 7 K to 300 K, while the average phonon energy in 2 L WS2 is estimated to be almost twice of that for 1 L WS2. These observations illustrate that the interlayer interaction not only change the phonon characteristics for WS2, but also impact the energy band structure and the exciton dynamics, including exciton radiative recombination and exciton-phonon interaction.

Theoretical analysis by Mindlin theory and experimental measurements of the piezoceramic circular bimorphs in resonance

This paper investigates the free vibration characteristics for piezoceramic bimorphs in series connections by using theoretical analysis, numerical calculation, and experimental measurement. Series- and parallel-type piezoceramic bimorphs under fully-clamped boundary conditions are analyzed in this study. The theoretical solutions are derived base on the Mindlin's plate theory to explore the coupled out-of-plane (transverse) and in-plane (planar) resonant vibration characteristics; the numerical calculations based upon finite-element method are also performed and agree very well with the theoretical results for resonant frequency and corresponding mode shape. Two optical techniques, amplitude- fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), and an impedance analysis are used to validate the theoretical and numerical results. It is shown that there is no difference between theoretical and numerical results regarding vibration characteristics of series- and parallel-type piezoceramic bimorphs. However, the experimental findings obtained by impedance analysis reveal that the boundary condition plays an important role for the excited vibration modes of parallel-type piezoceramic bimorphs. The imperfect clamped-circumference simulation in experimental procedure will result in some unexpected vibration modes arising, which can be distinguished between out-of-plane and in-plane modes by AF-ESPI measurement.

Effect of Freezing out Vibrational Modes on Gas-Phase Fluorescence Spectra of Small Ionic Dyes.

While action spectroscopy of cold molecular ions is a well-established technique to provide vibrationally resolved absorption features, fluorescence experiments are still challenging. Here we report the fluorescence spectra of pyronin-Y and resorufin ions at 100 K using a newly constructed setup. Spectra narrow upon cooling, and the emission maxima blueshift. Temperature effects are attributed to the population of vibrational excited levels in S1, and that frequencies are lower in S1 than in S0. This picture is supported by calculated spectra based on a Franck-Condon model that not only predicts the observed change in maximum, but also assigns Franck-Condon active vibrations. In-plane vibrational modes that preserve the mirror plane present in both S0 and S1 of resorufin and pyronin Y account for most of the observed vibrational bands. Finally, at low temperatures, it is important to pick an excitation wavelength as far to the red as possible to not reheat the ions.

Deep learning-based topology design of periodic barrier for full-mode waves

A deep learning model is proposed to solve the design problem of periodic wave barrier with consideration of full-mode waves including in-plane mixed mode and out-of-plane shear mode, and the effect of site conditions on design is taken into account. The proposed model is composed of a variational autoencoder (VAE) and an autoencoder (AE) with two pretrained decoders. It can perform designs for different situations and give multiple structures for the same target within a very short time. Large number of targets in the testing set are considered, and the designed results highly meet the expectations. A periodic wave barrier is designed by the approach for a practical example, and the vibrations in main frequency range are attenuated greatly. The deep learning method makes the design of periodic wave barrier smart, efficient, accurate, and universal.