Love wave propagation in one-dimensional piezoelectric quasicrystal multilayered nanoplates with surface effects

The exact solutions for the propagation of Love waves in one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)nanoplates with surface effects are derived.An electro-elastic model is developed to investigate the anti-plane strain problem of Love wave propagation.By introducing three shape functions,the wave equations and electric balance equations are decoupled into three uncorrelated problems.Satisfying the boundary conditions of the top surface on the covering layer,the interlayer interface,and the matrix,a dispersive equation with the influence of multi-physical field coupling is provided.A surface PQC model is developed to investigate the surface effects on the propagation behaviors of Love waves in quasicrystal(QC)multilayered structures with nanoscale thicknesses.A novel dispersion relation for the PQC structure is derived in an explicit closed form according to the non-classical mechanical and electric boundary conditions.Numerical examples are given to reveal the effects of the boundary conditions,stacking sequence,characteristic scale,and phason fluctuation characteristics on the dispersion curves of Love waves propagating in PQC nanoplates with surface effects.

Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

无界域上具有记忆的非自治Plate方程随机吸引子的存在性

研究无界域上一类具有衰退记忆和加性噪声的非自治Plate方程解的长时间行为.利用一致估计验证了解的拉回渐近紧性,获得了其随机吸引子的存在性.

Static deformation of a multilayered one-dimensional hexagonal quasicrystal plate with piezoelectric effect

Quasicrystals （QCs） are sensitive to the piezoelectric （PE） effect. This paper studies static deformation of a multilayered one-dimensional （1D） hexagonal QC plate with the PE effect. The exact closed-form solutions of the extended displacement and traction for a homogeneous piezoelectric quasicrystal （PQC）plate are derived from an eigensystem. The general solutions for multilayered PQC plates are then obtained using the propagator matrix method when mechanical and electrical loads are applied on the top surface of the plate. Numerical examples for several sandwich plates made up of PQC, PE, and QC materials are provided to show the effect of stacking sequence on phonon, phason, and electric fields under mechanical and electrical loads, which is useful in designing new composites for engineering structures.

Prediction of one-dimensional CrN nanostructure as a promising ferromagnetic half-metal

Searching for one-dimensional(1D)nanostructure with ferromagnetic(FM)half-metallicity is of significance for the development of miniature spintronic devices.Here,based on the first-principles calculations,we propose that the 1D CrN nanostructure is a FM half-metal,which can generate the fully spin-polarized current.The ab initio molecular dynamic simulation and the phonon spectrum calculation demonstrate that the 1D CrN nanostructure is thermodynamically stable.The partially occupied Cr-d orbitals endow the nanostructure with FM half-metallicity,in which the half-metallic gap(?s)reaches up to 1.58 eV.The ferromagnetism in the nanostructure is attributed to the superexchange interaction between the magnetic Cr atoms,and a sizable magnetocrystalline anisotropy energy(MAE)is obtained.Moreover,the transverse stretching of nanostructure can effectively modulate?s and MAE,accompanied by the preservation of half-metallicity.A nanocable is designed by encapsulating the CrN nanostructure with a BN nanotube,and the intriguing magnetic and electronic properties of the nanostructure are retained.These novel characteristics render the 1D CrN nanostructure as a compelling candidate for exploiting high-performance spintronic devices.

Size effect on light propagation modulation near band edges in one-dimensional periodic structures

Periodic photonic structures can provide rich modulation in propagation of light due to well-defined band structures.Especially near band edges,light localization and the effect of near-zero refractive index have attracted wide attention.However,the practically fabricated structures can only have finite size,i.e.,limited numbers of periods,leading to changes of the light propagation modulation compared with infinite structures.Here,we study the size effect on light localization and near-zero refractive-index propagation near band edges in one-dimensional periodic structures.Near edges of the band gap,as the structure's size shrinks,the broadening of the band gap and the weakening of the light localization are discovered.When the size is small,an added layer on the surface will perform large modulation in the group velocity.Near the degenerate point with Dirac-like dispersion,the zero-refractive-index effects like the zero-phase difference and near-unity transmittance retain as the size changes,while absolute group velocity fluctuates when the size shrinks.

A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping,the physical plane problems are transformed into regular mathematical problems in quasicrystals(QCs).The analytical solution to an elliptical orifice problem with asymmetric cracks in one-dimensional(1D)orthorhombic QCs is obtained.By using the Dugdale-Barenblatt model,the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed.Finally,the size of the atomic cohesive force zone is determined precisely,and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.

Robust Damage Detection and Localization Under Complex Environmental Conditions Using Singular Value Decomposition-based Feature Extraction and One-dimensional Convolutional Neural Network

Ultrasonic guided wave is an attractive monitoring technique for large-scale structures but is vulnerable to changes in environmental and operational conditions(EOC),which are inevitable in the normal inspection of civil and mechanical structures.This paper thus presents a robust guided wave-based method for damage detection and localization under complex environmental conditions by singular value decomposition-based feature extraction and one-dimensional convolutional neural network(1D-CNN).After singular value decomposition-based feature extraction processing,a temporal robust damage index(TRDI)is extracted,and the effect of EOCs is well removed.Hence,even for the signals with a very large temperature-varying range and low signal-to-noise ratios(SNRs),the final damage detection and localization accuracy retain perfect 100%.Verifications are conducted on two different experimental datasets.The first dataset consists of guided wave signals collected from a thin aluminum plate with artificial noises,and the second is a publicly available experimental dataset of guided wave signals acquired on a composite plate with a temperature ranging from 20℃to 60℃.It is demonstrated that the proposed method can detect and localize the damage accurately and rapidly,showing great potential for application in complex and unknown EOC.

A New One-dimensional Aluminium Fluorophosphate Templated by Organic Amine

A new one-dimensional aluminum fluorophosphate, AlP2O5（OH）3F·0.5[H2dien] （dien=diethylenetriamine）, was solvothermally synthesized by using organic amine as the structure directing agent, and its structure was determined by single-crystal X-ray diffraction. The complex inorganic architecture consists of trans-corner-sharing AlO4F2 octahedra chain decorated by phosphate tetrahedra along both sides of the -F-Al-F-Al-F- backbone displaying a series of Al2P three-membered rings, which will represent a new fundamental structural type in metal phosphates. The results of CHN elemental analysis, EDS, and TGA are also presented. Crystal data： C4H18Al2F2N3O16P4, monoclinic, space group P21/c with a=6.9107（14）, b=15.749（3）, c=8.9741（18） , β=109.829（2）o, V=918.8（3） 3, Z=2, Mr=580.05, Dc=2.097 g/cm3, μ=0.618 mm-1, S=1.022, F（000）=590, the final R=0.0510 and wR=0.1284 for 1607 observed reflections （I 〉 2σ（I））.

Analysis of Dynamical Behavior of One-Dimensional Real Maps: An Executable Dynamical Programming Software Approach

The dynamical behavior of real-world phenomena is implausible graphically due to the complexity of mathematical coding. The present article has mainly focused on some one-dimensional real maps’ dynamical behavior irrespective of using coding. In continuation, linear, quadratic, cubic, higher-order, exponential, logarithmic, and absolute value maps have been used to scrutinize their dynamical behavior, including the characteristics of the orbit of points. Dynamical programming software (DPS.exe) will be proposed as a new technique to ascertain the dynamical behavior of said maps. Thus, a mathematician can automatically determine one-dimensional real maps’ dynamical behavior apart from complicated programming code and analytical solutions.

Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film

In this paper,we investigate the interfacial behavior of a thin one-dimensional(1D)hexagonal quasicrystal(QC)film bonded on an elastic substrate subjected to a mismatch strain due to thermal variation.The contact interface is assumed to be nonslipping,with both perfectly bonded and debonded boundary conditions.The Fourier transform technique is adopted to establish the integral equations in terms of interfacial shear stress,which are solved as a linear algebraic system by approximating the unknown phonon interfacial shear stress via the series expansion of the Chebyshev polynomials.The expressions are explicitly obtained for the phonon interfacial shear stress,internal normal stress,and stress intensity factors(SIFs).Finally,based on numerical calculations,we briefly discuss the effects of the material mismatch,the geometry of the QC film,and the debonded length and location on stresses and SIFs.

Generative optimization of bistable plates with deep learning

Bistate plates have found extensive applications in the domains of smart structures and energy harvesting devices.Most bistable curved plates are characterized by a constant thickness profile.Regrettably,due to the inherent complexity of this problem,relatively little attention has been devoted to this area.In this study,we demonstrate how deep learning can facilitate the discovery of novel plate profiles that cater to multiple objectives,including maximizing stiffness,forward snapping force,and backward snapping force.Our proposed approach is distinguished by its efficiency in terms of low computational energy consumption and high effectiveness.It holds promise for future applications in the design and optimization of multistable structures with diverse objectives,addressing the requirements of various fields.

Imaging plate scanners calibration and the attenuation behavior of imaging plate signals

Based on previously reported work, we propose a new method for calibrating image plate(IP) scanners, offering greater flexibility and convenience, which can be extended to the calibration tasks of various scanner models. This method was applied to calibrate the sensitivity of a GE Typhoon FLA 7000 scanner. Additionally, we performed a calibration of the spontaneous signal attenuation behavior for BAS-MS, BAS-SR, and BAS-TR type IPs under the 20±1℃ environmental conditions, and observed significant signal carrier diffusion behavior in BAS-MS IP. The calibration results lay a foundation for further research on the interaction between ultra-short, ultra-intense lasers and matter.

Modeling Geometrically Nonlinear FG Plates: A Fast and Accurate Alternative to IGA Method Based on Deep Learning

Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.

The interaction between a shaped charge jet and a single moving plate

Reactive armour is a very efficient add-on armour against shaped charge threats.Explosive reactive armour consists of one or several plates that are accelerated by an explosive.Similar but less violent acceleration of plates can also be achieved in a completely inert reactive armour.To be efficient against elongated jets,the motion of the plates needs to be inclined against the jet such that a sliding contact between the jet and the plates is established.This sliding contact causes a deflection and thinning of the jet.Under certain circumstances,the contact will become unstable,leading to severe disturbances on the jet.These disturbances will drastically reduce the jet penetration performance and it is therefore of interest to study the conditions that leads to an unstable contact.Previous studies on the interaction between shaped charge jets and flyer plates have shown that it is mainly the forward moving plate in an explosive reactive armour that is effective in disturbing the jet.This is usually attributed to the higher plate-to-jet mass flux ratio involved in the collision of the forward moving plate compared to the backward moving plate.For slow moving plates,as occurs in inert reactive armour,the difference in mass flux for the forward and backward moving plate is much lesser,and it is therefore of interest to study if other factors than the mass flux influences on the protection capability.In this work,experiments have been performed where a plate is accelerated along its length,interacting with a shaped charge jet that is fired at an oblique angle to the plate’s normal,either against or along the plate’s velocity.The arrangement corresponds to a jet interacting with a flyer plate from a reactive armour,with the exception that the collision velocity is the same for both types of obliquities in these experiments.The experiments show that disturbances on the jet are different in the two cases even though the collision velocities are the same.Numerical simulations of the interaction support the observation.The difference is attributed to the character of the contact pressure in the interaction region.For a backward moving plate,the maximum contact pressure is obtained at the beginning of the interaction zone and the contact pressure is therefore higher upstream than downstream of the jet while the opposite is true for a forward moving plate.A negative interface pressure gradient with respect to the jet motion results in a more stable flow than a positive,which means that the jet-plate contact is more stable for a backward moving plate than for a forward moving plate.A forward moving plate is thus more effective in disturbing the jet than a backward moving plate,not only because of the higher jet to plate mass flux ratio but also because of the character of the contact with the jet.

Performance analysis of single-focus phase singularity based on elliptical reflective annulus quadrangle-element coded spiral zone plates

Optical vortices generated by the conventional vortex lens are usually disturbed by the undesired higher-order foci,which may lead to additional artifacts and thus degrade the contrast sensitivity. In this work, we propose an efficient methodology to combine the merit of elliptical reflective zone plates(ERZPs) and the advantage of spiral zone plates(SZPs) in establishing a specific single optical element, termed elliptical reflective annulus quadrangle-element coded spiral zone plates(ERAQSZPs) to generate single-focus phase singularity. Differing from the abrupt reflectance of the ERZPs, a series of randomly distributed nanometer apertures are adopted to realize the sinusoidal reflectance. Typically, according to our physical design, the ERAQSZPs are fabricated on a bulk substrate;therefore, the new idea can significantly reduce the difficulty in the fabrication process. Based on the Kirchhoff diffraction theory and convolution theorem, the focusing performance of ERAQSZPs is calculated. The results reveal that apart from the capability of generating optical vortices,ERAQSZPs can also integrate the function of focusing, energy selection, higher-order foci elimination, as well as high spectral resolution together. In addition, the focusing properties can be further improved by appropriately adjusting the parameters, such as zone number and the size of the consisted primitives. These findings are expected to direct a new direction toward improving the performance of optical capture, x-ray fluorescence spectra, and forbidden transition.

Unsteady MHD Casson Nanofluid Flow Past an Exponentially Accelerated Vertical Plate:An Analytical Strategy

In this study,the characteristics of heat transfer on an unsteady magnetohydrodynamic(MHD)Casson nanofluid over an exponentially accelerated vertical porous plate with rotating effects were investigated.The flow was driven by the combined effects of the magnetic field,heat radiation,heat source/sink and chemical reaction.Copper oxide(CuO)and titanium oxide(TiO2)are acknowledged as nanoparticle materials.The nondimensional governing equations were subjected to the Laplace transformation technique to derive closed-form solutions.Graphical representations are provided to analyze how changes in physical parameters,such as the magnetic field,heat radiation,heat source/sink and chemical reaction,affect the velocity,temperature and concentration profiles.The computed values of skin friction,heat and mass transfer rates at the surface were tabulated for various sets of input parameters.It is perceived that there is a drop in temperature due to the rise in the heat source/sink and the Prandtl number.It should be noted that a boost in the thermal radiation parameter prompts an increase in temperature.An increase in the Prandtl number,heat source/sink parameter,time and a decrease in the thermal radiation parameter result in an increase in theNusselt number.The computed values of the skin friction,heat andmass transfer rates at the surface were tabulated for various values of the flow parameters.The present results were compared with those of previously published studies andwere found to be in excellent agreement.This research has practical applications in areas such as drug delivery,thermal medicine and cancer treatment.

Dirac method for nonlinear and non-homogenous boundary value problems of plates

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

Micro defects formation and dynamic response analysis of steel plate of quasi-cracking area subjected to explosive load

As the protective component,steel plate had attracted extensive attention because of frequently threats of explosive loads.In this paper,the evolution of microstructure and the mechanism of damage in the quasi-cracking area of steel plate subjected to explosive load were discussed and the relationships between micro defects and dynamic mechanical response were revealed.After the explosion experiment,five observation points were selected equidistant from the quasi-cracking area of the section of the steel plate along the thickness direction,and the characteristics of micro defects at the observation points were analyzed by optical microscope(OM),scanning electron microscope(SEM) and electron backscattered diffraction(EBSD).The observation result shows that many slip bands(SBs) appeared,and the grain orientation changed obviously in the steel plate,the two were the main damage types of micro defects.In addition,cracks,peeling pits,grooves and other lager micro defects were appeared in the lower area of the plate.The stress parameters of the observation points were obtained through an effective numerical model.The mechanism of damage generation and crack propagation in the quasicracking area were clarified by comparing the specific impulse of each observation point with the corresponding micro defects.The result shows that the generation and expansion of micro defects are related to the stress area(i.e.the upper compression area,the neutral plane area,and the lower tension area).The micro defects gather and expand at the grain boundary,and will become macroscopic damage under the continuous action of tensile stress.Besides,the micro defects at the midpoint of the section of the steel plate in the direction away from the explosion center(i.e.the horizontal direction) were also studied.It was found that the specific impulse at these positions were much smaller than that in the thickness direction,the micro defects were only SBs and a few micro cracks,and the those decreased with the increase of the distance from the explosion center.

Constitutive Behavior of the Interface between UHPC and Steel Plate without Shear Connector:From Experimental to Numerical Study

The application of ultra-high performance concrete(UHPC)as a covering layer for steel bridge decks has gained widespread popularity.By employing a connection without a shear connector between the steel plate and UHPC,namely,the sandblasted interface and the epoxy adhesive with sprinkled basalt aggregate interface,the installation cannot only be simplified but also the stress concentration resulting from the welded shear connectors can be eliminated.This study develops constitutive models for these two interfaces without shear connectors,based on the interfacial pull-off and push-out tests.For validation,three-point bending tests on the steel-UHPC composite plates are conducted.The results indicated that the proposed bilinear traction-separation model for the sandblasted interface and the trapezoidal traction-separation model for the epoxy adhesive with sprinkled basalt aggregate interface can generally calibrate the interfacial behavior.However,the utilization of the experimentally determined pure shear strength underestimates the load-carrying capacity of the composite plates in the case of three-point bending tests.By recalling the Mohr-Coulomb criterion,this underestimation is attributed to the enhancement of the interface shear strength by the presence of normal stress.