Magneto-Electro-Elastic Analysis of Doubly-Curved Shells: Higher-Order Equivalent Layer-Wise Formulation

Recent engineering applications increasingly adopt smart materials,whose mechanical responses are sensitive to magnetic and electric fields.In this context,new and computationally efficient modeling strategies are essential to predict the multiphysic behavior of advanced structures accurately.Therefore,the manuscript presents a higher-order formulation for the static analysis of laminated anisotropic magneto-electro-elastic doubly-curved shell structures.The fundamental relations account for the full coupling between the electric field,magnetic field,and mechanical elasticity.The configuration variables are expanded along the thickness direction using a generalized formulation based on the Equivalent Layer-Wise approach.Higher-order polynomials are selected,allowing for the assessment of prescribed values of the configuration variables at the top and bottom sides of solids.In addition,an effective strategy is provided for modeling general surface distributions of mechanical pressures and electromagnetic external fluxes.The model is based on a continuum-based formulation which employs an analytical homogenization of the multifield material properties,based on Mori&Tanaka approach,of a magneto-electro-elastic composite material obtained from a piezoelectric and a piezomagnetic phase,with coupled magneto-electro-elastic effects.A semi-analytical Navier solution is applied to the fundamental equations,and an efficient post-processing equilibrium-based procedure is here used,based on the numerical assessment with the Generalized Differential Quadrature(GDQ)method,to recover the response of three-dimensional shells.The formulation is validated through various examples,investigating the multifield response of panels of different curvatures and lamination schemes.An efficient homogenization procedure,based on the Mori&Tanaka approach,is employed to obtain the three-dimensional constitutive relation of magneto-electro-elastic materials.Each model is validated against three-dimensional finite-element simulations,as developed in commercial codes.Furthermore,the full coupling effect between the electric and magnetic response is evaluated via a parametric investigation,with useful insights for design purposes of many engineering applications.The paper,thus,provides a formulation for the magneto-electro-elastic analysis of laminated structures,with a high computational efficiency,since it provides results with three-dimensional capabilities with a two-dimensional formulation.The adoption of higher-order theories,indeed,allows us to efficiently predict not only the mechanical response of the structure as happens in existing literature,but also the through-the-thickness distribution of electric and magnetic variables.A novel higher-order theory has been proposed in this work for the magneto-electro-elastic analysis of laminated shell structures with varying curvatures.This theory employs a generalized method to model the distribution of the displacement field components,electrostatic,and magneto-static potential,accounting for higher-order polynomials.The thickness functions have been defined to prescribe the arbitrary values of configuration variables at the top and bottom surfaces,even though the model is ESL-based.The fundamental governing equations have been derived in curvilinear principal coordinates,considering all coupling effects among different physical phenomena,including piezoelectric,piezomagnetic,and magneto-electric effects.A homogenization algorithm based on a Mori&Tanaka approach has been adopted to obtain the equivalent magneto-electro-mechanical properties of a two-phase transversely isotropic composite.In addition,an effective method has been adopted involving the external loads in terms of surface tractions,as well as the electric and magnetic fluxes.In the post-processing stage,a GDQ-based procedure provides the actual 3D response of a doubly-curved solid.The model has been validated through significant numerical examples,showing that the results of this semi-analytical theory align well with those obtained from 3D numerical models from commercial codes.In particular,the accuracy of the model has been verified for lamination schemes with soft layers and various curvatures under different loading conditions.Moreover,this formulation has been used to predict the effect of combined electric and magnetic loads on the mechanical response of panels with different curvatures and lamination schemes.As a consequence,this theory can be applied in engineering applications where the combined effect of electric and magnetic loads is crucial,thus facilitating their study and design.An existing limitation of this study is that the solution is that it is derived only for structures with uniform curvature,cross-ply lamination scheme,and simply supported boundary conditions.Furthermore,it requires that each lamina within the stacking sequence exhibits magneto-electro-elastic behavior.Therefore,at the present stage,it cannot be used for multifield analysis of classical composite structures with magneto-electric patches.A further enhancement of the research work could be the derivation of a solution employing a numerical technique,to overcome the limitations of the Navier method.In this way,the same theory may be adopted to predict the multifield response of structures with variable curvatures and thickness,as well as anisotropic materials and more complicated boundary conditions.Acknowledgement:The authors are grateful to the Department of Innovation Engineering of Univer-sity of Salento for the support.

Detection of Nonlinear Behavior Induced by Hard Limiting in Voltage Source Converters in Wind Farms Based on Higher-order Spectral Analysis

In recent years, sub-synchronous oscillation accidents caused by wind power integration have received extensive attention. The recorded constant-amplitude waveforms can be induced by either linear or nonlinear oscillation mechanisms. Hence, the nonlinear behavior needs to be distinguished prior to choosing the analysis method. Since the 1960s, the higher-order statistics(HOS) theory has become a powerful tool for the detection of nonlinear behavior(DNB) in production quality control wherein it has mainly been applied to mechanical condition monitoring and fault diagnosis. This study focuses on the hard limiters of the voltage source converter(VSC) control systems in the wind farms and attempts to detect the nonlinear behavior caused by bi-or uni-lateral saturation hard limiting using the HOS analysis. First, the conventional describing function is extended to obtain the detailed frequency domain information on the bi-and uni-lateral saturation hard limiting. Furthermore, the bi-and tri-spectra are introduced as the HOS, which are extended into bi-and tri-coherence spectra to eliminate the effects of the linear parts on the harmonic characteristics of hard limiting in the VSC control system, respectively. The effectiveness of the HOS in the DNB and the classification of the hard-limiting types is proven, and its detailed derivation and estimation procedure is presented. Finally, the quadratic and cubic phase coupling in the signals is illustrated, and the performance of the proposed method is evaluated and discussed.

Pipeline thickness estimation using the dispersion of higher-order SH guided waves

Thickness measurement plays an important role in the monitoring of pipeline corrosion damage. However, the requirement for prior knowledge of the shear wave velocity in the pipeline material for popular ultrasonic thickness measurement limits its widespread application. This paper proposes a method that utilizes cylindrical shear horizontal(SH) guided waves to estimate pipeline thickness without prior knowledge of shear wave velocity. The inversion formulas are derived from the dispersion of higher-order modes with the high-frequency approximation. The waveform of the example problems is simulated using the real-axis integral method. The data points on the dispersion curves are processed in the frequency domain using the wave-number method. These extracted data are then substituted into the derived formulas. The results verify that employing higher-order SH guided waves for the evaluation of thickness and shear wave velocity yields less than1% error. This method can be applied to both metallic and non-metallic pipelines, thus opening new possibilities for health monitoring of pipeline structures.

Photoinduced Floquet higher-order Weyl semimetal in C_(6) symmetric Dirac semimetals

Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges.Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).

Opinion consensus incorporating higher-order interactions in individual-collective networks

In the current information society, the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors are the research hot topics in the field of opinion dynamics. First, in this paper, a two-layer network consisting of an individual-opinion layer and a collective-opinion layer is constructed, and a dissemination model of opinions incorporating higher-order interactions(i.e. OIHOI dissemination model) is proposed. Furthermore, the dynamic equations of opinion dissemination for both individuals and groups are presented. Using Lyapunov's first method,two equilibrium points, including the negative consensus point and positive consensus point, and the dynamic equations obtained for opinion dissemination, are analyzed theoretically. In addition, for individual opinions and collective opinions,some conditions for reaching negative consensus and positive consensus as well as the theoretical expression for the dissemination threshold are put forward. Numerical simulations are carried to verify the feasibility and effectiveness of the proposed theoretical results, as well as the influence of the intra-structure, inter-connections, and higher-order interactions on the dissemination and evolution of individual opinions. The main results are as follows.(i) When the intra-structure of the collective-opinion layer meets certain characteristics, then a negative or positive consensus is easier to reach for individuals.(ii) Both negative consensus and positive consensus perform best in mixed type of inter-connections in the two-layer network.(iii) Higher-order interactions can quickly eliminate differences in individual opinions, thereby enabling individuals to reach consensus faster.

Time-Domain Higher-Order Boundary Element Method for Simulating High Forward-Speed Ship Motions in Waves

The hydrodynamic performance of a high forward-speed ship in obliquely propagating waves is numerically examined to assess both free motions and wave field in comparison with a low forward-speed ship.This numerical model is based on the time-domain potential flow theory and higher-order boundary element method,where an analytical expression is completely expanded to determine the base-unsteady coupling flow imposed on the moving condition of the ship.The ship in the numerical model may possess different advancing speeds,i.e.stationary,low speed,and high speed.The role of the water depth,wave height,wave period,and incident wave angle is analyzed by means of the accurate numerical model.It is found that the resonant motions of the high forward-speed ship are triggered by comparison with the stationary one.More specifically,a higher forward speed generates a V-shaped wave region with a larger elevation,which induces stronger resonant motions corresponding to larger wave periods.The shoaling effect is adverse to the motion of the low-speed ship,but is beneficial to the resonant motion of the high-speed ship.When waves obliquely propagate toward the ship,the V-shaped wave region would be broken due to the coupling effect between roll and pitch motions.It is also demonstrated that the maximum heave motion occurs in beam seas for stationary cases but occurs in head waves for high speeds.However,the variation of the pitch motion with period is hardly affected by wave incident angles.

A Study of a Moral Dilemma Stories Teaching Model Focusing on the Development of Higher-Order Thinking --"Synthetic polymers" as an example

Cultivating students'higher-order thinking is one of the important goals of modern education,and innovative teaching model is an effective way to achieve this goal.Aiming at the inadequacy of the existing moral dilemma stories approach in the transformation of knowledge and behavior,this research constructs a new Project Based Learning-Ethical Dilemma Stories(PBL-EDS)Teaching Model applicable to China's secondary education stage based on the innovative features of the moral dilemma stories approach on the core competencies,taking the chemistry subject as an example to carry out practice,and puts forward suggestions for the implementation of the teaching model.Chemistry as an example to carry out the practice,and suggestions are made for the implementation of the teaching model.

Teaching Practice Research on Space English under BOPPPS Model from the Perspective of Higher-order Thinking Skills Training

It is the core mission of educational reform in the new era to cultivate students’higher order thinking skills.On the basis of clarifying the connotation of higher-order thinking skills,this paper analyzes the internal connection between BOPPPS teaching model and the cultivation of higher-order thinking skills.Then,in line with the 6 teaching steps under BOPPPS,the implementation strategy and specific path of the cultivation of high order thinking skills in Space English teaching practice are elaborated,serving as reference for developing high order thinking skills in other ESP courses.

APPLICATIONS OF HIGHER-ORDER UPWIND SCHEME FOR PROJECTILES IN TRANSONIC FLOW

针对弹丸跨音速粘性绕流流场进行了数值仿真研究，并与实验进行了对比。数值仿真的控制方程为雷诺平均的Navier-Stokes方程，湍流模型采用Baldwin-Lomax模型，应用了四阶的MUSCL TVD格式。结果表明，该方法可以取得高清晰度的流场结构。

The Inertial Manifolds for a Class of Higher-Order Coupled Kirchhoff-Type Equations

In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial manifolds are proved by using spectral gap condition. The main result we gained is that the inertial manifolds are established under the proper assumptions of M(s) and gi(u,v), i=1, 2.

Fission and Fusion of Localized Coherent Structures for a Higher-Order Broer-Kaup System

Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.

Application of higher-order KdV-mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

Higher-order Korteweg-de Vries （KdV）-modified KdV （mKdV） equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV-mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.

The Inertial Manifold for a Class of Nonlinear Higher-Order Coupled Kirchhoff Equations with Strong Linear Damping

This paper considers the long-time behavior for a system of coupled wave equations of higher-order Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of the inertial manifold while such equations satisfy the spectral interval condition.

Influence of higher-order ionospheric delay correction on GPS precise orbit determination and precise positioning

At present, Global Navigation Satellite Systems（GNSS） users usually eliminate the influence of ionospheric delay of the first order items by dual-frequency ionosphere-free combination. But there is still residual ionospheric delay error of higher order term. The influence of the higher-order ionospheric corrections on both GPS precision orbit determination and static Precise Point Positioning（PPP） are studied in this paper. The influence of higher-order corrections on GPS precision orbit determination, GPS observations and static PPP are analyzed by neglecting or considering the higher-order ionospheric corrections by using a globally distributed network which is composed of International GNSS Service（IGS） tracking stations. Numerical experimental results show that, the root mean square（RMS） in three dimensions of satellite orbit is 36.6 mme35.5 mm. The maximal second-order ionospheric correction is 9 cm, and the maximal third-order ionospheric correction is 1 cm. Higher-order corrections are influenced by latitude and station distribution. PPP is within 3 mm in the directions of east and up. Furthermore, the impact is mainly visible in the direction of north, showing a southward migration trend, especially at the lower latitudes where the influence value is likely to be bigger than 3 mm.

Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results.

兼顾能力与知识状态的Higher-Order CD-CAT选题方法

Higher-order CD-CAT的选题方法是传统单目标(即只对知识状态自适应)选题方法,这将导致被试能力的测量精度不高.基于此,在高阶模型和PWKL选题方法的框架下,该文开发了适用于Higher-order CD-CAT的新选题方法,该方法在选题时能同时兼顾能力和知识状态.实验结果表明:与传统选题方法相比,新选题方法的能力和知识状态估计精度都更高,并且在题库安全性上也具有明显的优势.

Tunneling dynamics of Bose-Einstein condensates with higher-order interactions in optical lattice

The nonlinear Landau Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate （BEC） with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters （i.e., the modulation amplitude and frequency） and the strength of periodic potential.

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.

Typical adaptive neural control for hypersonic vehicle based on higher-order filters

A typical adaptive neural control methodology is used for the rigid body model of the hypersonic vehicle. The rigid body model is divided into the altitude subsystem and the velocity subsystem. The proportional integral differential(PID) controller is introduced to control the velocity track. The backstepping design is applied for constructing the controllers for the altitude subsystem.To avoid the explosion of differentiation from backstepping, the higher-order filter dynamic is used for replacing the virtual controller in the backstepping design steps. In the design procedure,the radial basis function(RBF) neural network is investigated to approximate the unknown nonlinear functions in the system dynamic of the hypersonic vehicle. The simulations show the effectiveness of the design method.